What were the nine planets in 1899? I'm currently reading Planetary Geology, in which they state

When Ceres [...] was discovered in 1899, it was considered as the lost tenth planet.

Uranus and Neptune had been discovered, but Pluto wasn't know yet at the time. What were the nine planets back then? The bodies we now call planets + the Moon?

Short Answer:
I can't make any sense out of what Planetary Geology says.
Long Answer:
I can't make any sense out of what Planetary Geology says.  But here is some data about the changing number of planets believed to exist in our solar system during the 19th century.
Here is a link to the Wikipedia article Planet, specifically to the section "Objects Formerly Considered to be Planets".
https://en.wikipedia.org/wiki/Planet#Objects_formerly_considered_planets 1
It has a long list of 27 objects considered to be planets at one time but later reclassified as the sun, or natural satellites (moons), or asteroids. By 1854 all of those objects - including Ceres - had been reclassified as not being planets. So after 1854 or so the number of accepted planets was 8 until 1930, 9 from 1930 to 2006, and 8 from 2006 to the present.
I note that if someone numbered the objects still considered to be planets in order of their discovery, the list of planets would included 6 planets including Earth up to 1781 when Uranus was discovered, and then 8 planets when Ceres was discovered in 1801.  Then 9 planets when 2 Pallas was discovered in 1802, 10 planets when 3 Juno was discovered in 1804, and 11 planets when 4 Vesta was discovered in 1807.  When Neptune was discovered in 1846 it could be classed as the 8th planet by those who discounted the asteroids or as the 12th planet by those who counted Ceres, Pallas, Juno, & Vesta.
If the planets are numbered in order of increasing size, Ceres would have been number 1 when it was discovered in 1801, become 2 in 1802, and eventually become number 9 when 9 Metis was discovered in 1848, assuming that astronomers of that era could tell that Ceres was larger than other asteroids.  Ceres would become number 10 when 10 Hygiea was discovered in 1849, 11 when 11 Parthenope was discovered in 1850, and eventually number 15 when 15 Eunomia was discovered in 1851.
If the planets are numbered in order of decreasing size, Ceres would have become number 8 when it was discovered in 1801 and would have remained so until Neptune was discovered in 1846, making Ceres number 9 until being reclassified as an asteroid in the 1850s.  Unless one of the other largest asteroids was ever believed to be larger than Ceres.
If planets were numbered inwards from the outermost known one, the list in 1801 would have been 1 Uranus, 2 Saturn, 3  Jupiter, 4 Ceres.  in 1802 2 Pallas would become 4 and Ceres 5.
In 1846 Neptune would be discovered and Ceres would become # 6.  In 1849 10 Hygiea was discovered and Ceres would become # 7.  In 1852 16 Psyche was discovered making Ceres # 8. In 1852 22 Kalliope was discovered making Ceres # 9. In 1853 24 Themis was discovered making Ceres # 10.   In 1854 28 Bellona was discovered making Ceres number 11. And in 1854 31 Euphrosyne was discovered, making Ceres number 12.
But I should note that none of the asteroids after 15 Eunomia, discovered in 1851, were ever considered to be planets.
If planets were numbered outwards from the sun, as is normal, Mercury would be 1, Venus 2, Earth 3, Mars 4, and 1 Ceres would become 5 in 1801.  Ceres would become 6 in 1804 when 3 Juno was discovered, 7 in 1807 when 4 Vesta was discovered, 8 in 1845 when 5 Astrea was discovered, 9 in 1847 when 6 Hebe was discovered, 10 in 1847 when 7 Iris was discovered, 11 in 1847 when 8 Flora was discovered, 12 in when 9 Metis was discovered, 13 in 1850 when 11 Parthenope was discovered, 14 in 1850 when 12 Victoria was discovered, 15 in 1850 when 13 Egeria was discovered, 16 in 1851 when 14 Irene was discovered, and 17 in 1851 when 15 Eunomia was discovered.
So if planets and "planets" were numbered in order of increasing size, Ceres would be ninth between the discovery of 9 Metis on 25 April 1848 and the discovery of 10 Hygiea on 12 April 1849, and the tenth until the discovery of 11 Parthenope on 11 May 1850.
So if planets and "planets" were numbered in order of decreasing size, Ceres would be ninth between the discovery of Neptune on 24 September 1846 and being reclassified as an asteroid in the 1850s,and would never have been considered the tenth planet in size.  If Ceres was still considered to be a planet, it would have been considered the tenth largest planet after Pluto was discovered in 1830, but Ceres was no longer considered a planet by then.
So if planets are numbered inwards from the outermost known planet, Ceres would have been considered the ninth planet between the discovery of 22 Kallipe on November 16, 1852 and the discovery of 24 Themis on April 5 1853, and the tenth planet between April 5, 1853 and the discovery of 28 Bellona on March 1, 1854.
Except that as far as I know no asteroids after 15 Eunomia discovered in 1851 were ever listed as planets.
So if planets are numbered outwards from the innermost known planet, Ceres would have been considered the ninth planet between July 1, 1847 when 6 Hebe was discovered and August 13 1847 when 7 Iris was discovered, and the tenth planet between August 13 1847 and October 18 1847 when 8 flora was discovered.
After Urban Le Verrier used discrepancies in the orbit of Uranus to predict the existance of a planet beyond Uranus, and Neptune was discovered in 1846, Le Verrier studied the orbits of other planets.  In 1859 Le Verrier deduced that there should be a planet orbiting inside the orbit of Mercury, which he named Vulcan.
Observations of objects believed to be Vulcan were often made but never confirmed.  In 1915 Einstein's general theory of relativity provided an alternate theory of gravity which explains the motions of mercury without the planet Vulcan.
When Vulcan was was believed in it was probably considered to be larger than Ceres, which would have made Ceres the tenth largest planet, except that Ceres was no longer considered a planet.
All things considered, I believe that the only possibly ninth planet that some astronomers might have believed to exist in 1899 was Vulcan.  So if Ceres was discovered in 1899 it might have been considered the tenth planet to be discovered.  Except that Ceres was discovered in 1801, 98 years before 1899.
And by 1899 some astronomers had already attempted to calculate the orbit of a planet believed to be beyond Neptune, a planet X, "X" for unknown, a search which eventually led to the more or less accidental discovery of Pluto.
But as far as I know nobody announced any discovery of a new planet in 1899 which turned out to be false but would have been the tenth planet to be discovered if both it and either Vulcan or Planet X was real.
So I have no idea what Planetary Geology meant by stating:

When Ceres [...] was discovered in 1899, it was considered as the lost tenth planet.


Can an astronomical telescope view objects on Earth? I am new to telescopes and I'm planning to buy an astronomical telescope like the "Celestron AstroMaster 114 EQ Reflector". Just curious to know whether it can be used to view objects on Earth (e.g. traffic and people miles away from tall buildings). Telescopes are used to observe stars; they must have higher power than binoculars. Right?

Yes, but many (not all) telescopes made for astronomy will invert the image. Presenting the image upright is important for terrestrial instruments, but it doesn't matter for astronomy. Also, it usually requires fewer optical components to make an instrument that inverts the image.

Also, terrestrial instruments are made to operate in an environment where there's plenty of ambient light (daylight), whereas many telescope designs (such as truss dobsonians) are built to operate in a dark environment and are usually hampered by excess ambient light.

So, in a nutshell, yes, you could turn a telescope towards objects here on Earth, and it would work, but for best results and easiest operation just get some good binoculars.

Finally, "power" is a much misunderstood characteristic of optical instruments. It is technically true that a large dobsonian could in theory outperform any pair of binoculars you could care to try, but in practice a large optical stack is difficult to swing around and is fickle with regard to collimation, thermal equilibrium, etc. If you're willing and able to put up with the operating difficulties, with the necessity to flip the image around, etc, then I guess that indeed a large dobsonian could surpass anyone's little binoculars in a terrestrial context.

