How do we calculate heat flow or cooling rate for no fusion brown dwarf star? I was reading this article and it said something that didn't sit right with me.

"SIMP0136 still gives off light mostly in the infrared wavelengths, as its temperature is now approximately 830° C (1,526° F)," Gagné told us. "It will take it approximately 10 billion years more before it reaches 0° C"

SIMP0136 was classified as a brown dwarf star but when they just recently figured out its mass to be only 12.7 times that of Jupiter they downgraded it to a gas giant planet.  The threshold to qualify as a brown dwarf is 13 Jupiter masses.

Like gas giant planets, brown dwarf stars do not gave enough mass for fusion to occur so the term star is a bit misleading.  Since there is no fusion, then it should eventually cool down.  The 10 billion year cool down time to go from its present 830 deg C to 0 deg C seems way too long.  How do they calculate this?

Whether or not the object is just above or below the threshold (about 13 Jupiter masses) at which the core will become hot enough to burn deuterium is not really relevant to the calculation you wish to understand. The object has cooled beyond the point at which D burning has ceased. It has also pretty much contracted to a minimum sized configuration where electron degeneracy pressure supports it. Therefore very little gravitational potential energy can contribute to subsequent thermal evolution.

All that is left is to calculate the thermal energy content (roughly $3kT/2 \times N_i$ - the number of hydrogen and helium ions, where $T$ is the internal temperature; the degenerate electrons contribute very little to the heat capacity) and then divide this by the luminosity radiated from the surface. The calculation is a little more complex than that because the luminosity fades as the brown dwarf cools.

Just for kicks - here is a back of the envelope calculation. The central temperature of a contracting ball of gas is given by the virial theorem. The brown dwarf you are talking about will contract until D burning (nearly) starts at about $10^{6}$ K - let's assume that is an upper limit to the current core temperature. The average temperature in the interior will be a bit lower than that (let's divide by 2), so $\langle T \rangle \sim 5\times 10^{5}$ K.

If the mass is about $0.012 M_{\odot}$ and it is made almost totally of hydrogen, then the number of protons is about $N_i \sim 1.4 \times 10^{55}$.

Thus the total thermal energy is $E \sim 3N_i k\langle T \rangle/2 \sim 1.5\times 10^{38}$ J.

The current luminosity $L \sim 4 \pi \sigma R^2 T_s^{4}$, where $T_s \simeq 1100$ K is the surface temperature and $R$ is the radius, which will be about the same as Jupiter, i.e. $R\sim 70,000$ km. Thus $L \sim 5 \times 10^{21}$ W.

The current cooling timescale is $E/L \sim 10^{9}$ years - but this is a lower limit.

I am not surprised that this is somewhat lower than your estimate because the cooling time gets much longer as the object cools. This is clearly seen when looking at a proper model calculation; for example see the picture below taken from Burrows et al. (1997).

The lines show the cooling tracks of surface temperature versus (log) time. The red curves are "planets", the green are "brown dwarfs" - the dividing line is the D-burning threshold - seen as a plateau in the the green brown dwarf curves at early times. Your object is around this threshold. I have marked two points on the plot - the first corresponding to a 13 Jupiter mass object with a surface temperature of 1100K (you can see it must already be at least a hundred million years old) , the second marks the same object when it has cooled to about 273 K (zero Celsius). It does indeed occur after about 10 billion years.


How do I make a custom pulsar map? I'm looking to make a custom pulsar map like the one on the Voyager Records, but for an arbitrary location within the Milky Way Galaxy. I'm not even sure where to begin.

The pulsar map used by Pioneer and Voyager is a diagram of the position of the Sun relative to 14 galactic pulsars. It encodes their positions, distances, and pulse periods, which in theory makes it a decent tool for identifying where the Solar System is (although there are some issues with it). To make a similar map for an arbitrary point in the galaxy, you'd need to find a selection of pulsars near that location, and encode the same amount of information. To do that, you need a database of pulsars.

The Australian Telescope National Facility (ATNF) has a really excellent pulsar catalogue that I like to use, with over 2600 entries. You can query it fairly easily using a number of parameters, including distance, dispersion measure, coordinates, pulse period, etc. This makes it a handy tool to match observations with already known pulsars, but it should also be well-suited to your needs. You can get a list of pulsar names, coordinates, periods and distances by checking the JName, RaJ, DecJ, P0 and Dist parameters in the search interface, then click the button to get a table of the results. You should then be able to compute the positions of all of the pulsars in the catalogue in your coordinate system of choice, then re-compute their positions with respect to a chosen location in space.

The output of the first hundred rows looks like this:

---------------------------------------------------------------------------------------------------------------------------------------------------
#     NAME                     RAJ                                DECJ                               P0                                     DIST
                               (hms)                              (dms)                              (s)                                    (kpc)
---------------------------------------------------------------------------------------------------------------------------------------------------
1     J0002+6216    cwp+17     00:02:58.17          2  cwp+17     +62:16:09.4          1  cwp+17     0.1153635682680         14  cwp+17     *
2     J0006+1834    cnt96      00:06:04.8           2  cn95       +18:34:59            4  cn95       0.69374767047           14  cn95       0.86
3     J0007+7303    aaa+09c    00:07:01.7           2  awd+12     +73:03:07.4          8  awd+12     0.3158731909             3  awd+12     1.40
4     J0011+08      dsm+16     00:11:34           114  dsm+16     +08:10               8  dsm+16     2.55287                  0  dsm+16     5.40
5     B0011+47      dth78      00:14:17.75          4  hlk+04     +47:46:33.4          3  hlk+04     1.240699038946          11  hlk+04     1.78

6     J0023+0923    hrm+11     00:23:16.878141      9  abb+18     +09:23:23.8652       3  abb+18     0.003050203104480002     7  abb+18     1.11
7     J0024-7201Z              00:24:06.041         2  frk+17     -72:05:01.480        6  frk+17     0.004554447383906        3  frk+17     2.56
8     J0024-7204aa  phl+16     00:24:05.67          0  mam+06     -72:04:52.62         0  mam+06     0.00184                  0  phl+16     2.69
9     J0024-7204ab  phl+16     00:24:08.1615        5  frk+17     -72:04:47.602        2  frk+17     0.0037046394947985       6  frk+17     2.54
10    B0021-72C     mld+90     00:23:50.3546        1  frk+17     -72:04:31.5048       4  frk+17     0.00575677999551635     14  frk+17     4.69

11    B0021-72D     mlr+91     00:24:13.88092       6  frk+17     -72:04:43.8524       2  frk+17     0.00535757328486573      9  frk+17     4.69
12    B0021-72E     mlr+91     00:24:11.10528       5  frk+17     -72:05:20.1492       2  frk+17     0.00353632915276244      4  frk+17     4.69
13    B0021-72F     mlr+91     00:24:03.85547      10  frk+17     -72:04:42.8183       2  frk+17     0.00262357935251262      4  frk+17     4.69
14    B0021-72G     rlm+95     00:24:07.9603        1  frk+17     -72:04:39.7030       5  frk+17     0.00404037914356515     14  frk+17     4.69
15    B0021-72H     mlr+91     00:24:06.7032        2  frk+17     -72:04:06.8067       6  frk+17     0.00321034070935032     11  frk+17     4.69

16    B0021-72I     mlr+91     00:24:07.9347        2  frk+17     -72:04:39.6815       7  frk+17     0.00348499206166289     13  frk+17     4.69
17    B0021-72J     mlr+91     00:23:59.4077        1  frk+17     -72:03:58.7908       5  frk+17     0.00210063354535246      5  frk+17     4.69
18    B0021-72L     rlm+95     00:24:03.7721        3  frk+17     -72:04:56.923        2  frk+17     0.0043461679994616       4  frk+17     4.69
19    B0021-72M     mlr+91     00:23:54.4899        3  frk+17     -72:05:30.756        2  frk+17     0.0036766432176002       3  frk+17     4.69
20    B0021-72N     rlm+95     00:24:09.1880        2  frk+17     -72:04:28.8907       7  frk+17     0.00305395434626085     10  frk+17     4.69

21    J0024-7204O   clf+00     00:24:04.65254       6  frk+17     -72:04:53.7670       2  frk+17     0.00264334329724357      5  frk+17     4.69
22    J0024-7204P   clf+00     00:24:20            29  rft+16     -72:04:10           62  rft+16     0.0036430207             3  rft+16     4.69
23    J0024-7204Q   clf+00     00:24:16.4909        1  frk+17     -72:04:25.1644       6  frk+17     0.00403318118457258     15  frk+17     4.69
24    J0024-7204R   clf+00     00:24:07.5851        2  frk+17     -72:04:50.3954       5  frk+17     0.00348046270749329     13  frk+17     4.69
25    J0024-7204S   clf+00     00:24:03.9794        1  frk+17     -72:04:42.3530       4  frk+17     0.00283040595787912      8  frk+17     4.69

26    J0024-7204T   clf+00     00:24:08.5491        5  frk+17     -72:04:38.932        3  frk+17     0.0075884798073671      12  frk+17     4.69
27    J0024-7204U   clf+00     00:24:09.8366        1  frk+17     -72:03:59.6882       4  frk+17     0.00434282669639233     12  frk+17     4.69
28    J0024-7204V   clf+00     00:24:05.67          0  mam+06     -72:04:52.62         0  mam+06     0.00481016762            7  rft+16     4.69
29    J0024-7204W   clf+00     00:24:06.058         1  rft+16     -72:04:49.088        2  rft+16     0.0023523445319370       3  rft+16     4.69
30    J0024-7204X   fre08      00:24:22.38565       9  rft+16     -72:01:17.4414       7  rft+16     0.00477152291069356      5  rft+16     4.69

31    J0024-7204Y   frk+17     00:24:01.4026        1  frk+17     -72:04:41.8363       4  frk+17     0.00219665714352123      5  frk+17     4.69
32    J0024-7204Z   fre08      00:24:05.67          0  mam+06     -72:04:52.62         0  mam+06     0.004554                 0  fre08      4.69
33    J0026+6320    jml+09     00:26:50.561         8  jml+09     +63:20:00.87         5  jml+09     0.318357731235           1  jml+09     6.42
34    J0030+0451    lzb+00     00:30:27.42781       4  abb+18     +04:51:39.7113      14  abb+18     0.0048654532112551       3  abb+18     0.32
35    J0033+57      hrk+08     00:33                0  hrk+08     +57                  0  hrk+08     0.315                    0  hrk+08     2.25

36    J0033+61      hrk+08     00:33                0  hrk+08     +61                  0  hrk+08     0.912                    0  hrk+08     1.64
37    J0034-0534    bhl+94     00:34:21.83422       8  dcl+16     -05:34:36.722        3  dcl+16     0.0018771818845850       2  aaa+10b    1.35
38    B0031-07      lvw69a     00:34:08.8703        1  cbv+09     -07:21:53.409        2  cbv+09     0.9429509945598         17  hlk+04     1.03
39    J0034+69      slr+14     00:34                3  slr+14     +69:43              18  slr+14     0.03680412              16  slr+14     2.28
40    B0037+56      dtws85     00:40:32.362         6  hlk+04     +57:16:24.91         6  hlk+04     1.1182253452412         13  hlk+04     2.42