But very large magnification always reduces the field of view. Go ahead and crank magnification all the way up, and it's like looking through a straw. It's hard to locate anything. Astronomers have specific methods to deal with this difficulty, but for a terrestrial observation the narrow field of view is a liability, not an advantage.

There's a reason why various optical instruments have evolved into different shapes and designs to operate in different environments. "Horses for courses", as they say.


How much are Neptune's and Uranus' orbits perturbed by Pluto and other KBOs? Reading another question, I came across the argument that inconsistencies in Neptune's and Uranus' orbits lead to the discovery of Pluto.  This brief write-up mentions Percival Lowell and William H. Pickering by name as two people who looked for the theoretical 9th planet.

My question is, were inconsistencies in Neptune's and Uranus' orbits detectable by early 20th century methods or were these scientists just chasing calculation or estimation errors with dreams of finding the next planet.  My (guess) is that Pluto is much too small, and too far away and just one of many similar mass kuiperbelt objects, so it's unlikely that it was really discovered by measured inconsistency in Uranus/Neptune orbits method, (despite the fact that there are articles that say that's precisely how Pluto was discovered).

In a nutshell, that's the question.  Was the wobble that Pluto's causes on Neptune's orbit observable by 1910-1930 observation methods.  And related, was the wobble that the entire kuiperbelt (some 20 to 50 times the mass of little pluto, but much more spread out), was that wobble detectible by 1910-1930 methods.

Hard math isn't necessary to me for an answer, as I find the math hard to follow sometimes, so feel free to answer with or without mathematical calculations.

Since (1) the mass of the Pluto/Charon system is very small compared with Neptune, and (2) their orbits are in 2:3 resonance, so the perturbation of Neptune's orbit would have been undetectable. University of Rochester has a good explanation of this.

  The Accidental Discovery of Pluto

  Later supposed perturbations of the orbits of Uranus and Neptune suggested
  the presence of yet another planet beyond the orbit of Neptune.
  Eventually, in 1930, a new planet Pluto was discovered, but we now
  know that the calculations in this case were also in error because of
  an incorrect assumption about the mass of the new planet. It is now
  believed that the supposed deviations in the orbits of Neptune and
  Uranus were errors in measurement because the actual properties of
  Pluto would not have accounted for the supposed perturbations. Thus,
  the discovery of Pluto was a kind of accident


Finding a location geographically of a celestial object, in this case the moon at one of its quarters Years ago it was mentioned to me the New Yorker magazine had a Young Moon “contest”; who could find the youngest moon; the thinnest crescent after a new moon. I knew enough to know that I would have to know exactly when the new moon occurred and more importantly where. The Thin Crescent wouldn’t be too hard as it would follow closely the sun. Still, not knowing where the new moon happened meant that I could see anything from nothing to a one day old moon. I knew the moon traversed about 13 degrees of arc a day in so doing about 7% Of its disc was illuminated so my chance of seeing a very thin crescent depended on the new moon happening to the east of me by some 6 to 12 hours, as the “record” was something in the realm of 9hours.

So the question arose in me “Where on the globe would an observer see any of the quarterly phases exactly over their meridian?” This question led to almanacs that used hours, minutes, seconds and hundredths of seconds of measurements, all starting from the celestial spheres Greenwich or zero longitude, the Vernal Equinox, that semi-fixed(a 26,000 year cycle) starting place for celestial longitude. My question is, how can I find and use that “exact” beginning zero “longitude?

I am being hobbled here by being forced to use the very nomenclature I don’t understand. I mean I understand it, it’s simple enough, I just don’t know where to start. How do I find right ascension 18h23m52.34s on the celestial sphere? Is there a bright star at the vernal equinox that is used to fix that spot in the sky?

I begin to think I’m communicating with a machine that can’t extrapolate...no matter, as long as I get an education. Ok then here’s a question: how can I find right ascention(ra)18h 23m 52s standing out in the desert some night? I don’t need declination as the object is large and I’ll know it when I see it.

How do I find right ascension 18h23m52.34s on the celestial sphere?

You use a star chart that shows the lines of right ascension and declination. Based on the stars that the line passes by, you can estimate the line in the real sky. It is similar to looking at a map of the Earth and using latitude and longitude to locate a city. (By the way, 0 hours right ascension, 0 degrees declination is the location of the vernal equinox on the celestial sphere. The bright star at that location is the Sun at the moment of the vernal equinox ;-)

Perhaps your question should be "How do I locate the young crescent Moon?". The answer to that question is that it would be better to calculate the azimuth of the Sun at sunset, and the altitude and azimuth of the Moon at 10 minute intervals afterwards. Based on knowing where the Sun was located on the horizon at sunset and the difference between the Moon and Sun, you can estimate where the Moon should be in the sky. There is no need to know where right ascension and declination are located among the stars (other than calculating the position of the Sun and Moon); the sky will be bright, so it is unlikely that there will be any stars visible that will help you locate the line of right ascension.


Layout of the universe I've been working on a space game in my spare time, and lately I've been thinking on how to lay out the universe. Though I've searched around and found it hard to get a good view of what the universe looks like. I did find a lot of good sources, though I'm a very visual learner and found it hard to get a good picture of the universe with what I found. I also don't know what the good, reliable, accurate and up-to-date sources were.

So, are there any good visual sources to get a picture of the universe? Preferably a TV-series or a very well illustrated book, or perhaps even computer program.

Edit: I'm looking for a more general view of the universe. Like what do galaxies look like, and what is their scale. As I understand they contain a combination of planets, solar systems, star clusters, ... Though I couldn't get a good picture of how dense they are. Is there a lot of space (relatively) between these solar systems and star-clusters. I found that our solar system is about 4 light-hours big, though are the neighbouring ones average light years or thousands of light-years away? And in the space between them, is it mostly empty or is there space dust?
The same question for whatever our galaxy circles around (if it does) and what is between different galaxies. (And perhaps what else is there of galaxy-size out there?)

I got a vague view of all of this from reading texts, though I feel like I'm missing a whole lot.

Edit 2: I'm not looking for properties of different planets, that's on a too small scale. In the game I'm planning on making a fictional universe (perhaps randomly generated, though not yet decided), but I want the broad layout to be realistic.

Edit 3: I just found this: http://htwins.net/scale2/ This helped me A LOT in getting a sense of the relative size of things.

Thanks a lot!

Here is an overview of different scales we may look at the universe. On scales beyond it's almost homogeneous, and we get at the border of the visible universe. Many detailed images are available, e.g. from the Hubble Space Telescope.

If you need a three-dimensional description of the universe, your program will probably need to read portions of star, cloud, star cluster or galaxy catalogs, similar to a planetarium software.

The general structure of the universe, and its contents may be summarized the following way:

The observable universe has a diameter in the order of 10s of billions of lightyears; it depends on which of the several notions of distance is chosen. For distances below a few hundred million lightyears the notions get similar.
The universe is about 13.8 billion years old, started as a hot and dense state (Big Bang), expands, and is almost 3-dimensional Euclidean plus one time dimension on large scales; that kind of space plus time is called a Minkowski space-time. Its average temperature is now near 2.7 K; we can detect a background of this temperature as cosmic microwave background (CMB); the CMB is thought to be the redshifted afterglow of its state as hot plasma at 380,000 years after the Big Bang.
The universe mainly consists (according to current models) of dark energy (about 70%); that's invisible; dark energy is thought to be equally distributed, although this is going to be investigated in more detail.
Most (about 63%) of the matter is cold (slow) and "dark", but not equally distributed. Dark matter is thought to form large halos around galaxies and galaxy clusters. It's invisible and interacts via gravity with ordinary matter. It can be inferred from gravitational lensing and the velocity distribution of stars within galaxies.
Much of the remaining matter consists of hot (fast) neutrinos; they are very hard to detect, but they can be detected, and they can be inferred from nuclear decay measurements.
Part of the energy of the universe consists of photons (e.g. radiowaves, light, x-rays, gamma rays, magnetic and electric fields).
A minor part (about 5%) of the universe consists of atoms and ions (simplified called baryonic matter); that's the kind of matter we know from our immediate experience.
About half of the baryonic matter in the universe is thought to be the intergalactic medium made of a rarified plasma, consisting of hydrogen atoms, protons, electrons, helium ions. It's thought to form huge filaments around voids of roughly 100 million light years diameter.
The filaments connect and embed galaxy superclusters. Our local galaxy group is part of the Virgo supercluster.
Galaxy superclusters are made of galaxy clusters (diameter up to about 30 million lightyears), like the Virgo cluster, and galaxy groups (diameter up to about 10 million lightyears), like the Local Group. Sometimes an intermediate grouping (between supercluster and cluster) like a galaxy cloud is defined.
Galaxy clusters contain up to about 1000 galaxies, galaxy groups less than 50. Galaxies may have sizes about 100,000 lightyears across, and consist (besides a halo of dark matter) mainly of interstellar gas and dust. After galaxy collisions this gas may be consumed by star formation or removed from the galaxy. A galaxy typically contains billions of stars. Interstellar gas of different temperature is distinguished.
Galaxies can contain stars across the Hertzsprung-Russel diagram, neutron stars, black holes, sometimes supernovae, and rougue planets, probably also smaller rocks ejected from planetary systems. Stars can be grouped to binary, ternary or larger systems of stars up to open and globular star clusters. Globular clusters are usually old, located in the halo of a galaxy, and contain up to about a million, mostly old stars, may be with a black hole (IMBH) in their center. Open clusters are mostly young and in the galactic disk. A couple of different galaxy types are distinguished, e.g. elliptical and spiral galaxies. Dense molecular clouds may be the location where stars form and start as open clusters.
The distance between stars is usually a few lightyears; in globular clusters it's well below a lightyear. In the galactic center (bulge) stars are also closer to each other. The diameter of a star can vary from about 10 kilometers (neutron stars) to several astronomical units (red supergiants), the mass from about 13 Jupiter masses for brown dwarfs (or by a stricter definition from 0.075 solar masses for red dwarfs) to  several 100 solar masses.
A galaxy center is mostly populated by a supermassive black hole (SMBH), with about 0.1% the mass of the galaxy, the mass of the SMBH can vary from galaxy to galaxy.
Galaxies can collide and temporarily form irregular galaxies.
Planetary systems around stars seem to be common; they are thought to form from protoplanetary disks shorty after the central star has formed. The outermost part of planetary systems may reach out half a lightyear, to the limits of the Hill sphere of the central star; it depends on the distance and mass of neighbouring stars. Planets can form outside the Roche limit of a star; small asteroids can survive closer to the central star for some time. A planetary system can contain planets, dwarf planets, moons, asteroids, trojans, comets, dust, magnetic fields, stellar wind.

That's certainly still incomplete, and most of the notions can be subdivided to much more detail.


Cosmology calculator where curvature density $\Omega_k$ can be independently set? I am looking for a cosmology calculator that does not have the default that
$$\Omega_k = 1 - (\Omega_r + \Omega_m + \Omega_{\Lambda}).$$
I particularly want to run
$$\Omega_r = \Omega_m = \Omega_{\Lambda} = 0, \ \text{and} \ \Omega_k = -1.$$
Can this be done?

The density parameter of cosmology, $\Omega$, is defined as the ratio of the energy density of all forms of matter vs. the critical density.
The forms of matter may include nonrelativistic matter (dust, $\Omega_m$, itself perhaps a sum of baryonic matter, $\Omega_b$ and dark matter, $\Omega_{\rm DM}$) with equation of state, that is, the ratio of its pressure to its energy density, $w=p/\rho\sim 0$; dark energy, aka., the cosmological constant, $\Omega_\Lambda$, with $w=-1$; radiation, $\Omega_\gamma$ (or maybe $\Omega_r$) with equation of state $w=1/3$; or indeed, anything else. So rather than spelling out all possibilities, let me just denote the sum of it all as $\sum\Omega$.
As I mentioned, every one of these $\Omega$-s is a ratio of the corresponding energy density to the critical density: $\Omega_x=\rho_x/\rho_{\rm crit}$, where $\rho_{\rm crit}=3H^2/8\pi G$ with $H=\dot{a}/a$.
The "critical density" is the density at which the universe is spatially flat, i.e., has no spatial curvature, $k=0$. In other words, when $\sum\Omega=1$ exactly, we have a spatially flat universe.
If $\sum\Omega\ne 1$, the universe has (positive or negative) curvature. This is expressed using $\Omega_k$, which can be thought of as being defined by
$$\Omega_k=1-\sum\Omega.$$
To offer a little more detail:
This $\Omega_k$ behaves formally as the density parameter of a perfect fluid with negative pressure, $w=-1/3$. To see this, it is instructive to look at the Friedmann equations:
$$\begin{align}\left(\frac{\dot{a}}{a}\right)^2+\frac{k}{a^2}&=\frac{8\pi G\rho}{3}+\frac{\Lambda}{3},\\ \frac{\ddot{a}}{a}&=-\frac{4\pi G}{3}\left(\rho+3p\right)+\frac{\Lambda}{3},\end{align}$$
where $a$ is the scale parameter, $\rho$ represents the energy density of everything that is not the cosmological constant or spatial curvature and $p$ is the corresponding pressure. However, we can also move the $k/a^2$ term to the right-hand side of the first Friedmann equation, and then re-express both the $k$ term and $\Lambda$ in the form of effective densities and pressures, namely $\rho_\Lambda=\Lambda/8\pi G$, $p_\Lambda=-\rho_\Lambda$, $\rho_k=3k/8\pi Ga^2$, $p_k=-\rho_k/3$, and get
$$\begin{align}\left(\frac{\dot{a}}{a}\right)^2&=\frac{8\pi G(\rho+\rho_\Lambda+\rho_k)}{3},\\ \frac{\ddot{a}}{a}&=-\frac{4\pi G}{3}\left[(\rho+\rho_\Lambda+\rho_k)+3(p+p_\Lambda+p_k)\right].\end{align}$$
This form makes it explicit that the sum of all $\rho$-s is indeed the critical density and thus unavoidably, by definition, $\Omega_k=1-\sum\Omega$.


Why aren't neutron stars full of dark matter? Dark matter interacts with the gravitational force right? Well, unlike black holes, neutron stars are actually visible, and they're an enormous gravitational sink, so dark matter should collect to them.

But if all that is true, which it seems to be, why haven't astronomers detected or used neutron stars to detect dark matter?

Yes, neutron stars might actually accumulate weakly interacting dark matter and this allows some observational constraints on its nature. Basically, the temperature and continued existence of neutron stars places bounds on the density and interaction cross-section of dark matter.

A dark matter particle that does not interact with matter will just have its trajectory bent by the gravity field of a heavy object, so most unbound particles will just swoop past on a hyperbolic trajectory. But as discussed in (Adams & Laughlin 1997), if there is some matter-dark matter interaction then the particle may scatter from a matter particle and now have less than escape velocity. This way white dwarfs and neutron stars would indeed accumulate dark matter in their cores. The rate of accumulation is proportional to $\rho v \sigma$ where $\rho$ is the dark matter density, $v$ the average relative velocity and $\sigma$ the cross section. Adams & Laughlin estimate that a white dwarf star would accumulate its own mass in $10^{25}$ years, but this is going to be depend on the cross section (if it is too small the dark matter will pass through) which is at present unknown.

Were this accumulation the only thing happening it would eventually make white dwarfs and later neutron stars implode. However, dark matter is plausibly a mix of particles and antiparticles that annihilate each other at a rate $\sim \rho^2$; in an enriched environment like a white dwarf core this would produce energy from emitted photons heating things up. Adams & Laughlin estimate the luminosity as to about $10^{-12}L_\odot$, which is imperceptible in the current era but would eventually keep white dwarfs at 63 K in the far future (until the dark matter halo runs out).