41    J0045-7042    mfl+06     00:45:25.69         17  mfl+06     -70:42:07.1         13  mfl+06     0.63233580002            6  mfl+06     59.70
42    J0045-7319    mmh+91     00:45:35.16          7  kbm+96     -73:19:03.0          2  kbm+96     0.92627590497            3  kbm+96     59.70
43    B0045+33      dtws85     00:48:33.98          3  hlk+04     +34:12:08.0          4  hlk+04     1.217094296058           8  hlk+04     4.50
44    J0050+03      dsm+16     00:50:31           113  dsm+16     +03:48               8  dsm+16     1.36656                  0  dsm+16     25.00
45    J0051+0423    snt97      00:51:30.1           2  snt97      +04:22:49            6  snt97      0.35473179890            1  snt97      1.25

46    J0053+69      slr+14     00:53                3  slr+14     +69:39              18  slr+14     0.832938                28  slr+14     2.75
47    J0054+66      hrk+08     00:54                0  hrk+08     +66                  0  hrk+08     1.39                     0  hrk+08     0.90
48    J0054+69      kkl+15     00:54:28            25  kkl+15     +69:26               2  kkl+15     *                        0  *          2.35
49    B0052+51      dtws85     00:55:45.378        10  hlk+04     +51:17:24.97        11  hlk+04     2.115171148865           4  hlk+04     1.94
50    B0053+47      dtws85     00:56:25.51          2  hlk+04     +47:56:10.5          3  hlk+04     0.472036662076           7  hlk+04     1.12

51    J0057-7201    ckm+01     00:57:44.0           4  ckm+01     -72:01:19            2  ckm+01     0.7380624426             2  ckm+01     3.48
52    J0058+6125    hrk+08     00:58                0  hrk+08     +61:25               0  hrk+08     0.637                    0  hrk+08     2.61
53    J0059+50      slr+14     00:59                2  slr+14     +50:02              18  slr+14     0.996009                61  slr+14     2.61
54    J0100-7211    lfmp02     01:00:43.03         11  mgr+05     -72:11:33.6          5  mgr+05     8.020392                 9  mgr+05     59.70
55    J0101-6422    kcj+12     01:01:11.1163        2  kcj+12     -64:22:30.171        2  kcj+12     0.0025731519721683       2  kcj+12     1.00

56    J0102+4839    hrm+11     01:03                0  hrm+11     +48:00               0  *          0.00296                  0  hrm+11     2.38
57    B0059+65      dbtb82     01:02:32.958        16  hlk+04     +65:37:13.40        11  hlk+04     1.679164229064          12  hlk+04     1.98
58    J0103+54      kkl+15     01:03:37            20  kkl+15     +54:02               5  kkl+15     0.354304                 6  kkl+15     2.01
59    J0106+4855    pga+12     01:06:25.06          1  pga+12     +48:55:51.8          2  pga+12     0.0831573050050          6  pga+12     3.06
60    J0108-1431    tnj+94     01:08:08.347016     88  dtbr09     -14:31:50.1871      11  dtbr09     0.807564614019          20  hlk+04     0.21

61    B0105+65      dls72      01:08:22.64          5  hlk+04     +66:08:34.0          3  hlk+04     1.2836598429             5  hlk+04     1.46
62    B0105+68      dtws85     01:08:29.50          2  hlk+04     +69:05:52.63        11  hlk+04     1.071118109859           5  hlk+04     1.98
63    J0111-7131    mfl+06     01:11:28.77          9  mfl+06     -71:31:46.8          6  mfl+06     0.68854151164            5  mfl+06     59.70
64    J0112+66      slr+14     01:12                3  slr+14     +66:22              18  slr+14     4.30124                 70  slr+14     2.42
65    J0113-7220    ckm+01     01:13:11.09          3  ckm+01     -72:20:32.20        15  ckm+01     0.32588301613            1  ckm+01     59.70

66    B0114+58      stwd85     01:17:38.661         3  hlk+04     +59:14:38.39         3  hlk+04     0.1014390664824         20  hlk+04     1.77
67    J0125+62      slr+14     01:26                3  slr+14     +62:35              18  slr+14     1.708233                98  slr+14     2.40
68    J0131-7310    mfl+06     01:31:28.51          3  mfl+06     -73:10:09.34        13  mfl+06     0.348124045581           7  mfl+06     59.70
69    J0133-6957    lml+98     01:33:32.46          1  dsb+98     -69:57:29.68         3  dsb+98     0.463473741703           3  dsb+98     2.44
70    J0134-2937    mld+96     01:34:18.6824        3  lwy+16     -29:37:17.042        7  lwy+16     0.136961610513651       14  lwy+16     25.00

71    J0136+63      slr+14     01:36                3  slr+14     +63:42              18  slr+14     0.717895                27  slr+14     9.12
72    J0137+1654    lxf+05     01:37:23.88          1  lxf+05     +16:54:42.1          4  lxf+05     0.4147630265082          5  lxf+05     3.06
73    J0139+33      ttm+18     01:39:10           120  ttm+18     +33:10              15  ttm+18     *                        0  *          1.47
74    J0139+5621    cvh+14     01:39:38.56          2  cvh+14     +56:21:36.8          4  cvh+14     1.77534382596           10  cvh+14     2.41
75    B0136+57      dth78      01:39:19.7401       12  cbv+09     +58:14:31.819       17  cbv+09     0.272450630950          15  hlk+04     2.60

76    B0138+59      mth72      01:41:39.938         8  hlk+04     +60:09:32.30         7  hlk+04     1.2229485205457         18  hlk+04     2.30
77    J0141+63      slr+14     01:41                2  slr+14     +63:08               8  slr+14     0.04668588              49  slr+14     8.77
78    J0146+31      ttol16     01:46:15            40  ttol16     +31:04              10  ttol16     0.9381                   0  ttol16     1.83
79    J0146+6145    ims94      01:46:22.42         10  pkw+03     +61:45:02.8          7  pkw+03     8.6889941                4  dk14       3.60
80    B0144+59      stwd85     01:47:44.6457       17  ywml10     +59:22:03.293       15  ywml10     0.19632137543003        16  ywml10     1.58

81    B0148-06      mlt+78     01:51:22.701        11  hlk+04     -06:35:02.8          4  hlk+04     1.464664549334           7  hlk+04     25.00
82    J0152+0948    clm+05     01:52:23.73          5  clm+05     +09:48:10            2  clm+05     2.74664729014           10  clm+05     2.48
83    B0149-16      mlt+78     01:52:10.8536       17  hlk+04     -16:37:52.99         4  hlk+04     0.8327416126878         13  hlk+04     0.92
84    J0156+04      dsm+16     01:56:01           114  dsm+16     +04:02               8  dsm+16     *                        0  *          25.00
85    B0153+39      dtws85     01:56:55.2           3  hlk+04     +39:49:29            5  hlk+04     1.81156061131           10  hlk+04     4.91

86    B0154+61      dls72      01:57:49.93          3  hlk+04     +62:12:25.90        17  hlk+04     2.35174493646            7  hlk+04     1.39
87    J0158+21      dsm+13     01:58:29            32  dsm+13     +21:08               8  dsm+13     0.5053                   0  dsm+13     1.57
88    J0201+7005    kkl+15     02:01:41.344         7  kkl+15     +70:05:18.11         6  kkl+15     1.349184471846          10  kkl+15     1.17
89    J0205+6449    mss+02     02:05:37.92247      15  bkr+13     +64:49:41.3343      10  bkr+13     0.06571592849324         9  lrc+09     3.20
90    B0203-40      mlt+78     02:06:01.268         9  smd93      -40:28:04.33        14  smd93      0.630550140847           6  smd93      1.26

91    J0211-8159    lml+98     02:11:59.0           3  dsb+98     -81:59:36.2          3  dsb+98     1.0773327013             8  dsb+98     1.52
92    J0212+5222    bck+13     02:12:52.2           6  bck+13     +52:22:45           13  bck+13     0.376386292              1  bck+13     1.56
93    J0214+5222    slr+14     02:14:55.2713       34  slr+14     +52:22:40.95        19  slr+14     0.02457529479071        22  slr+14     1.16
94    J0215+6218    llc98      02:15:56.626        10  hlk+04     +62:18:33.37        10  hlk+04     0.548879819155           3  hlk+04     2.00
95    J0218+4232    nbf+95     02:18:06.358569      4  dyc+14     +42:32:17.37515      8  dyc+14     0.00232309053151224      8  dcl+16     3.15

96    J0220+36      ttol16     02:20:50            60  ttol16     +36:22              15  ttol16     1.0297                   0  ttol16     2.25
97    J0229+20      dsm+13     02:29:03            32  dsm+13     +20:58               8  dsm+13     0.8069                   0  dsm+13     2.09
98    B0226+70      dtws85     02:31:13.99          3  hlk+04     +70:26:33.88        17  hlk+04     1.466820306152           7  hlk+04     1.76
99    J0241+16      dsm+13     02:41:46            31  dsm+13     +16:04               8  dsm+13     1.5454                   0  dsm+13     0.94
100   J0242+62      hrk+08     02:42:35             3  cvh+14     +62:56:50           36  cvh+14     0.592                    0  hrk+08     0.22

The peculiar numbers are links in the table to the referenced publications that are the sources of the data. Ignoring those, the output is pretty simple to parse (manually or via a script, if you want).

Some things to keep in mind:

Not all of the pulsars have all five parameters, so not all of the entries will be useful for you.
This isn't a complete list of all pulsars in the galaxy; it's just the most comprehensive one I know (and have used). We only know a small fraction of the total galactic pulsar population.
Keep your units in mind. Right ascension is given in hours-minutes-seconds format, declination is give in degrees-minutes-seconds format, and distances are in kiloparsecs.

This information should allow you to create a pulsar map for use within the Milky Way. It might not be terribly helpful, given our small (and incomplete) sample, but it's a start.


Diameter of the moon from the diameter seen in the telescope I'm reading a chapter on convex lenses and it has this diagram:

The chapter explains that triangles ABC and ADE are similar. Thus, ratio of CB to DE is equal to the ratio of BA to AD.
Does this mean that

if I look at the moon in the telescope that is 1 m long,
and the moon appears to be (I will make up a number) 1 cm in diameter,
knowing that the distance between moon and Earth is 384,000 km,

I can conclude that the moon is 3,840,000 m in diameter?
This is coming from 384,000 km / 1 m = X / 1 cm or, when converted to meters, 384,000,000 / 1 = X / 0.01

A telescope wouldn't have a single lens, I'm sure you know. If you were to use the setup in your diagram, focusing the image of the moon on a flat surface, you could find its diameter with the method provided. The distances f in the diagram are the focal length of the lens, where a very distant object will be in sharp focus, and that's where you'd end up placing the flat surface.