Other, more elaborate, calculations lead to accretion estimates that are higher. If the rate were high enough, then we would not see any cool dense objects - so white dwarf and neutron star cooling gives some bounds on the possible density and cross sections, albeit not very strict ones. For example, one model suggests that neutron stars would level out at 10,000 K. Cool star observations can also already rule out some dark matter models.

There are even some arguments that super-earth planets in dense dark matter halos might be heated significantly, although this may require unrealistically dense halos and big cross sections. The current heath flow of Earth does give some constraints on how strongly it can interact.

So neutron stars are not directly giving us dark matter detection, but they (and planets and white dwarfs) are giving us some information.


What telescopes have observed anomalies in the light curve of Tabby's star, KIC 8462852? KIC 8462852, the F-star that inexplicably dims by up to 20% for short periods, is still getting alot of attention. A slow continuous dimming by about 0.3% a year has been identified recently. But all anomalies I know of come from the Kepler space telescope. It is an F3-star at 1500 ly distance. Shouldn't it be easy to observe its light curve with even relatively modestly sized ground based telescopes? Have such observations been done and have they confirmed any anomalies? You see, I suspect something weird went wrong with the Kepler telescope here.

EDIT: There have been studies of its brightness on archived historic photographs. But I'm more interested in observations simultaneous as Kepler or since then, to confirm either a gradual dimming or short deep dips.

I do not know whether complimentary observations of the light curve are being done, but I will try to answer the rest of the question.

Is it easy to observe the light curve with ground-based telescopes? No, it's quite difficult. From the Kepler homepage:

  Since transits only last a fraction of a day, Kepler must monitor all target stars continuously. Their brightnesses must be measured at least once every few hours.

It goes on to explain how the observed field was chosen - no downtime due to it being too close to the sun, no obstruction by asteroids, etc.

A ground-based telescope has the obvious problem that it can't observe during the day, so you need several telescopes in different parts of the world, and combine their measurements. Since the distortion patterns, viewing conditions, instrument characteristics etc. are all different, combining the data is anything but trivial if you want a precision measurement.

In short, a change in the point spread function between telescopes might introduce both systematic and statistical errors in your brightness measurement. Kepler is only one instrument and optically highly stable.

Is KIC 8462852 bright enough for a small ground-based telescope? Certainly. Its magnitude is 11.7, while Kepler wants to observe stars brighter than 14th magnitude (link above). This magnitude calculator estimates a limiting magnitude of 17 for a 1m mirror.

It takes time to set up an observation. Large telescopes like the VLT accept requests for observation time twice a year. After your observing proposal is accepted, it will still take weeks or months until your observation is actually made. For smaller telescopes, it might be easier and quicker, but it will take time to set up a monitoring programme, even if telescope time is available.

However, there are ground-based, long-term monitoring programmes. COSMOGRAIL is one that comes to mind. From their homepage:

  Obtaining regular observing time on telescopes in good sites was (and is still) not easy

and they've been going for a number of years by now.

So, it would be technically challenging but possible. Politically, it might not be so easy: Every observatory wants to make the best use of the observing time they have, and most are oversubscribed (more time asked for than available). You need a fairly solid science case to block several telescopes around the world for several years, but the result you'd get if all goes well is merely confirmation of someone else's result.


Do planets have effect on velocity of Earth? There is method for finding extrasolar planets called Transit-timing variation. If I understood correctly, exoplanets accelerate or decelerate each other (according on their position), so we can observe irregularities in transit times of some exoplanet.
Now, for our solar system, can we observe similar effect here? Why time of Earth's orbit around Sun is always 365.256 days, even though other planets are always in different places? Shouldn't Earth year be always differently long?

The Milankovitch Cycles which explain the glacial and interglacial phases of the Ice Age include changes in the Earth's orbital eccentricity (which implies a change in the variation of the velocity even if the orbital period remains roughly constant), the primary contribution to which is the gravitational influence of Jupiter and Saturn.
Since our Solar System is much more widely-spaced than the typical Kepler systems, and the planets aren't in resonant orbital configurations, the variations take place over much longer timescales and have relatively small amplitudes.
Planet-planet interactions are also observed for other planets. As an example, Park et al. (2017) list various contributions to the perihelion precession of Mercury, the bulk of which is due to perturbations from the other planets (principally Venus, Jupiter, the Earth and Saturn). The famous contribution from general relativistic effects amounts to about 43″/century out of a total 575″/century.


Does gravitational lensing provide time evolution information? When we see multiple images of the same object because of the phenomenon of gravitational lensing, do all the images show the lensed object at the same point in time?

Does it take the same amount of time for light from the lensed object to reach us no matter what image we look at or are we watching the lensed object at different points in time and if so, how big can the difference in time typically be?

Time delays between the light received from multiple lensed images is a well known and commonly studied phenomenon. A typical example can be found in Koopmans et al. (2003) where they study a quadruple lens system formed by a forefround object at z=0.6 and a background source at z=1.4. The time delays measured are 31-77 days and this seems to be typical for the objects studied so far.

The delay depends on the difference in path length taken by the multiple images. This in turn depends on the distance to the source and the distance between the source and the lensing object and on the mass distribution around the lensing object. It also depends on the expansion rate of the universe, which gives a route to estimating the Hubble parameter.

A rule of thumb appears to be that the delay is of order $r_s/c$, where $r_s = 2GM/c^2$, where $M$ is the mass of the lens interior to the path of the light ray.
$$ \tau \sim 10^{-5} \left(\frac{M}{M_{\odot}}\right)\ {\rm sec}$$
So for a $10^{12}M_{\odot}$ foreground lensing galaxy (a big spiral like the Milky Way), the delay is about 100 days.


How to calculate true equinox position? I'm trying to calculate the state of the Earth at a given time using Keplerian orbital elements from this page. It has the following instruction:

  Compute the coordinates, $\mathbf r_{ecl}$, in the J2000 ecliptic plane, with the x-axis aligned toward the equinox:

So after this calculation we are supposed to know direction of some equinox. But there exists the phenomenon of precession of equinoxes, so this direction shouldn't in general be fixed. I assume the equinox mentioned in that document is some "mean" equinox for the range of dates the data are valid for.

So, how do I calculate the true equinox position/direction, given these data?

Caption of Table 1 in the OP's reference contains:

  Keplerian elements and their rates, with respect to the mean ecliptic and equinox of J2000

So, "the equinox" mentioned in step 5 cited in the OP refers to the mean equinox of J2000. Now the main problem is what the mean equinox actually is.

According to Oxford Reference, mean equinox is

  The direction to the equinox at a particular epoch, with the effect of nutation subtracted. The mean equinox therefore moves smoothly across the sky due to precession alone, without short-term oscillations due to nutation.

This means that the term equinox, as used in astronomy, doesn't only mean the discrete events of vernal and autumnal equinoxes, but also the direction which the perpendicular$^\dagger$ to the Earth's axis points to at any moment of time. Thus we can conclude that the equinox of J2000 is the direction this perpendicular points to at the epoch J2000, not at 20 March 2000 or any other.

So to get the true orientation of the Earth at the event of equinox we should use a precession+nutation model to advance the orientation at the Epoch to the date required.

$^\dagger$ the one lying in the ecliptic plane, of course


What is the current routine of modern astronomy? With about all visible stars catalogued, measured and photographed it seems that chapter is closed. I realize currently while amateur astronomy is big on cataloguing all asteroids in the Solar System, the "Big Boys" are now primarily busy with discovery of extrasolar planets. But that's certainly not all. Sure there's a lot of unique research, new, unexpected discoveries, assorted "odd" research like SETI, and so on, but I'd like to know what is the "daily bread" of every astronomer nowadays?

What are the current typical, routine tasks of an average professional astronomer? What is being observed/measured/searched for? What challenges occupy most effort and time? Or am I wrong assuming there even is such a thing, and every observatory is a unique snowflake?

What you say is not quite true: the search for exoplanets is clearly intensive, but it is far from the only things astronomers are looking at. Most of the time, in two words, the situation is: resolution & wavelength. Whatever the field (if you are interested in galaxies, interstellar medium, stars and so on) you want more resolution, to resolve smaller scales (most stars are still points even with our best telescopes, or we are still far from resolving individual stars in galaxies!), to have more informations, to understand better the underlying physics. You want more wavelength, because spectroscopy gives you much more phsyical information than a single wavelength observation, for example. And to combine both is sometimes challenging: to have high resolution observations in infrared is not that easy, and it can be crucial for some fields (if you ever want to see a star forming, you better observe it in infrared, since this baby is embedded in its gas cloud that shields very efficiently its radiation).

That being said, the routine tasks of an astronomer would be

extract information from the current data. It involves a lot of coding, with Python, IDL, or more specific astronomy-oriented languages as IRAF or MIDAS. Data reduction is an important part of the job, because it is in general challenging to extract data from the raw signal you will get.
write papers about these data and the inferred informations
read a lot of papers to stay tune with the latest discoveries of other teams
write proposals to ask for more observation time/better observations/bigger telescopes
drink a lot of coffee

The three first points probably takes an almost equal amount of time for any astronomer; point 4 takes even more time for older astronomers; point 5 is also crucial for all the good things that come out of discussions over a good ol' bowl of coffeine.

Complements:

To answer to your comment and to give you an overview of the current research, I can think of:

Hershel data in infrared. People try to understand better the interstellar medium and the star formation processes in our galaxy, the formation of early galaxies, and the chemical composition and evolution of the Universe with these data.
Planck data in longer wavelength. These data are useful to understand the first age of the Universe (searching for anistropy in the CMB), but also to have an other view of the galaxy and the interstellar medium in these wavelengths.
Very Large Telescope data. There are plenty of different kind of data out of these telescope, mostly in the visible and infrared ranges, and mostly in spectroscopy. Almost everything is studied with these data, from galaxies evolution to stars in the nearby galaxies.
ALMA data in millimeter/submillimeter ranges. The same kind of objects are studied with ALMA and Herschel: early galaxies, interstellar medium and molecular clouds. How galaxies form and evolve? How stars form? In which environment? What are the dominent processes in star formation?
HESS data, in the gamma ray range. Gamma rays offer a window on the non-thermal Universe, i.e. all the extreme events occuring in the Universe. It can give precious informations about gamma-ray bursts, supernovæ, AGN (the active galactic nuclei) etc.

That's for the big projects (with a strong European bias, sorry folks I know better what's done on this side of the ocean). You can add to that all the missions to study exoplanets (like Kepler), missions to study our solar system planets (Cassini, Huygens, Messenger, Juno, all the Mars missions etc.), plus all the other facilities around the world to study anything and everything, from stellar dynamic to planet's composition. The main problem is always to understand how such structure (from the large scale structures in the Universe to small scale structures in the galaxy), object (from galaxies to satellites), phenomenon occurs, forms, appears. To understand what are the dominant physical processes at play.

Astronomy is still craving for data; the more data you have, the better your statistic will be, and hopefully the better your understanding will also be.


How close to a brown dwarf would a planet need to be to receive as much light as Earth? How close to a brown dwarf would an orbiting planet need to be in order to receive as much sunlight as Earth receives from the Sun?

Brown dwarfs are born moderately hot and luminous and then they contract and cool. Thanks to electron degeneracy in their cores, they never become hot enough to ignite hydrogen (though there is a brief deuterium burning phase) and as a result their fate is to cool and fade.

The plot below (from Burrows et al. 1997) shows how the luminosity behaves as a function of time since birth (age) for objects of various mass. The brown dwarfs are the green and red tracks (some would call the red tracks giant planets). The curves are labelled in Jupiter masses. The highest mass brown dwarf is 73 Jupiter masses, the next one down is 70$M_J$ and then the green curves count down in steps of 5$M_J$ to 15$M_J$, then the first red curve is at 13$M_J$ and the red curves count down in steps of 1$M_J$.

The axes are logarithmic (to base 10). Thus when the y-axis says -2, it means the brown dwarf is one hundredth the luminosity of the Sun, -3 = one thousandth etc. The x-axis is logarithmic in units of billions of years. Most brown dwarfs observed in the Galaxy will be in the range 1-10 billion years (i.e. between 0 and 1 on this x-axis).

The flux received by a planet in orbit around a star/brown dwarf will be proportional to the its luminosity divided by orbital radius squared. From this we can write that the orbital radius where a similar flux to that of the Earth around the Sun will be received is
$$ R = \left( \frac{L_{BD}}{L_{\odot}} \right)^{1/2}\ {\rm au} $$
$$ \log\left(\frac{R}{1\ {\rm au}}\right) = 0.5 \log \left(\frac{L}{L_{\odot}}\right)$$

This you can get you answer immediately from the graph below. Choose the mass of your brown dwarf and its age. Find the log luminosity on the y-axis and halve this value. That is the the log of the orbital radius in astronomical units where a planet would receive the same amount of flux as the Earth from the Sun.

e.g. Consider a 50$M_J$ brown dwarf that is a billion years old. Find the appropriate green curve and see that the y-axis value for x=0 (1 billion years) is -4.2. The log of the orbital radius (in au) at which a planet would receive the same amount of flux from the brown dwarf as does the Earth from the Sun would be -2.1. In linear units, this is $10^{-2.1} = 0.0079$ au, or 1.19 million km.

A further issue to consider is that the brown dwarf surface will be far cooler than the Sun and also changes (cools) with time. This means that the radiation received from the planet will push further and further into the infrared as the brown dwarfs gets older and hardly any of the received radiation will be in the visible part of the spectrum.


Is there a way to know the time according the moon appearance? Is it possible know the time according to the moon location? To look at the sky at night and then determine what the time is.

It is not easy.

Knowing the time means (roughly) knowing the position of the sun. If you are in the Northern Hemisphere, then the sun is (roughly) South at midday, East at 6am, West at 6pm and so on.

The moon orbits the Earth, so the angle between the sun and the moon is always changing. It may be possible so reason as "The moon is at first quarter, so the angle between the sun and moon is 90 degrees. I can use the position of the moon to determine the position of the sun (below the horizon) and so estimate the time."  There are problems with this, for example when the moon is nearly full, it will move through quite a large angle relative to the sun, with only a very small change in the amount of illumination.

With careful measurements and an almanack, it would be possible to find the local solar time. This wouldn't account for daylight saving time, or civil time that differs from solar time. There are much easier methods: get a sundial during the day and an hourglass for the nighttime. Or a watch.


Probability of finding life-supporting exoplanets We've found over a thousand exoplanets by now, but how many of them could support life? What percentage of newly found planets are potentially life-harbouring? Or haven't we found any exoplanets that meet these criteria yet?

The question can be rephrased into: How many exoplanets have been found that could harbour life? As of early May 2015 the number appears to be about 30, see the Habitable Exoplanet Catalog on the Planetary Habitability Laboratory's web site.

You should also note that exoplanet detection methods will bias this sample in favour of Super-Earths.


Do stars tend to fuse all hydrogen even when the mass is small? Suppose a brown dwarf requires only one more hydrogen atom to become massive enough to start fusion, what will happen if we add a hydrogen atom to it?

It fuses until the mass is dropped and then fusion stops suddenly
It starts to fuse until all hydrogen use up

Which one is correct?

The difference between a brown dwarf and a star is not a sharp boundary. A brown dwarf is simply a ball of gas where the (small) fusion rate is incapable of providing a significant fraction of the luminosity (which is mainly provided by gravitational contraction).