What type of galaxy is LEDA 14884? A new image of deep space was released yesterday, showing tons of galaxies. One in particular (named "LEDA 14884") looks very puzzling (like an ear), zoomed in below:

Article says it's a ring-shaped galaxy. Is there a more precise characterisation in terms of well-known galaxy typologies (irregular perhaps)? Perhaps the angle is confusing it's otherwise usual shape?

This is almost certainly an example of a collisional ring galaxy. It's listed as such (under the alternate name AM 0417-391) in the catalog of Madore et al. 2009; here is a panel showing the galaxy from one of their figures:

Image (probably from the Digitized Sky Survey) of AM 0417-391 = LEDA 14884), taken from Figure 5 of Madore et al. (2009). "RN" = "ring nucleus"; "Cn" = possible "companion" galaxies -- though some of these are in this case parts of the ring.
These are thought to be the result of a smaller galaxy colliding more or less head-on with a larger disk galaxy. The smaller galaxy passes through (so these are sometimes called "drop through" collisions), but leaves behind a pronounced "ripple" in the gas, which becomes concentrated in an expanding ring and forms stars at a high rate; this shows up as a ring of gas and bright, young stars. Since most such collisions will be off-center (i.e., the smaller galaxy won't pass through the exact center of the bigger galaxy), the ring will be asymmetric, as is clearly the case for LEDA 14884.
These are very rare systems; Madore et al. (2009) quote an estimated frequency of 0.01% of galaxies in the local universe being collisional ring galaxies.


Largest non-hot gas giants Excluding 'fluffy' or 'puffy' gas giants that are 'inflated by heat from their stars, what is the maximum radius of a gas giant planet.  I keep reading things like "...Jupiter is 'about' as big as they get...", but I can't seem to find a specific number to go with that word "about".

Assuming a gas giant was made up of the highest plausible ratio of Hydrogen, and the lowest plausible ratios of other elements (and not significantly heated by the star), just how big could a gas giant get before it started shrinking again under its own weight/gravity?

Is it really just 1 Jupiter radius? 1.0001? 1.1? 1.3?

According to the models of Mordasini et al. 2012 it is about 13 Earth radii (about 1.2 Jupiter radii) for gas giants older than a billion years.

Younger gas giants that are still contracting significantly can be bigger. How much bigger is wrapped up in uncertainties in the formation mechanism and the core mass and composition.

Gas giant mass-radius relationships from Mordasini et al. 2012. The colour coding corresponds to the fraction of heavy elements in the planet. The larger planets have smaller fractions of heavy elements.


What is the closest one could get to a black hole and still stand a realistic chance of escape? This question is inspired by the one asked here:

Is there any stable orbit around a black hole?

and I note that (though I've heard of these before) there are, apparently, 3 important fundamental "zones of inescapability" with regard to a black hole that can be identified on the basis of physical principles and which can be defined by the Schwarzschild $r$ coordinate and its critical radius $r_S$: one of these is, of course, the event horizon, at $1\ r_S$, from which no escape at all is possible. The second one is the "photon sphere", here referred to as the zone at the "innermost bound circular orbit", at $1.5\ r_S$, at which a photon (particle of light) traveling at right angles (i.e. constant $r$-coordinate) can complete one circuit around the hole and within which only impossibly powerful rockets could get you out. Orbits above this point but below the "innermost stable circular orbit", out to $3\ r_S$, are possible but require a continuous application of (likely ungodly large) engine propulsion. Above this, more-or-less normal orbits are possible, though they precess more and more rapidly as the general-relativistic effect that is incipient with the orbits of the planets becomes fully mature in these environs.

Now, the trick, of course, is the qualifiers regarding propulsion: "impossibly powerful", "ungodly large" which basically are likely words for "it can't be done with realistic technology". Which, then, of course, is what begs this question - what can be done with such?

For my "realistic" scenario, a generous interpretation will be used which is "a matter-antimatter fueled spacecraft with a wet mass 100x its dry mass". The goal is for the craft to execute one of two manoeuvres:

lower itself into an orbit around the hole, orbit a few times, and then take off again (so it must have fuel for both trips) and return to where it launched from, and
establish a "slingshot" trajectory around the hole that takes it as close as possible before shooting it back out into space (this may be easier?).

I consider this "reasonable" because any travel to a black hole will already be an extreme problem in interstellar travel, much less the kinds of targets that will already be in use for this kind of proposal which will almost surely have to be supermassive black holes to be interesting and thus requiring travel at least to the center of the Galaxy (~200 000 Pm) if not intergalactically (distances of many Zm), with tera- or petaseconds of travel time (thousands to millions of years) at least, or something like wormholes if they are possible. Hence I presume the technology to make such a craft will be readily available to any civilization that is capable of pulling this feat off to begin with.

The reason we need supermassive black holes is tidal forces and ideally we want to get as close to the horizon as possible. Possible targets may be Sagittarius A* and M87* (the black hole that the picture was taken of), both supermassive black holes, the latter much more so still, at the centers of galaxies. However, M87* presents the additional challenge of an extremely active matter environment around it, which may foreclose that possibility even further, though even Sgr A* might be too much. Hence, failing that, we can just consider a hypothetical black hole of mass equal to either, that is suitably "quiet", if nothing else is possible. (or perhaps imagine that with M87*, it has entered a quiescent period by the time the ships arrive as compared to the time when it sent the images we saw)

What would be the closest approach possible, in both scenarios, while still having enough fuel to get away (or not being destroyed by other effects)? We should also assume that the craft starts out at great distance where gravity is hopefully unremarkable, but do not budget for more than 250 Ms shipboard total mission time (a bit less than 2893 days of 86.4 ks each), measured from time of release from mission departure station to time of return.

The simplest case is for a rocket that does not fire its engine when it approaches the black hole from afar, and hence follows a geodesic trajectory. In this case the closest you can get is $3r_s$, but you can make an arbitrary number of turns around the black hole.

The reason for this is that the counterpart of a hyperbolic orbit corresponds to moving in the effective potential $V(r)=-GMm/r+L^2/2\mu r^2 - G(M+m)L^2/c^2\mu r^3$ (this is the Wikipedia version of the formula; different authors use different measures). For a given energy and angular momentum this means that either you can come in from infinity and fall into the black hole (for low energy and angular momentum) or the potential has a maximum greater than your energy and you will turn back. The closest you can get the maximum to go to the hole is $r=3r_s$ (as your angular momentum increases).

However, the angular velocity behaves as $d\theta / d\tau = (L/\mu)/r^2$: you will swirl around a lot as you get close to the black hole. Since a carefully selected trajectory will have energy and angular momentum so that you turn around almost exactly at the potential maximum where the derivative $V'(r)\approx 0$ the proper time spent there will be long and you can get as many turns as you want. The orbital frequency as seen from the outside is 2200 Hz $(M_\odot/M)$ (!) (source).

Note that all of this is freefall: the only thing to worry about is tidal forces, but that is not much of an issue near a SMBH. The velocity needed is of course in principle zero at infinity if you come in along a parabolic orbit.

The second question is if one can "slingshot". I assume this refers to an Oberth manoeuvre rather than a gravitational slingshot, which is unpowered. Gravitational slingshots from black holes can give you any change in angle, but the velocity change is just like the classical case. Rotation does not affect this, except by making the angular shift weirder. Note that for prograde orbits around an extremal spinning black hole the ISCO approaches the horizon radius, so the above unpowered flybys can in principle get right up  to the horizon.

For the powered manoeuvre I don't have a full answer; I would actually like to see it answered (see this question and my half-answer to it). The basic story looks like that for velocity-at-infinity increasing manoeuvres you should not get closer than $3r_s$. But for a sightseeing trip close to the horizon spending some of your fuel (and mass) ought to work.

What you need to do is to fire the engines powerfully enough to change the sign of your radial velocity and retain more total kinetic energy than the potential maximum. The potential maximum is due to angular momentum.

For the freefall radial trajectory with no angular momentum you will have $(dr/d\tau)^2=(E/mc^2)^2-c^2(1-r_s/r)$, so if you start with zero velocity at $r=\infty$ (hence $E=mc^2$) the inward radial velocity will be $dr/d\tau = c\sqrt{r_s/r}$. So you need $\Delta v =2c\sqrt{r_s/r}$ to escape again this way. We can rearrange the formula into $$r_{escape}= \frac{r_s}{\left(\Delta v / 2c\right)^2}$$

In your case $m_0/m_1=100$ and I assume $I_{sp}\approx 0.6c$,  $\Delta v = c \tanh \left( \frac{I_{sp}}{c}\log\left(\frac{m_0}{m_1}\right)\right) = 0.9921c$, and $r_{escape}=4.0642 r_s $. That demonstrates that the purely radial approach is not a good choice; adding a bit of lateral thrust would allow a closer approach.

I don't have the full answer for the lateral case. If you come in along a flyby orbit that approaches the ISCO you can slow down a bit so you now are on an inspiralling trajectory. To escape you need to pay roughly twice the potential difference between your final radial distance orbit and the maxmimum of the new potential.

Again, rotating black holes allow you to use the Penrose process to gain a lot of angular momentum by dumping reaction mass in the right direction. However, the efficiency is proportional to the total momentum of the reaction mass and is rather negligible for non-relativistic rockets. Hence rockets not powered by antimatter will likely not benefit much from this possibility.


Anti matter in Jupiter magnetic field? My question is based in this Wikipedia article about the Jupiter magnetic field:
https://en.wikipedia.org/wiki/Magnetosphere_of_Jupiter

Jupiter magnetic field generates plasma and accelerates ionized molecules, eventually producing collisions. Is anti matter generated naturally under this scenario?

Yes it is. See this 2012 blog post by Paul Gilster:

https://www.centauri-dreams.org/2012/05/17/powering-up-the-antimatter-engine/

It says things like this:

  Antimatter in space is an idea that James Bickford (Draper Laboratory) analyzed in a Phase II study for NASA’s Institute for Advanced Concepts, for he had realized that high-energy galactic cosmic rays interacting with the interstellar medium (and also with the upper atmospheres of planets in the Solar System) produce antimatter. In fact, Bickford’s calculations showed that about a kilogram of antiprotons enter the Solar System every second, though little of this reaches the Earth. To harvest some of this incoming antimatter, you need a planet with a strong magnetic field, so Jupiter is a natural bet for Baxter’s scientists, who go there to forage.