A star will contract and reach a minimum luminosity, whilst a brown dwarf's luminosity will monotonically decrease throughout its life. The core becomes degenerate and it is this that provides the pressure that supports a brown dwarf, even though it becomes colder.

If you add some mass to a brown dwarf, then the result depends when you add it. If you add it early during the strong contraction phase then you might get a low-mass star. If it is added after the brown dwarf is degenerate, then it could contract further, but do so without increasing the temperature enough to ignite hydrogen strongly. This is an interesting problem that deserves a model simulation!

If fusion can start to any degree, then convective mixing in these very low mass objects will very gradually (trillions of years), turn nearly all their H to He.


How many astronomers are there in the world today? How many now living individuals have a PhD in astrophysics, or by some other definition can be reasonably classified as astronomers? I think Richard Feynman once said that only one in a million is an astronomer, I would think there are many more today.

"The worldwide community of professional astronomers is only about 10,000; most are located in the us (with about 1,000 in the UK and 250 in Australia)." From So You Want to Be an Astronomer by Duncan Forbes.

Another source stated that the number of professional astronomers is about the size of a small town.


What is the fastest a galaxy or other body has been measured to (or can) travel? Our solar system travels at an average speed of 515,000 mph and our galaxy at 1.3 million mph through space. What is the fastest moving body in space recorded and the fastest can a black hole or galaxy travel through the universe?

Hubble velocities

The Universe expands and carries galaxies away from each other with a relative velocity proportional to the distance between them. This is Hubble's law, and if the Universe is infinitely large, there is no limit to how fast two galaxies may recede from each other. In our observable Universe, the most distant galaxy observed (GN-z11; Oesch et al. 2016) recedes from the Milky Way at more than twice the speed of light ($c\simeq300\,000\,\mathrm{km}\,\mathrm{s}^{-1}$).

Peculiar velocities

However, this is not a motion through space, which seems to be what you are asking about. Nothing is able to travel through space faster than the speed of light.

Galaxies generally move through space with velocities of the order of a few $100\,\mathrm{km}\,\mathrm{s}^{-1}$; in massive clusters, they may acquire velocities of a few $1000\,\mathrm{km}\,\mathrm{s}^{-1}$ (e.g. Karachentsev et al. 2006). These so-called peculiar velocities are wrt. to the "global" frame, i.e. the frame in which an observer that follows the cosmic expansion lies still. This is also the frame in which the cosmic microwave background is (statistically) the same in all directions.$^\dagger$

Black holes, stars, planets, and gas cloud move around in the reference frame of their galaxies with characteristic velocities of the order of $100\,\mathrm{km}\,\mathrm{s}^{-1}$, so this will typically be smaller than that of their host galaxy, if the galaxy lies in a large cluster.

When massive celestial bodies such as neutron stars or black holes merge, they reach velocities of the order of half the speed of light, as discussed further in Rob Jeffries' answer. This is as measured in the frame of the center of mass.

Velocities of particles

EDIT: The following was written before the question was changed to emphasize celestial bodies:
Much higher velocities are found for small particles such as cosmic rays; these are massive particles accelerated to extreme energies, e.g. by supernova explosions. The record holder of such particles is still (I think) the so-called Oh-My-God particle which traveled at $0.9999999999999999999999951c$ (in Earth's frame), much faster than the velocities reached in the Large Hadron Collider.

$^\dagger$Of course you can always define a frame that moves with almost the speed of light, such that all object acquire that speed "artificially", but then the Universe isn't isotropic anymore.


Limits of space telescope? Watching this video describing the "next generation" space telescope, it seems like the biggest mirror will be ~6 meters in diameter.
Theoretically, if a telescope was built in space instead of shipping it pre-built, and the mirror was, not a few meters, but a few kilometers, (and whatever other important aspects of a space telescope that a novice like myself has no idea about, multiply them by a few orders of magnitude) would it provide benefits proportional to the size difference?

Yes, absolutely! The performance of any telescope depends on its diameter. A larger instrument not only collects more light, but also provides better resolution than a smaller instrument. The resolution limit is calculated from:
$R_{arcsec}\ = {1.22\ \lambda \over D_{mm}}$
whereas limiting magnitude is calculated from
$L_{mag}\ =\ 2.5\ +\ 5\ log\ D_{mm}$
I suppose there are eventual limits to $R_{arcsec}$, but I have never heard of any. As for limiting magnitude, as it’s a logarithmic formula, it grows very slowly as $D_{mm}$ increases, but a larger telescope is still a gain.
The whole thing is to balance $R_{arcsec}$, $L_{mag}$, and $$$, of course!


What comet's tail did Earth pass through before Halley's? This answer to Any record of the Earth passing through the tail (not trail) of a comet? mentions

Earth passed through the tail of Halley's Comet in 1910. It caused a bit of a panic due to claims that cyanogen detected in the tail would cause harm: https://en.wikipedia.org/wiki/Halley%27s_Comet#1910

and links to the February 8, 1910 New York Times item Comet's poisonous tail; Yerkes Observatory Finds Cyanogen in Spectrum of Halley's Comet which includes the following sentence:

Only once, as far as known, has the earth passed directly through the tail of a comet, and at that time no unusual phenomena were noticed except that there were abundant showers of meteors.

Question: What comet's tail did Earth pass through before Halley's? This should be a recorded historic event, but it wouldn't necessarily have to have been recognized as such at the time. The goal here is to figure out most likely what event is being described in the quoted sentence.

 (click for larger)

The quotation is probably referring to The Great Comet of 1861.
According to this Wikipedia article: https://en.wikipedia.org/wiki/C/1861_J1

The comet may have interacted with the Earth in an almost
unprecedented way. For two days, when the comet was at its closest,
the Earth was actually within the comet's tail, and streams of
cometary material converging towards the distant nucleus could be
seen.

This was reported in newspapers at that time:
https://www.newspapers.com/image/424095911/?terms=comet%20tail&match=1
and also prior to the close approach of Borelli's Comet in 1903.
https://www.newspapers.com/image/85101704/?terms=%22%20borelli%20comet%22&match=1

From  this archive of C/1861 J1 (Great Comet of 1861) from http://cometography.com/lcomets/1861j1.html

Further reading:

Great Comets in History by Donald K. Yeomans (April 2007) JPL/Caltech
Comet C/1861 J1 (Great comet) in JPL Horizons database
Periodic Comets Found in Historical Records
Do Comets C/1861 G1 (THATCHER) And C/1861 J1 (Great Comet)
Have a Common Origin?
International Comet Quarterly
Forward-Scattering Enhancement of Comet Brightness. I. Background and Model (large PDF, Int Comet Quart April 2007)
Forward-Scattering Enhancement of Comet Brightness. II. The Light Curve of C/2006 P1 (McNaught)  (large PDF, Int Comet Quart October 2007) also here
Forward-Scattering Enhancement of Comet Brightness. III. Prospects for C/2010 (Elenin) as viewed from the Earth and SOHO, STEREO-A, and STEREO-B spacecraft (large PDF, Int Comet Quart August 2011?) also here


If any object could become a black hole, could any object become a neutron star? A black hole doesn't necessarily need to form from a star; theoretically, it could form from any extremely dense object. In fact, many astronomers differentiate certain black holes, like supermassive ones, from stellar ones (ones that form from stars).

However, could the same apply for neutron stars? Neutron stars only form because of the intense gravity during a star's collapse: electron capture is forced to happen, and the majority of the star becomes neutrons. Could this potentially happen to non-stellar objects, if the gravity forces electron capture?

If so, why don't we see as many of these "neutron objects" as we do non-stellar black holes?