But it also says Saturn's a better bet, and that Earth is handier, along with this:

  The problem with this — and this has been noted by The Physics arXiv Blog and Jennifer Ouellette in recent days — is that PAMELA could come up with only 28 antiprotons over the course of 850 days of data acquisition. There is no question that Bickford is right in seeing how antimatter can be produced locally. In fact, the paper on the PAMELA work says this: “The ﬂux exceeds the galactic CR antiproton ﬂux by three orders of magnitude at the current solar minimum, thereby constituting the most abundant antiproton source near the Earth.” But does the process produce enough antimatter to make local harvesting a serious possibility?

If you want some antimatter, buy a banana. I kid yet not. See the Symmetry article antimatter from bananas. Flip Tanedo says this: “While researching natural sources of antimatter, I discovered a curious article about a naturally occurring potassium isotope that, some fraction of the time, decays via positron emission. The conclusion was that: The average banana (rich in potassium) produces a positron roughly once every 75 minutes”. Better still, buy a whole bunch of bananas!


how does redshift prove expansion is accelerating? My astronomy teachers never would answer this for me... Redshift obviously indicates an object (such as another galaxy) is moving away, but how do we know its acceleration from this? It's my understanding that the instantaneous redshift of an object is an indicator solely of its instantaneous velocity, and we have certainly not been observing redshift long enough to compare and determine a change in velocity

If you can, please avoid using complex math in your answer.

You're right, a redshift will give you a measure of a velocity, not an acceleration. I'm assuming when you say acceleration, you're referring to the accelerating expansion of the universe so you're not looking at the particular acceleration of an object (which you could get from examining the force of gravity imparted on that object).

So in addition to a redshift, you need to find a way to independently measure the distance. To get out to an appreciable redshift (z~0.5), Type Ia supernova are used as "standard candles". They are considered standard because they're believed to be from white dwarfs that explode because they have reached their maximum possible mass, the Chandrasekhar limit, of 1.4 solar masses. Therefore, when they explode, they should all look about the same and any difference in brightness would be from how far they are away from us. So they measured the distance and the redshift of the galaxy the supernova originated from to determine the expansion of the universe appears to be accelerating over time.


Is the Universe really expanding at an increasing rate? Here's what I just read from Wikipedia's page on the Hubble Space Telescope:

  While Hubble helped to refine estimates of the age of the universe, it also cast doubt on theories about its future. Astronomers from the High-z Supernova Search Team and the Supernova Cosmology Project used ground-based telescopes and HST to observe distant supernovae and uncovered evidence that, far from decelerating under the influence of gravity, the expansion of the universe may in fact be accelerating. The cause of this acceleration remains poorly understood; the most common cause attributed is dark energy.

I don't take this at face value because we should expect more distant objects to have higher observed speeds and therefore higher observed red-shifts. Here's why.

Let's start with a model where the Universe expanded very fast early on, but has been slowing down ever since due to gravity, as one would normally expect.
Remember that, the farther away a cosmic object is, the farther back in the past we are observing it. An object 1,000 light years away, if it's light is reaching us now, is being observed in its state that existed 1,000 years ago. We are effectively looking through a time machine.
So if we observe a more distant object, we're observing an older state of that object. Therefore, we are observing it at a time when the Universe was expanding faster than it is now, so it has higher red-shifts.

And isn't that what we observe today? The more distant the galaxy, the higher its red-shift? This is not inconsistent with a "normal" model where the expansion is slowing down due to gravity.

What am I missing? Why are scientists trying to explain such things with weird dark matter and dark energy that otherwise have never been detected or found evidence of and aren't needed for any other model, and in fact get in the way of our models of physics and quantum dynamics?

I don't take this at face value because we should expect more distant
  objects to have higher observed speeds and therefore higher observed
  red-shifts.

That's true.   That was the original Hubble discovery - the farther away things were, the faster they were moving away from us.

  Here's why.  Let's start with a model where the Universe expanded very
  fast early on, but has been slowing down ever since due to gravity, as
  one would normally expect.

Yes - that's what everybody thought following Hubble's discovery.

  Remember that, the farther away a cosmic object is, the farther back
  in the past we are observing it. An object 1,000 light years away, if
  it's light is reaching us now, is being observed in its state that
  existed 1,000 years ago. We are effectively looking through a time
  machine.

This is not lost on Astrophysicists.

  So if we observe a more distant object, we're observing an older state
  of that object. Therefore, we are observing it at a time when the
  Universe was expanding faster than it is now, so it has higher
  red-shifts.

OK, 2 points.   2nd point first.   The red-shift has to do with relative velocity, not speeding up or slowing down.    Something can be more red-shifted and slowing down and something can be less red-shifted and speeding up, especially since the acceleration/deceleration is comparatively slow compared to the relative velocity.

and other point - lets keep in mind, we don't know what a galaxy 3 billion light years away is doing now.  We can guess and we can run models, but we can only see what it's doing 3 billion years ago.

  And isn't that what we observe today? The more distant the galaxy, the
  higher its red-shift? This is not inconsistent with a "normal" model
  where the expansion is slowing down due to gravity.

Yes, the more distant the galaxy the higher it's red-shift.    But no, that's not inconsistent with expansion.  That's what you'd see, expansion or contraction, because red-shift is just relative velocity.

  What am I missing? Why are scientists trying to explain such things
  with weird dark matter and dark energy that otherwise have never been
  detected or found evidence of and aren't needed for any other model,
  and in fact get in the way of our models of physics and quantum
  dynamics?

A lot of these ideas are confusing.   They're confusing to scientists too, especially when they were first discovered - so you're not alone.

Dark matter was observed because galaxies were behaving strangely.   The stars in the outer arms of the galaxy were observed to be moving much too fast and faster than the stars more towards the middle of the galaxy and that made no sense.   The galaxies also weighed too much and the only way to explain this was extra mass in kind of a halo around the galaxy, but this extra mass, also, didn't interact with electromagnetic waves like the mass here on earth does - so they called this extra mass (and there's a lot of it, more than there is regular mass), but since it's invisible, they called it "dark matter" and it's not dark like dirt or coal, it's dark as in - invisible.   It's completely transparent to light, but it has mass and they still don't know what it is.  They have some OK theories, but nothing definite.

Now, dark energy - think about the big bang and all matter flying apart - the galaxies twice as far are moving away twice as fast, BUT, as you said, because of gravity, we should see the galaxies that are twice as far moving away more than twice as fast, cause the nearer the galaxy, the more time it's had to slow down - aha, they thought, if we can compare the speed of the galaxies 4 billion light years away to the speed of the galaxies 2 billion light years away to the speed 1 billion light years - etc, etc and measure it all carefully, we can measure the rate at which gravity is slowing down the universe. - that makes sense right.

And with careful measurement of Type 1A supernovas, which temporarily outshine entire galaxies - with remarkable consistency (what they call a standard candle - a very bright standard candle, but a standard candle all the same) - with that, they thought they could measure the gravitational slow down of expansion - exactly what you're talking about.

The problem was, the measurements told them the opposite of what they expected to find.   The measurements told them that the galaxies 2 billion light years away were traveling slightly more than half as fast as the galaxies 4 billion light years away, and so on.  They checked this, cause it had to be wrong, then they re-checked it, and re-checked again and the only conclusion was, stuff out there is speeding up, not slowing down - cause that's what the telescopes tell us.

Dark energy wasn't a hair-brained scheme that mad scientists thunk up.  It was an observed reality that nobody expected (well, cept just maybe for Einstein and his cosmological constant, but that's another story).

Dark energy's just a name anyway.   They have to call it something, even if they're not sure what it is or how it works.


Tidal lock of earth and moon As the Moon is tidally locked to Earth, that means, from Earth we can only ever see one side of the moon.

Can we see all the sides of the Earth, from the moon?

The Earth and the Moon do interact, but because they have different sizes and masses the effect on each is different.

The Moon rotates once in its orbit around the Earth, causing it to constantly show the same face. This was the Earth's effect on the Moon due to tidal dragging by gravity.

It's pretty stable, the Moon will continue to show the same face to the Earth even as the tidal forces cause it to orbit farther and farther away.

We actually see slightly more than 50% of the Moon. The Moon's orbit causes its aspect to nod because its orbit is slightly elliptical and shimmy because it's not orbiting directly over the equator. Over time we actually see almost 60 percent of the surface of the Moon (an effect called libration).

The Moon's effect on the Earth has been to slow its daily rotation to 24 hours. In the past, the Moon was much closer to the Earth, and the day was much shorter. As time passes and the Moon moves into a wider orbit, the length of the Earth's day will increase (see e.g. this Scientific american post).

I've read that the Moon would recede to a certain point, then begin approaching the Earth again, but unfortunately the Sun will swell into a red giant before then and swallow the Earth and the Moon.


Why is sodium such a common ion for in ion tails? I was doing research about ion tails of planetary bodies and noticed that ion tails composed of sodium were common. For example, Mercury and the Moon both have ion tails made of sodium. Why is sodium, as opposed to other ions, commonly seen in ion tails?

From http://science.nasa.gov/science-news/science-at-nasa/2000/ast26oct_1/:

  "When a Leonid meteoroid hits the Moon it vaporizes some dust and
  rock," explains Jody Wilson of the Boston University Imaging Science
  Team. "Some of those vapors will contain sodium (a constituent of Moon
  rocks) which does a good job scattering sunlight. If any of the impact
  vapors drift over the lunar limb, we may be able to see them by means
  of resonant scattering. They will glow like a faint low-pressure
  sodium street lamp."

Also, relative to other elements, sodium has a low ionization energy.


Are there currently any planned or proposed missions to measure the gravitational fields of other planets in our solar system? I just recently found out about the GRACE Nasa mission which basically mapped out the gravitational anomalies of earth as well as serving extensively in the study of earths geology and the movement of its distribution of water. While I continued reading about it I came across GRAIL which did a similar job but over our moon.

Link here to learn about GRACE: GRACE

Here for GRAIL: GRAIL

What i'm now wondering is are there space agencies or organizations considering missions to any of the other planets in our solar system and attempting to measure their gravitational anomalies in a similar manner hopefully giving vital information on their inner structure or formation.

There are no such missions in an advanced state of planning, however we do have a good idea of the gravity field around Mars, gleaned from observations of anomalies in the orbits of the various orbital probes.

These data were gathered into a map of the gravity field of Mars

According to that NASA article:

  The map was derived using Doppler and range tracking data collected by NASA's Deep Space Network from three NASA spacecraft in orbit around Mars: Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO).

The research is published as Antonio Genova et al. 2016, Seasonal and static gravity field of Mars from MGS, Mars Odyssey and MRO radio science, Icarus, vol. 272, pp. 228-245; doi: 10.1016/j.icarus.2016.02.050

In addition, the Cassini Spacecraft has made detailed gravitational measurements of Saturn and and along with imaging, internal structure details of its moon Enceladus. Also the Juno Spacecraft has made detailed measurements of Jupiter's internal structure via maps of it's gravity field as well.


Where a database of different z values of redshift can be found? I was working on reshift details for various galaxies but do not know any database to find the z values given to redshift galaxies. Can anyone help?

There are some great databases with a lot of information in them, when you found the galaxy you looked for, somewhere on the page there should be redshift information if it is has been measured at some point.

The NED/ipac database is quite nice for galaxies (https://ned.ipac.caltech.edu/).
Or SIMBAD is also great (http://simbad.u-strasbg.fr/simbad/).


The name of a particular low extinction region There is a region called Baade's window.

I remember there is a similar region called "somebody's window", which also has a low amount of dust.

Does anyone know the name?

The Lockman hole?

http://en.wikipedia.org/wiki/Lockman_Hole

It has a column density of neutral hydrogen of $6\times10^{19}$ cm$^{-2}$, which will correspond to very little dust.

Two others I've heard of towards the Galactic bulge are known as the Sgr I and Sgr II windows.

Finally, I offer "Stanek's window" towards the bulge, which has been referred to in a number of the Chandra Galactic plane X-ray surveys but appears to have no refereed publication associated with its discovery. I found this on arXiv.  http://arxiv.org/abs/astro-ph/9802307  It is at $l=0.25$, $b=-2.15$ and has $E(B-V) \sim 0.6$.


What causes Titan a moon to have a denser atmosphere than that of a Mars? I'm wondering about Mars and Titan. If Mars is larger than Titan how come it lost most of its atmosphere? Mars also has a magnetic field while Titan doesn't. Yet Titans atmospheric pressure on the surface is a whopping 1.5 times that of Earth's.

Question: What causes Mars not to have much of an atmosphere, but Titan does?

Mars and Titan differ markedly in distance from the Sun, composition, and possibly geological activity.

Titan is about 6.3 times as remote from the Sun as is Mars, which means Titan receives about 1/40th solar radiation that Mars does, with about the same reduction in solar wind. Mars' small size coupled with its much closer proximity to the Sun allowed the solar wind to rip much of Mars' atmosphere away. Despite the marked differences between the atmospheres of Venus, Earth, and Mars, the atmospheric loss rates (in terms of mass loss per unit time) from these three planets are estimated to be about the same. This rate represents a pittance for Venus' very large atmosphere of Venus, a small amount for Earth's somewhat large atmosphere, but a huge proportional loss rate for Mars. Titan is spared to some extent.

Mar's average density is 3.93 g/cm3. Mars is a terrestrial planet. Titan's average density is less than half that, 1.88 g/cm3. Titan is an icy moon: some rock, but a lot of volatiles. There's a lot of ammonia mixed in with the water ice (and possibly liquid water deep down, if Titan's core is warm). Some hypothesize that Titan regenerates its atmosphere via releases of ammonia. Sunlight splits ammonia near the top of Titan's atmosphere into hydrogen and nitrogen. The hydrogen escapes, but not the nitrogen.

Finally, Mars is most likely dead geologically. It's covered with craters that may date back to the Late Heavy Bombardment. Titan exhibits some signs of being somewhat active, geologically. It too has craters, but it's not as plastered with them as is Mars. It's mountains appear to be younger, at least according to some. The geological activity may help to regenerate Titan's atmosphere.


Which is really larger, Big Dipper or Small Dipper, in 3D If we take the convex hull of the 3D coordinates of the stars in Ursa Major and Ursa Minor: which hull has larger volume?

This is meant semi-humorous but we might also learn some interesting points from good answers, e.g. which metric to use when mass distorts space or how to measure with respect to frames of reference.

Update: to those asking about which stars to consider, just choose e.g. the canonical 7 stars of each. But this question is less about one arbitrary number and more about which things to consider, e.g. to show beginners that a bright star is not always close (and the other way around), and that size can be different in 3d than our arbitrary 2d-perspective.

To calculate that you will have to build a 3D model based upon the distance of each of their stars and then calculate the resulting 3D object's volume. I know this may not answer the question, but I give the way to answering it. It's not an easy job.

Making a quick guess based upon the distances of the stars of both constellations in my opinion I guess the Small Dipper has a bigger volume since it's starts have bigger distance differences ranging from < 100 ly up to > 500 ly. In the case of the Big Dipper all distance are very similar since all stars come from the same open cluster. Their distance range between 78 and 124 ly.

Source:

Small Dipper stars
Big Dipper stars

Useful resources:

Big Dipper 3D model


Can we see the past image of Earth because of curving light by massive objects? I know massive objects can curve light, can we capture the image of past Earth by lights from Earth that curved by massive objects?

Light can be made to do this around black holes, sort of. At a certain distance from a black hole you have what's called a photon sphere. At this distance, determined by the mass of the black hole, photons travel in orbits because of the space-time curvature.

So to answer your question, maybe.

Firstly, a massive entity would need to be located at some point in space in order to influence the photons into an orbit - okay yes, possible. Secondly, this massive object would need to have a mechanism of instantaneously disappearing from space-time in order for the photos to tangentially come out of orbit and back towards earth.

I read on a previous question on Physics.SE that there is no such solution to the Einstein Field Equations which allows for a massive object to just disappear - the closest thing would be for the density distribution of the object to change but I can't say if that would yield the result you are asking about.

Rob Jeffries mentioned that images do exist which suggest that photons experience such a change in trajectory - this could happen on paths which are very close to a photon sphere-like one, but deviate enough from it to allow photos to escape.


Can hawking radiation be eaten by another blackhole? Just a theory, from this video. At last, only the black holes are gonna exist and even they'll decay because of hawkings radiation.

As black holes emit hawkings radiation, then if one emits it, another should absorb it, this will create infinite loop kind of thing & universe is never gonna be empty as blackholes will keep on refilling!

Question: Can a black hole absorb hawkings radiation from another black hole?

(this question is quite obvious if we think that black holes can absorb anything but how's that gonna make the universe empty)

Black holes can "eat" Hawking radiation, but the radiation has to be directed towards the black hole before it can be "eaten". Black holes are pretty small, and space is very very very big.

So as a black hole evaporates, and gives off" Hawking radiation, some may eventually fall into another black hole, but most will not. It will just travel out into space, travelling forever (or until it is red-shifted to such low energy that it loses an individual identity - the so-called "heat death").  We can't picture this because our brains are not equipped to deal with the massive amounts of time. But on these time scales there is nothing very mysterious about a black hole evaporating and so vanishing. It is no more mysterious than a candle flame going out.

Here is a metaphor:

There are some children in a field, each child is carrying some balls (the children represent black holes, the balls are the mass of the black holes and the field is the universe).

The children are walking away from each other (the represents the expansion of the universe*)

Roughly every minute each child throws a ball in a random direction. (This is Hawking radiation)

If the ball passes another child, he catches it and adds it to his collection (Radiation falling into the black hole).

If a child runs out of balls, he sits down, he is out of the game and can't catch any more balls (this is the black hole running out of mass, and so evaporating).

Will the game end?

Most of the balls will never be caught by other children because they are not thrown in the right direction. Eventually, all the children will be sitting down and all the balls will be lost (This is the "heat death")

*This isn't quite right because it is an expansion, not walking from a centre, there is no centre to the universe.


How to find the radius of a satellite not knowing the mass If I know the semi-major axis, the density of the planet, and orbital period.. how can I find the radius of the satellite?  I can't think of any formula to use.

How to find the radius of a satellite not knowing the mass:
If I know the

semi-major axis,
density of the planet, and
orbital period..

how can I find the radius of the satellite? I can't think of any formula to use.

I have a hunch that you've misunderstood the question, and that it asks for the radius of the planet not the artificial satellite, and that's certainly doable. Otherwise, why would the planet's density be a given?

The equation that links semi-major axis, mass of the planet, and orbital period is:
$$T=2 \pi \sqrt{\frac{a^3}{GM}} $$
where $G$ is the gravitational constant 6.674E-11 m^3 s^-2  kg^-1.
Moving things around we get
$$\frac{4 \pi^2 a^3}{T^2G} = M $$
Density is mass per volume, or:
$$\rho = \frac{M}{\frac{4}{3} \pi R^3} = \frac{3M}{4 \pi R^3}$$
Moving that around we get
$$R = \left(\frac{3M}{4 \rho \pi}\right)^{1/3}$$
Put in the earlier result for $M$, we get
$$R = a \left(\frac{3 \pi}{\rho T^2G}\right)^{1/3}$$

For Earth's average density, Wikipedia says 5514 kg/^3, for its radius, try 6,371,000. meters. For the ISS at 400 km (400,000 meters) above the Earth, use 92.5 minutes (5550 sec). It should all work out nicely!
The reason this works with average density, even though Earth's density is higher in the core than the surface is the application of Newton's shell theorem.


How close would the sun have to get to Earth for there to be severe consequences? According to earthsky.org the Earth gets 3 million miles closer to the Sun than its usual distance of about 93 million miles on average.

My question is, how close would the earth have to be to the sun for there to be problems with our survival?

I'm going to use Gm (1 gigameter = $1\times10^9$m) and degrees Celsius for this answer.

By getting closer to the Sun, probably the most major problem would be the increase in temperature.

A while ago I wrote a program that calculates the effective surface temperature of a planet. Having dug it back out, I've played around with the values a bit. It's important to note that the effective temperature is not the same as the actual surface temperature, since it doesn't account for Earth's atmosphere. If Earth had no atmosphere, it would be the correct actual temperature.

At our current distance of (avg.) 149.6Gm, the effective temperature is 257K, or -16°C (some websites cite other values ±2°C). NASA cites an actual average temperature of 15°C. Assuming a linear relationship between effective temperature and actual temperature, we can assume that $T_{actual} = T_{eff}+31 \pm 2$.

So, what would happen if we moved, say, 10Gm closer?

Well, the effective surface temp is now -7°C, and I'm guessing the actual temperature would be about 24°C. This is an increase of 9°C. We would probably still be able to survive, but with difficulties. For starters, the sea level would rise by over 40m, leading the world to look (at the best) like this. Not an easy situation, but nevertheless survivable.
Of course, there would be other effects like an increase in extreme weather, the mass extinction of species, and probably a whole load of things that are hard to foresee, but I'm not going to try to predict them.

So, what about a move towards the Sun of 20Gm?

The effective temperature is now ~3°C, and the surface temperature is about 34°C. Things start to get bad now. All of the ice caps have melted. Once fertile areas are now barren deserts. Surviving is hard, but possible, although famine is now a major problem across much of the world (especially around the equator). The Gulf Stream may have stopped, oddly enough cooling down some of western Europe and all of Britain. It's not looking good.

What about 50Gm?

The effective temperature is 42°C; the actual one is around 73°C. Where the Sun's habitable zone begins and ends is disputed, but now, at 0.65AU away from the sun, it's quite likely that we're not in it. It's very hard to predict what happens now. Humans would likely have to stay underground to remain alive, and food would be a major issue. The ecosystem would be pretty much destroyed, having not had a chance to adapt to the new temperature.