There can be no such thing as a "supermassive neutron star". The theoretical upper mass limit for a neutron star is somewhere between 2.2 and 3 solar masses. Any more massive and they inevitably form black holes. So I am not clear what kind of "neutron objects" you were thinking of?
Nor is it clear what you mean by "non-stellar" objects that will have the densities required to make neutron-degenerate matter? There aren't any apart from (I) the cores of massive stars at the ends of their lives. (II) Massive white dwarfs if they accrete matter over and above their Chandrasekhar limit. Furthermore, there is a minimum mass for a neutron star. Although the observed lower limit to those seen in nature is (so far) around $1.15 M_{\odot}$, there is a theoretical lower limit of about $0.1$ to $0.2M_{\odot}$ set by the stability of the neutron against decay in self-gravitating material ( See https://physics.stackexchange.com/questions/143166/what-is-the-theoretical-lower-mass-limit-for-a-gravitationally-stable-neutron-st/143174#143174 ).
It is true if you could arrange to compress any matter to densities above $\sim 10^{15}$ kg/m$^3$ it would form neutron-degenerate material. But this requires (as far as we know) the conditions I listed above.


Annual path polar chart for a star I've often come across sun path charts like this (Wikimedia Commons) that show the position of the sun at any point of the year, at any time of day, for a specific location (or a set of locations), on an azimuth-elevation polar plot:

I'd like to get the exact same chart (or data, to create my own chart) for any given star, such as Aldebaran or Sirius, for a given point on Earth.

I'm looking into Stellarium scripting, as well as the HYG stellar database (I am not familiar with the mathematics of right ascension and declination, or how to convert this to azimuth-elevation like in the example). Is this a very unusual data product to ask for?

I wrote some JavaScript to help answer my question. It's in terrible shape right now, but it plots the hourly position of Aldebaran in azimuth & elevation when viewed from Dayton, Ohio, USA, every fortnight for a year:

http://fasiha.github.io/starpath/

The source code is at https://github.com/fasiha/starpath but everything in it is hardcoded. However, when I have a bit of time, I can make it into a nice little webapp where you can input your position and select a celestial object (or inputs its RA/dec) and see the same plot—possibly along with information about when the sun obscures it.


What would happen if a planet is removed from the solar system? More exactly what would to happen to us/Earth in general if any of the gas giants is removed by magic from the solar system ?

How long would it take after such change before we notice it ?

How major and would life resist to it ?

EDIT

For instance if Saturn or Jupiter is removed, what would happen ?

This question isn't really very clear or practical. You need to add quite a bit of information, eg which planet?

If Sedna vanished, it would be detectable by instruments, but we would not notice.
Jupiter or Mars might make a bigger difference. We could spot it straight away by the naked eye.

Of course Earth life would be fine at first (unless it was Earth that was removed ...) but the orbits of asteroids and other bodies may be perturbed, which could lead to an influx of asteroid strikes - potentially - in the longer term.


How does this strategy for chasing the sunset work? In Randall Munroe's What If? blog he tackles this question:

  What is the longest possible sunset you can experience while driving, assuming we are obeying the speed limit and driving on paved roads?

His final answer is the following, which allows you to experience about a 95 minute sunset. But the diagram isn't the most self-evident. What does the diagram mean, and how does the strategy work?

  If you're in northern Norway on a day when the Sun just barely sets and then rises again, the terminator (day-night line) moves across the land in this pattern:

  To get a long sunset, the strategy is simple: Wait for the date when the terminator will just barely reach your position. Sit in your car until the terminator reaches you, drive north to stay a little ahead of it for as long as you can (depending on the local road layout), then u-turn and drive back south fast enough that you can get past it to the safety of darkness.

I would go to the Arctic circle, where you can experience an almost perpetual sunset, without having to drive around.

Edited to answer the question: My interpretation of the diagram, is:

The terminator at a certain time near sunset, is the one shown towards the east (darkness approaches), running NE/SW.
As time progresses, it moves into the top horizontal location, running E/W; this consistent with the more northerly latitudes having continual daytime, coinciding with a certain parallel polar circle.
As morning approaches, the terminator moves towards the west (bringing daylight with it), and runs NW/SE.

I think the arrows would be better if the tip of the one on the right, joined the base of the one on the left, showing your car journey as a continuous one.


Fortran Fits writer/reader I recently inherited some Fortran 77 code that calls the IMFORT interface to write data out to an imh and pix files. I could not get this to compile on a modern compiler and it is not supported. So I decided to set off on writing a Fits writer in Fortran. I was able to make one but is ugly and does not properly handle the end card. I tried googling for a Fortran Fits writer but came up empty. Is there a library for astronomical Frotran codes that contains Fits writer exist out there.

The code may be better suited for stack overflow, but this is specialized to astronomy since no other science seems to use fits, so I figured I would be better off starting here.

It looks like CFITSIO has an interface for F77.

I'm always thinking about programmer time vs. computation time in research settings. If your data is reasonably small and simple in structure, I'd be very tempted to have Fortran write to a text file, and then use something like astropy to turn the text file into a FITS file. It's slow and icky, but it takes fifteen minutes of thinking if you've used astropy before.


How can the equation of state for cosmic strings and domain walls be derived? In this article which nicely explains why it is really the quantity $\rho + 3p$ which is relevant to determine if the expansion of the universe is accelerating or decelerating by making use of the for this question relevant second Friedmann equation

$$
\frac{\ddot{a}}{a} = -\frac{4\pi G}{3}(\rho + 3p)
$$

it is mentioned that for cosmic strings

$$
p = -\frac{\rho}{3}
$$

which has the effect that they dont contribute to the "non-inertial" expansion of the universe, and for cosmic domain walls we have

$$
p = -\frac{2 \rho}{3}
$$

which leads to an accelerated expansion of the universe.

Whereas I understand the derivations of such equations of state for radiation, "ordinary" matter, and a constant source of dark energy, I have not yet seen analog calculations for cosmic strings and domain walls.

So how can the equation of states for topological defects such as cosmic strings and cosmic domain walls be derived?

My topological defect cosmology is a little rusty, but I'm pretty sure this is how it goes.
Start with the fluid equation,
$$
\dot{\rho} + 3 {\dot{a} \over a} \left( \rho + p \right) = 0,
$$
and the equation of state,
$$
p = w \rho.
$$
Plug the equation of state into the fluid equation, assume a constant $w$, and you'll find
$$
\rho \propto a^{-3(1 + w)}.
$$
Now we'll find $\rho(a)$ for strings and sheets, and read $w$ off of them.
For cosmic strings, $\rho$ is
$$
\rho_{\rm string} = \sum^N_i {\lambda L_i \over V},
$$
where $N$ is the number of strings in our cosmic horizon, $\lambda$ is the linear density of the strings, and $L_i$ is the length of each string.

Here's the key: we've got to assume the length of any cosmic string scales with the expansion of the universe, since they're topological defects. Given that assumption, we can get the dependence of $\rho_{\rm string}$ on $a$:
$$
\rho_{\rm string}(a) \propto {a \over a^3} = a^{-2}.
$$
Thus,
$$
2 = 3(1 + w_{\rm string}),
$$
and $w_{\rm string} = -{1 \over 3}$.

Similarly, for domain walls, $\rho$ is
$$
\rho_{\rm wall} = \sum^N_i {\sigma A_i \over V},
$$
and since $A_i \propto a^2$, we get $w_{\rm wall} = -{2 \over 3}$.

Hope that helps!


MeerKAT's Epic Image of the Galactic Centre, what are we seeing? In this answer as well as this one, I've linked to New Jersey Institute of Technology's Dr. Dale Gary's nicely-written Physics 728 Radio Astronomy; Lecture #1 notes where I can see the image below. It links to Gizmodo.au's New South African Telescope Releases Epic Image Of The Galactic Centre.

I have heard of the Meerkat array earlier (Which 16 antenna locations are used for the MeerKAT radio image recently announced?), but I am wondering how to read further about this spectacular image. What is the scale for example? How would it look pasted into the arc of the Milky Way; just a tiny patch of a few arc-minutes, or several tens of degrees?