For fun, if we moved 100Gm closer, we'd be at about 205°C. Ouch. We're closer than Mercury now, and look how that planet's coping. Mercury ranges from -173°C to 427°C depending on various factors. Survival without massive life support is not possible.

Any closer, and things just get worse.

Hope this is a suitable answer for your question!


A factor of cos(declination) in the formula of apparent of drift velocity of stars The angular drift velocity of stars is not the same for all stars and goes as $\frac{1}{\cos(\delta)}$. I don't understand why it should depend on the declination. All stars have to cover an angle of 360° in one sidereal day. Why should the angular velocity depend on the declination at all?

All stars have to cover an angle of 360° in one sidereal day.

is close but incomplete; we should really say that right ascension covers 360° in one sidereal day.
Let me state that analogy: Imagine that you are near the north pole. You start walking with the velocity of 5 km/h to the east. In a short amount of time, you are at the beginning. You went through all the time zones and geographical longitudes. Now you fly to the equator and do the same. Now you need a lot of time to go around the Earth. Change of geographical longitude is same in both cases. But the angle, measured from the center of the Earth, is different - at the north pole 0° and at the equator 360°.
With that analogy, you can understand the stars movement.
Let me give the last proof: has the north pole star same angular speed as Rigel?


Blood Moon Identification in NASA reports Often I look at NASA's Eclipse Web Site. More specifically, I often look at the Index to Five Millennium Catalog of Lunar Eclipse. How can I tell if an eclipse results in a "blood moon"? I know not all lunar eclipses result in a blood moon, but I do know that some do. So how can I know if one is from looking at it? A blood moon is the phenomenon whereby the moon in total eclipse appears reddish in color as it is illuminated by sunlight filtered and refracted by the earth's atmosphere. (Google)

Edit:

James K says this question may be a duplicate of another question. I want to know how to identify "blood moons" from looking at NASA's reports. The other question is more general. However the answer may be the same.

"Blood moon" is not a term used scientifically. Therefore look for total lunar eclipses.

As some light is diffracted by earth's atmosphere, the moon is not entirely black but appears red. (Blue light is scattered, see why is the sky blue).

All total lunar eclipses will show a reddish colour. The brightness may vary according to the state of the atmosphere but the moon will never be black, or any other colour.

(James K contributed equally to this answer)


What is the thickness of the Solar System disk? What is the thickness in AU of the all planets' orbital plane height combined in the Solar System?
Excluding Pluto.
Looking for h

The thickness of the planetary disc is dominated by Neptune, due to its large orbital radius.
We can calculate a planet's maximum distance from the ecliptic $h$ from the inclination angle of its orbit $\theta$ and its aphelion distance $r$. We get a right triangle, with $r$ as the hypotenuse, so
$$h = r\sin\theta$$
The table below was calculated using data from the NASA Planetary Fact Sheet. Angles are in degrees, distances are in millions of kilometres.
Planet distance from the ecliptic plane.

Name
Inclination
Aphelion
Distance

Mercury
7.0
69.8
8.506

Venus
3.4
108.9
6.458

Earth
0.0
152.1
0.000

Mars
1.9
249.2
8.262

Jupiter
1.3
816.6
18.526

Saturn
2.5
1514.5
66.062

Uranus
0.8
3003.6
41.937

Neptune
1.8
4545.7
142.784

So the total thickness of the disc is $2×142.784 = 285.568$ million kilometres, which is almost $1.91$ au.

Here's the Python code I used to create that table:
from math import sin, radians

names = (
 'Mercury', 'Venus', 'Earth',
 'Mars', 'Jupiter', 'Saturn',
 'Uranus', 'Neptune',
)

# Orbit data from https://nssdc.gsfc.nasa.gov/planetary/factsheet/
# Inclination to ecliptic plane
inc = [7.0, 3.4, 0.0, 1.9, 1.3, 2.5, 0.8, 1.8]
# Aphelion in millions of kilometres
aph = [69.8, 108.9, 152.1, 249.2, 816.6, 1514.5, 3003.6, 4545.7]

print("|Name | Inclination | Aphelion | Distance|")
print("|-|-|-|-|")
for n, th, r in zip(names, inc, aph):
    # Perpendicular distance to eciptic
    h = r * sin(radians(th))
    print(f"|{n} | {th} | {r} | {h:.3f}|")

Here's a live version of the script running on the SageMathCell server.

As John Holtz mentions in the comments, the true $h$ value for a planet may be smaller than the value shown in my table. The table's $h$ value only occurs if the planet's argument of periapsis is ±90°. Fortunately, Neptune's argument of periapsis is currently ~272°, so my $h$ value should be fairly close to the true value.

James K has supplied a list of orbit inclinations to the Solar System's invariable plane. Here's the table using those values.
Planet distance from the Solar System invariable plane.

Name
Inclination
Aphelion
Distance

Mercury
6.34
69.8
7.708

Venus
2.19
108.9
4.161

Earth
1.57
152.1
4.167

Mars
1.67
249.2
7.262

Jupiter
0.32
816.6
4.561

Saturn
0.93
1514.5
24.582

Uranus
1.02
3003.6
53.468

Neptune
0.72
4545.7
57.121

That reduces Neptune's $h$ considerably! Uranus may even be the current "winner", depending on their arguments of periapsis with respect to the invariable plane.


Is a literal instance of Russell's teapot possible? Much has been said about Russell's teapot, and I accept as obvious that a teapot would be too small to be detectable in an orbit around the Sun by any reasonable method today, or by any method that can reasonably be expected to develop in the near future. But how small is "too small"? Is it possible that there are bodies the size of Phobos (or even the Moon) in the orbit around Uranus, for example?
If there is anything I know about the Solar System, it's that the gaps in the distances between planets are huge. How can we be sure that there are no large bodies inside those gaps? I guess our observations are mostly based on (the absence of) gravitational anomalies, but how precise are they? Is the "limit of detectability" smaller for orbits around Sun than for much larger orbits e.g. at Jupiter's distance?

The brightness of light received from a light source (or an object that reflects light) is inversely proportional to the square of the distance.
So if an astronomical object A which reflects light from the Sun back to Earth orbits at a distance of two AU from the Sun and an idental astronomic object B orbits at twice that distance, or at 4 AU, how much light will Earth get from the two objects at their oppositions?
Since object B is twice as far away from the Sun as object A, it's surface receives one quarter as much light from the Sun as object A.  Since object B will be three tiems as far from Earth at opposition as object A will be at opposition, its reflected light will be one ninth as bright.  So together, those two factors will make the light that Earth gets from object at its opposition one thirty sixth, or 0.02777, as bright as the light that Earth gets from object A at its opposition.
So the farther away from the Sun an astronomical object is, the less bright its reflected light will be as seen from Earth.
And if an object C has a higher albedo, or is more reflective than object D of the same size, it will seem brighter at the same distance.
The brighter a solar system object is as seen from Earth, the sooner it will be noticed and discovered.  The dimmer a solar system object is as seen from Earth, the longer it can remain undiscovered.
Thus the undiscovered objects in the solar system should be the ones which appear fainter as seen from Earth.
They may be fainter and dimmer as seen from Earth because their albedo is lower than objects at the same distance.  Or maybe because they are much smaller than other objects with the same albedo and distance.  Or maybe they are very large objects with high albedos but are very faint because they are very far away.
Over time, astronomers discover dimmer and dimmer objects in the solar system, objects which have darker surfaces, or are smaller, or are much farther from the Sun.
So the largest solar system objects likely to be discovered in the future are likely to be very far fromt he Sun and the Earth and thus appear many times dimmer than objects of equal size in the inner solar system.
You may have heard of the hypothetical Planet Vulcan, inside the orbit of Mercury, once used to explain certain problems with the orbit of Mercury.  It is no known that Vulcan could not possibly exist.  It would have been discovered long ago if it did exist.

None of these claims has ever been substantiated after more than forty years of observation. It has been surmised that some of these objects—and other alleged intra-Mercurial objects—may exist, being nothing more than previously unknown comets or small asteroids. No vulcanoid asteroids have been found, and searches have ruled out any such asteroids larger than about 6 km (3.7 mi).[4] Neither SOHO nor STEREO has detected a planet inside the orbit of Mercury.[4][23]

https://en.wikipedia.org/wiki/Vulcan_(hypothetical_planet)[1]
The largest solar system objects discovered in recent times have all been beyond the orbit of Neptune, and have been rather small.  Only a few of the largest ones have been large enough to classify as dwarf planets, and they are all smaller than Eerth's moon.
It is possible that there may be one or more as yet undiscovered planets in the outer solar system.  But since there are limits on how bright those planets could be and remain undiscovered, there are limits on how large and/or close they could be.

As of 2016 the following observations severely constrain the mass and distance of any possible additional Solar System planet:
An analysis of mid-infrared observations with the WISE telescope have ruled out the possibility of a Saturn-sized object (95 Earth masses) out to 10,000 AU, and a Jupiter-sized or larger object out to 26,000 AU.[6] WISE has continued to take more data since then, and NASA has invited the public to help search this data for evidence of planets beyond these limits, via the Backyard Worlds: Planet 9 citizen science project.[96]
Using modern data on the anomalous precession of the perihelia of Saturn, Earth, and Mars, Lorenzo Iorio concluded that any unknown planet with a mass of 0.7 times that of Earth must be farther than 350–400 AU; one with a mass of 2 times that of Earth, farther than 496–570 AU; and finally one with a mass of 15 times that of Earth, farther than 970–1,111 AU.[97] Moreover, Iorio stated that the modern ephemerides of the Solar System outer planets has provided even tighter constraints: no celestial body with a mass of 15 times that of Earth can exist closer than 1,100–1,300 AU.[98] However, work by another group of astronomers using a more comprehensive model of the Solar System found that Iorio's conclusion was only partially correct. Their analysis of Cassini data on Saturn's orbital residuals found that observations were inconsistent with a planetary body with the orbit and mass similar to those of Batygin and Brown's Planet Nine having a true anomaly of −130° to −110° or −65° to 85°. Furthermore, the analysis found that Saturn's orbit is slightly better explained if such a body is located at a true anomaly of 117.8°+11°
−10°. At this location, it would be approximately 630 AU from the Sun.[99]

https://en.wikipedia.org/wiki/Planets_beyond_Neptune[2]
New moons of the four giant planets are still being discovered, but the recent discoveries are all of tiny objects, less than 10 kilometers in diameter.


Why are the spherical and cartesian galactic coordinates in the ATNF Pulsar Catalogue different? I am trying to relate Galactic Latitude (b) and Longitude (l) (spherical coordinates) to galactic cartesian x,y,z coordinates in the ATNF pulsar catalog.

This query shows some sample data with G_l, G_b, XX, YY, and ZZ; excerpt:

------------------------------------------------------------------
#     NAME                     Gl     Gb     ZZ     XX     YY
                               (deg)  (deg)  (kpc)  (kpc)  (kpc)
------------------------------------------------------------------
1     J0002+6216    cwp+17     117.33 -0.07  -0.00  0.00   8.50
2     J0006+1834    cnt96      108.17 -42.98 -0.59  0.60   8.70
3     J0007+7303    aaa+09c    119.66 10.46  0.25   1.20   9.18

The description of the variables from the ATNF documentation are as follows:

GL:          Galactic longitude (degrees)
GB:          Galactic latitude (degrees)
[...]
ZZ:          Distance from the Galactic plane, based on Dist
XX:          X-Distance in X-Y-Z Galactic coordinate system (kpc)
YY:          Y-Distance in X-Y-Z Galactic coordinate system (kpc)

My understanding is that these variables should be related by the following equations:

tan(G_L) = YY/XX
tan(G_b) = XX/ZZ

However, when I test this assumption my calculated values are very different:

I have tried exploring the possibility that the x,y,z coordinate system may be oriented differently than I expect, but I can find no orientation that yields similar results for G_l or G_b:

Where could I have gone wrong? I feel like I am losing my mind not being able to convert these with simple trig.

The ATNF Pulsar Catalogue's galactic longitude and latitude are heliocentric,
but the origin of their rectangular coordinates is near the center of our galaxy.

The catalogue documentation,
section 6. Distances, says:

  The Galactocentric coordinate system (XX, YY, ZZ) is right-handed
  with the Sun at (0.0, 8.5 kpc, 0.0)
  and the ZZ axis directed toward the north Galactic pole.

From a heliocentric point of view
(U, V, W)
= (8.5 - YY, XX, ZZ).
Then $\tan{l} = V / U$ and $\tan{b} = W / \sqrt{U^2 + V^2}$
as you'd expect.


Semi-major axis, vs aphelion, vs mean orbital distance? The website Swinburne University of Technology (AU) gives the definition of semi-major axis as:

  ...half of the longest diameter of an ellipse.

This website give the definition of semi-major axis as:

  Half of the major axis is called the semi-major axis, and the semi-major axis is also the average sun-planet distance.

But the average sun-planet distance should be the average of the semi-major and semi-minor axes. I've also seen the mean orbital distance described as the semi-major axis in many other places, not just the one cited, so that seems to be a fairly consistent definition, too. But both seem to be inconsistent; how could it be both?

And it also seems to be that the semi-major axis ought to be the same as the aphelion distance, and the semi-minor axis ought to be the same perihelion.

Obviously, the confusion must be mine, but I'm not sure where I'm getting things wrong.

Edit: It occurred to me shortly after posting this and shutting down my computer for the day that (as I'm sure 90% of this SE community knows) the semi-major and semi-minor axes are measured to the center of the ellipse, whereas the aphelion and perihelion are measured to the Sun. I think I'm starting to understand how the semi-major axis can be both the mean orbital radius with respect to the sun and the largest distance from the center of the ellipse.

I think your confusion is just an incorrect (though not uncommon!) visualization of a planetary orbit. The parent star (usually) doesn't lie at the center of the ellipse, but at one of the foci; only for circular orbits are the foci at the same location as the center of the ellipse. Therefore, for non-circular orbits, the aphelion distance is greater than the semi-major axis, and the average of the semi-major and semi-minor axes is the average distance to the center of the ellipse - not the star.

Mathematically, note that the perihelion and aphelion distances are related to the semi-major axis $a$ and eccentricity $e$ by
$$R_p=a(1-e),\quad R_a=a(1+e)$$
As a quick check, adding these together and dividing by 2 yields $a$. In the case of a circular orbit, where $e=0$, we have $R_p=R_a=a$.


Hypothetical scenario, two nearby black holes I've always wondered what would happen if a hypothetical scenario, two black holes meet, with similar proportions:

Maybe one swallow the other one?

Or would make a bigger one between them.

This is actually a very nice example of why black holes are such extreme objects, they even break the basic rules arithmatic:

Black hole math: $$1 \text{ black hole} + 1 \text{ black hole} = 1 \text{ black hole}$$

(this is a little insider science joke)

A black hole is a region of space from which nothing, not even light, can escape. To achieve that it must have very strong gravity, so a lot of mass in a small region of space. So we may call it a "hole in spacetime", but it still has a mass.

In physical sense black holes can be described by only three quantities:

Its mass M (how much stuff was used to make it)
Its total angular momentum, J (how fast is it spinning)
Its electric charge, Q (does it have an electric/magnetic field)

All these three properties can change if the black hole is fed with 'stuff'. If you add matter the black hole mass increases. If that matter has (aligned) angular momentum, the black hole will spin faster and if the matter is charged, then the black hole charge changes accordingly.

When dealing with merging black holes, it is the mass property that is important. If I repeat the black-hole-math for its mass you get

$$ 1 \text{ black hole mass} + 1 \text{ black hole mass} = 2 \text{ black hole mass} $$

So a merger of two identical black holes just gives a single black hole with twice the mass.

Such black hole mergers are probably less hypothetical than you might think. They are considered to be likely method of creating supermassive black holes and are also considered as a potential source for gravitational wave emission.


What stabilizes rings or accretion disks? We think, more or less, that our Moon was formed from an accretion disk caused by a Mars-sized impactor. Cool.

Tidal forces can break apart a moon, causing rings.

Ashes to ashes, dust to dust: the moon came from an orbiting debris disk and may return to an orbiting debris disk someday.

What determines whether an accretion disk or ring system will form moons vs. remain as stable rings?

I believe the two biggest things that determine whether or not a ring system forms into a moon depends on are the parent planet's Roche Limit and whether or not there are other moons that can disrupt the ring.

The roche limit of a planet is how close a large body can orbit the planet without being torn apart by the planet's gravitational pull. The article I've referenced can show how this is calculated. Small moons like Jupiter's Metis can orbit within the roche limit as they are so small, the difference between the tidal forces acting on their near and far sides is not large enough to tug the moon apart.

The presence of other moons - or in the case of stellar disks, other planets - will play a large role. Like this article explains about our asteroid belt, the gravitational perturbations of Jupiter prevented a planet forming between it and Mars. Smaller bodies cannot easily gather together when a beast like Jupiter swings by to scatter them all!

This also means though that most asteroids within the belt are confined between Mars and Jupiter. Around Saturn's F ring, there are two small moons that slow down / speed up debris within the ring so that it remains gathered in a small space. This does keep rings and disks stable, but it also stops larger bodies forming.

Long story short; if the disk if far enough away from its parent, and nothing else large is orbiting nearby, you should get a moon / planet. If it's too close to the parent and being shepherded by another large body, it's more likely to remain a stable disk.


What constellations touch the 9-degree wide Zodiac? Say Barry, could you abuse the answer-your-own-question feature of
this site, and answer the following question:

As noted in How many constellations in the Zodiac? the
ecliptic itself touches 13 constellations, but the Encylopedia
Brittanica defines the Zodiac as "a belt around the heavens extending
9 [degrees] on either side of the ecliptic":

http://www.britannica.com/topic/zodiac

The Old Farmer's Almanac for 2014 (and previous years) notes (page
114) that Moon occasionally crosses into 5 "non-Zodiac" constellations
at times:

So, exactly which constellations are "in the Zodiac" if the Zodiac
extends 9 degrees on either side of the ecliptic?

And why 9 degrees? I know Venus can be as much as 8.25 degrees from
the ecliptic,

While I can't answer the 9 degrees part,
http://www.space.com/5417-ecliptic-zodiac-work.html notes, the band of
the zodiac actually passes through 22 constellations:

In fact, as pointed out by the well-known astronomical calculator,
Jean Meeus, along with Ophiuchus, there are nine other constellations
that occasionally can be visited by the Moon and planets: Auriga, the
Charioteer; Cetus, the Whale; Corvus, the Crow; Crater, the Cup;
Hydra, the Water Snake; Orion, the Hunter; Pegasus, the Flying Horse;
Scutum, the Shield; and Sextans, the Sextant.

So in truth, there really aren't twelve zodiacal constellations, but
twenty-two!


Relation between molecular cloud mass and galactic mass Would it be true to assume that the mass of a galaxy is approximately the mass of all molecular clouds detected within it, let's say, through CO observations and then converted to H$_2$?

The mass of an average galaxy appears to be totally dominated by dark matter, so your calculation would not give the galaxy mass.

Even if all you wanted was the baryonic (non dark matter) mass then what you suggest will be very much a lower limit. For example you can look at this paper by Chabrier (2001), who estimates that gas forms less than half the baryonic mass in the Milky Way. This fraction will be even lower in elliptical galaxies that are largely gas-free.

I am no expert, but I also think that even the gas component is dominated by ionised and atomic gas where you wouldn't expect to see CO emission and which are better traced by recombination lines or 21cm radiation respectively. In other words, the molecular gas is a fraction of the gas, which is a fraction of the baryonic mass, which is a small fraction of the total mass.

There is an extensive review of the "CO method" by Bolatto et al. (2013). The conclusion appears to be that the molecular gas mass can be estimated to around 30%, but that the conversion factor can depend on the star forming environment and on the metallicty of the gas in poorly understood ways.


What do the fusing 'onion layers' of a pre-supernova star look like to scale? I'm sure we've all seen the diagrams of various layers of element fusion from hydrogen to silicon in a star that's just about to go supernova.

(Picture from courses.lumenlearning.com)

I suspect these pictures grossly exaggerate the relative radii at which these fusing layers occur for the sake of readability. What would a more accurate to-scale picture of these fusing layers look like?

Now, I assume the answer will vary significantly based on the mass of the star, and I suspect in certain mass regimes some layers will not be fusing at all. I can think of a few other variables that may affect the answer too.

So in CYA fashion, I'll leave it up to the answerer to identify specific illustrative or interesting cases, as I'm not after a specific answer but rather a general feel for how large some of the layers are in comparison to the others.

Pre- supernova models often characterise the compactness of the core using a "compactness parameter" defined as
$$ \upsilon = \frac{(M/M_{\odot})}{R(M)/1000\ {\rm km}},$$
where $M$ is usually chosen to be $2.5M_{\odot}$ and $R(M)$ is the radius within which $M$ is contained.

Pre supernova models by Farmer et al. (2016) show that the central $2.5M_{\odot}$ of a massive star included the Carbon-burning core in a $15M_{\odot}$ (initial mass) star, but only contained the oxygen-burning core in a more massive star (models are presented up to 30$M_{\odot}$. i.e. Your answer is going to be mass and composition dependent (these models are for a solar metallicity initial composition).

In the $15M_{\odot}$ model (with mass-loss), $\upsilon \sim 0.08$ at core collapse, which means the carbon burning core would have been contained within 31,000 km. The $30M_{\odot}$ model is more compact with $\upsilon= 0.58$, indicating that the oxygen-burning core would have been contained within 4,300 km.

At collapse the iron core might have a mass of 1.4-1.8$M_{\odot}$, will be supported by electron degeneracy pressure and should have a size a bit smaller than a typical carbon white dwarf (radius of a few thousand km).

You can compare these sizes with the size of the entire red supergiant star, which might have a radius of a few au (e.g. Betelgeuse).

The shell-burning regions would be found out to slightly larger radii than this I think, but these numbers are a reasonable estimate. Looking in detail at the models I don't think that the final stages of pre- supernova evolution look anything like the strictly stratified onion-shell picture that is seen all over the internet.


Is the moon moving further away from Earth and closer to the Sun? Why? According to The NASA Moon Facts page:

  The moon is actually moving away from earth at a rate of 1.5 inches per year.

Why is the moon moving further away from the Earth? Is this a result of the moons formation that set it in motion to spiral away from us? Or is this a resultant force of the gravity from the Sun and other large bodies?

Yes, the moon is moving away from Earth at around 1.48" per year. According to the BBC:

The Moon is kept in orbit by the gravitational force that the Earth exerts on it, but the Moon also exerts a gravitational force on our planet and this causes the movement of the Earth's oceans to form a tidal bulge.
Due to the rotation of the Earth, this tidal bulge actually sits slightly ahead of the Moon. Some of the energy of the spinning Earth gets transferred to the tidal bulge via friction.
This drives the bulge forward, keeping it ahead of the Moon. The tidal bulge feeds a small amount of energy into the Moon, pushing it into a higher orbit like the faster, outside lanes of a test track.

So, tidal forces are ultimately what causes this to happen.
Also, there is a Wikipedia article on tidal forces:

Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon), and the primary planet that it orbits (e.g. the Earth). The acceleration causes a gradual recession of a satellite in a prograde orbit away from the primary, and a corresponding slowdown of the primary's rotation. The process eventually leads to tidal locking of first the smaller, and later the larger body. The Earth–Moon system is the best studied case.


Is it possible to see Callisto with the naked eye when it's at its greatest elongation from Jupiter? A quick search shows that Callisto has an apparent magntidue of 5.65, which would make it easily visible under relatively dark skies. Being the farthest Galilean moon, does it ever get far away from Jupiter for it to be discernable to the naked eye?

This has been an area of controversy for quite some time now, with no clear resolution (if you'll pardon the pun). There's been interest in supporting or refuting claims that observers were able to see the moons with the naked eye before Galileo. There are, of course, two major impediments (which you might well know about): brightness and angular separation from Jupiter.

The human eye has a diffraction-limited resolution of (roughly) one arcminute, whereas Callisto can reach separations from Jupiter of about 10 arcminutes - so, arguably, resolving it is not an issue, as it is with some other moons. However, we do have to deal with the problem that light from Jupiter could dominate any light we see from the moons (even if Ganymede and Callisto are too close to be separated and appear as one source). It's the same issue we get when observing faint sources near bright sources using a telescope, such as direct imaging of exoplanets.

If you do want to give this a shot, you might want to block out Jupiter's light with some foreground object, while making sure not to block out the moons. Choose a dark night when Callisto is at its greatest separation, and you might have a shot.

But not great odds, of course. I'd be surprised if you succeed. On the other hand, get yourself a good pair of binoculars and you won't have a problem.


Are magnetic field lines Spiral for Spiral Galaxies? If no, then how it look like topologically? I am an undergraduate doing summer project at USO. I am working on Sun's Magnetic field model. I got spiral graph for that, which looks like any spiral Galaxy. Do you think that there is some correlation between them. Or let me put this way, is magnetic field of Galaxy spiral?
Thank You in advance.

The short answer is: yes, magnetic fields in spiral galaxies are generally spiral in orientation. (But it probably isn't directly correlated with your solar model.)

For example, this is a map of radio polarization (a reflection of magnetic field direction) in the galaxy IC 342 by Beck et al. (2015):

(The short yellow lines are indicators of polarization, and thus magnetic field, direction. See here for details of the observation)

A very good, if somewhat technical, reference is Rainer Beck's recent (2015) review article "Magnetic Fields in Spiral Galaxies"; this discusses both observations of magnetic fields in nearby galaxies (and the Milky Way) and the models for how they might be generated.

He also discusses, for example, evidence for magnetica fields in the halos of galaxies; these are (seen in projection) sometimes radial and sometimes more X-shaped, as in the case of NGC 891:

(From Krause 2009; the short white lines indicate magnetic field line directions, based on radio polarization.)

The evidence for the Milky Way is somewhat ambiguous, for the usual reasons that it's hard to get a global picture of something you're inside of. One intriguing finding is that the magnetic field sometimes reverses direction as a function of radius; this hasn't been seen in other galaxies (though this may just be a function of resolution or the fact that we are measuring the Milky Way's magnetic fields primarily in a narrow layer of gas near the Galactic plane).


Constellation a celestial body is in Given its right ascension and declination, find out the constellation a celestial body is in.
Does anyone know of an algorithm (C#, js) for that?
It would read the constellation boundaries (e.g. constellations.bounds.json, at https://github.com/ofrohn/d3-celestial/tree/master/data) and figure the constellation out.
Thanks in advance!

If the coordinates are precessed to epoch B1875.0, the constellation boundaries lie neatly along the equatorial coordinate grid, allowing simpler tests against boundary segments.
Roman 1987 describes a basic algorithm and provides implementations in C and F77.
Glaschke 2010 makes a binary partition of the sky for fast lookup and provides an implementation in C.
Skyfield implements another fast lookup in Python, using lists sorted by right ascension and by declination.
It builds its data structure in build_constellations.py and uses it in constellationlib.py.


What is 'Dark Fluid'? Is this term official jargon/wording for 'Dark Matter'?
If so, why include the word "Fluid" if there is supposedly no viscosity in actual space. It would be like saying 'Hey, want to go swim in my 'gravel' pool?"
http://www.dailymail.co.uk/sciencetech/article-3013284/Is-dark-matter-FLUID-Mystery-particles-mapped-galaxy-clusters-results-suggest-not-particles-all.html

No, "dark fluid" is not a synonym for dark matter.
The Daily Mail article derives from a press release by the EPFL and an article in Science magazine, neither of which mention the word 'fluid'.
We don't know what dark matter is yet. There are several theories. One of them compares dark matter to a fluid:

Normally speaking, subatomic particles exchange momentum when they interact. Consequently, galactic collisions should also lead to interaction by dark matter particles and by studying it, we would have a better idea of what dark matter really is.
To verify whether dark matter is made up of particles, the researchers explored two possible outcomes. The first, was that particles of dark matter often interact, but don't exchange much momentum. The second was that they seldom interact, but exchange a lot of momentum.
If the first case was true, dark matter would slow down after the collision, since the greater frequency of the interactions would have drag-like effect. If the second case was proven to be true, then dark matter would likely be dispersed into space.
Surprisingly, the study discovered that the dark matter particles from two colliding galaxies, simply pass through each other, suggesting that dark matter particles do not interact with themselves, but have a more fluid-like character instead.

(emphasis mine). So they're not saying dark matter is exactly like a fluid, they're saying dark matter has some properties that are comparable to the behavior of fluids.


Is the passage of three asteroids near Earth today just coincidental? I just saw in the advertisement-laden tabloid Express that three near-Earth astroids will pass the Earth today:

  The first of the three, dubbed Asteroid 2018 TU4, will come as close as 0.03637 astronomical units (au) or 14.16 lunar distances. around 3.13pm BST (2.13pm2 UTC)
  The next asteroid to pass the Earth is Asteroid SL3 at around 3.36pm BST (2.36pm BST).
  Lastly, Asteroid 2018 TS1 will come closest to Earth at around 3.45pm BST (2.45pm UTC) today.

Question: Is this just coincidental, or is there some relationship between these three particular asteroids, perhaps in the past, that would make their near-coincident arrival more likely?

It is just a coincidence, and isn't that uncommon of an occurrence. You can see a list of all such occurrences on this page. Looking at the specific orbital parameters, the orbits are very different. They range from an eccentricity of .2-.5, periods of 349-725 days, and otherwise are just plain different. There are 7 listed in the next week of a similar closeness, so having 3 on a single day isn't particularly uncommon. Much further then a week doesn't really matter because these were only spotted recently, they are all 3 quite small objects. The oldest detection of the 3 was only September 30, and one was only spotted on October 10th.


Is there a formula for absolute magnitude that does not contain an apparent magnitude term? I have a star that I need to calculate the absolute magnitude of. I am given the temperature, luminosity, radius, mass, and distance in light-years. So I am wondering, what is the formula to compute this, using only these terms?

Yes. You derive the absolute bolometric magnitude by reference to the Sun. The Sun has a bolometric magnitude (i.e. integrated over all wavelengths) of about 4.75. Thus the difference in bolometric magnitudes is given by the log of the ratio of luminosities like so
$$ M_{\rm bol} = 4.75 -2.5 \log_{10} \left(\frac{L_*}{L_{\odot}}\right)\ ,$$
where $L_{\odot} = 3.8\times 10^{26}$ W is the luminosity of the Sun and $L_*$ is the luminosity of the star.
To get the absolute visual magnitude then you need to subtract a bolometric correction, which to first order, depends on the temperature of the star (it also depends to second order on the composition and gravity).
$$ M_V = M_{\rm bol} - BC_V\ .$$
A table of bolometric corrections vs temperature can be found in the 6th column of this authoritative table, which is in common use by astronomers/astrophysicists.


Account for radiation energy in the statement "total energy of universe is zero" I've read in Hawking's book The Theory of Everything that total energy of the Universe is zero. He explained this by saying that if there are two bodies separated by a distance and having some mass, they possess potential energy and the same amount of negative energy  with the gravitational field. Thus he concluded that total energy of the Universe  is zero. But here I've a question: how do we account for energy which is in the form of radiation?

The total energy of the universe consists of the mass energy of all the matter (both normal and dark), the mass-energy of the radiation and of the dark energy plus the gravitational potential energy of the universe (which is negative).  The hypotheses is that this sums to zero.  As far as I know, there is no experimental evidence for this.

But there is good evidence for the size of the various mass-energy terms.  The best current estimates are that the mass-energy of the universe is:

73% -- Dark energy
23% -- Dark matter
3.6% -- Interstellar gas
0.4% -- Stars (includes black holes)
v. small -- Relativistic neutrinos
v. small -- Radiation (CMB and stellar radiation combined)

This balance changes.  As the universe expands, the density of matter (dark and normal) varies as the inverse 3rd power of the size of the universe. (Matter stays the same and the volume expands as the cube of the radius.)

But the density of dark energy stays constant, since it is a property of empty space.

The density of radiation is proportional to the inverse 4th power of the radius, because not only does the increased volume dilute the radiation like it dilutes the matter, but also the radiation gets red-shifted, contributing an extra power of the radius.

(Incidentally, that means that the fraction of the total mass-energy of the universe in radiation decreases with time, and is estimated presently to be 1000:1 matter:radiation.)

So radiation seems simply to be too small to matter.