How will this compare to the radio image of Sag A* that we will see in the next day or two?

Also, if anyone knows, what are those spiky arcs sticking up, and those puff-ball things on the left?

Source: Gizmodo "The black hole at the centre of the Milky Way and filaments." Credit: SARAO, click for full size.

LaRosa et al 2000 present a 90 cm VLA image and catalog of sources near the galactic center.
Here is their schematic diagram with the 2°x1°, 18-33 cm band MeerKAT image region highlighted.

The compact source Sgr A* is a small dot within the bright, pear-shaped blob Sgr A right of center.
Recent millimeter VLBI images (Issaoun et al 2019) indicate a width on the order of 200 μas, or 1/7000 of a pixel in the image you uploaded.

The bright pair of blobs left of center, Sgr B1 and Sgr B2, are massive molecular clouds.

Most of the bubble shapes are either supernova remnants (SNRs) or H II regions ionized by UV-bright young stars.
The far left pair Sgr D has one of each.

The various non-thermal filaments (NTFs) align with the local magnetic field and emit synchrotron radiation but are not well understood otherwise.
The bundle of filaments near the center of the image are known as the galactic center radio arc (GCRA) or just the Arc.


Are hot stars like O-type stars entirely composed of helium? Hot stars like O-type stars show no hydrogen in their spectra. Does this mean they are made entirely of helium?

Any explanation would be really helpful.

The lines that appear in a stars spectrum mainly reflects its temperature not its composition, see here

O-type stars start out with the same sort of composition as other stars, that is they are mainly H and He (approximately 75% and 25% by mass) with traces heavier elements.


How do comets and other solar system bodies gain energy to exit the solar system? I recently learnt that some comets like C/1980 E1 (Bowell) interacted with objects like gas giants in the solar system and gained enough energy to exit the solar system. But from Physics, I know that only if the total mechanical energy of a body is positive, can the body exit the solar system. An interaction with a gas giant should merely convert some of the potential energy of the body to kinetic energy and the total energy of the body should remain unchanged. If so, how can such bodies achieve positive mechanical energy to exit the solar system?

The mechanism by which the path, speed and energy of a celestial object or an artificial spacecraft is altered by massive planets and bodies is Swing-by or gravity assist. Any encounter between a comet and a gas-giant like Jupiter is almost an elastic mechanical collision (though no physical contact occurs) and in any mechanical collision, energy exchange between the bodies undergoing collision takes place. In this case, when the comet C/1980 E1 passed closed to Jupiter, Jupiter passed on some of its mechanical energy to the comet, rendering its total mechanical energy positive and hence setting the comet free and no longer bounded to the solar system. It is the total mechanical energy of the Jupiter+C/1980 E1 that was conserved, not just that of the comet. But the small decrease in the mechanical energy of Jupiter would not have a significant impact on the massive planet.


How could a neutron star cause repeated 'fast radio bursts' detected coming from outside of the galaxy? According to the ScienceAlert article Mysterious repeating radio signals have been detected coming from outside our galaxy, based on the Letter to Nature "A repeating fast radio burst", there has been a series of signals detected that the article reports that scientists have not seen before.  From the article:

  Astronomers have detected repeating blasts of radio signals coming from deep space. These short-lived signals are known as 'fast radio bursts' (FRBs), and although we've heard them before, they were always thought to be one-off events coming from random locations. But for the first time ever, researchers have now heard repeating signals, all emanating from a single unknown source outside our galaxy.

Emphasis mine

In the Letter to Nature, it is hypothesised that the source could be that

  these repeat bursts with high dispersion measure and variable spectra specifically seen from the direction of FRB 121102 support an origin in a young, highly magnetized, extragalactic neutron star

This leads me to the question:

How could a neutron star cause repeated 'fast radio bursts' detected coming from outside of the galaxy?

The progenitors of FRBs have been tied to soft gamma-ray repeaters (SGRs), and are likely young magnetars displaying irregular atmospheric and magnetic activity. The earliest connection between the two - as far as I know - was made by Lyutikov (2002), who compared the outbursts to solar flares (the magnetar bursts are sometimes referred to as "giant pulses"), based on models by Thompson et al. (2002).

The theory is that currents dissipate into the neutron star's magnetosphere, at rates coupled to the star's crust. Slow deformation can allow dissipation to proceed at a constant rate, while "fractures" in the crust can lead to quick outbursts. The release of magnetic energy through reconnection may then be responsible for the radio outbursts. The evolution of the field is similar to the behavior of the Sun's magnetic field in the corona, leading to the analogy to solar flares.

Popov & Postner (2007) state that Lyutikov's model's predictions agree with several observed bursts. While the arXiv version of the Letter concerning FRB 121102  does not specifically delve into the model, it seems to support it, although there are doubts as to the feasibility of repeated giant flares.


What is space temperature around Earth? What is the equilibrium temperature that a black body will reach at the Earth's distance from Sun?

Assume you have a spherical blackbody.

The solar flux at the radius of the Earth is given to a good approximation by $L/4\pi d^2$, where $d = 1$ au. This is $f=1367.5$ W/m$^2$ (though note the distance between the Earth and the Sun has an average of 1 au).

If it is a blackbody sphere it absorbs all radiation incident upon it. Assuming this is just the radiation from the Sun (starlight being negligible), then an easy bit of integration in spherical polar coordinates tells us that the body absorbs $\pi r^2 f$ W, where $r$ is its radius.

If it is then able to reach thermal equilibrium and it entire surface is at the same temperature, then it will re-radiate all this absorbed power. Hence
$$\pi r^2 f = 4 \pi r^2 \sigma T^4,$$
where $T$ is the "blackbody equilibrium temperature". Hence
$$ T = \left( \frac{f}{4\sigma}\right)^{1/4} = 278.6\ K$$


Doppler Spectroscopy - Finding mass of an exoplanet An astronomer, T observed the spectrum of a distant star X. The spectral lines were observed to have tiny blueshifts and redshifts regularly with a period of 1.27 years. T concluded that the star is wobbling slightly due to a planet orbiting it. Let the estimated mass of the planet when

(a) eccentricity of the orbit e = 0 be k*10^23 kg
(b) and for e = 0.6 be x*10^22 kg.
Assume that there is only one major planet and the axis of rotation of the system is perpendicular to the line of sight.

Mass of Star = 23.86163 x 10^30 kg
Time Period = 463.55 days
Shift in wavelength = 1.7627 x 10^-5 nm

You have to find out 'k' and 'x'

I studied about the Doppler Spectroscopy method.
I know that the relation
$$
K = \left(\dfrac{2\pi G}{P_{orb}}\right) ^{1/3}\dfrac{M_p}{(M_{*}+M_p)^{2/3}}\dfrac{1}{\sqrt{1-e^2}}
$$
holds where K = radial velocity half amplitude.
How can I use the doppler shift given into this?
Thanks.

To use the Doppler shift, you need to know by how much the light is blue/red-shifted.

Suppose you have a light curve where the wavelength varies between $\lambda_1$ and $\lambda_2$. Using these wavelengths, the Doppler shift will give you an interval of radial velocities. This gives you a value for K that you can plug into your last equation to derive $M_p$.


How were the designations of "North" and "South" applied to the hemispheres of Mars? How was it decided which hemisphere was North and which hemisphere was South on Mars? Clearly, the designations "North" and "South" apply only to the hemispheres which contain the axis of rotation at their center, but what determined whether a hemisphere received "North" or "South" as its designation?

The research in other answers helped me come across the actual International Astronomical Union (IAU) standard:

  The north pole is that pole of rotation that lies on the north side of the invariable plane of the solar system.

The north of the invariable plane is the side that Earth's North pole points to. In fact, one of our other users has observed:

  The North Pole of any system being the pole on the same side as earth's north is indeed the correct definition. This applies to the Milky Way galaxy as well, in which case the North Galactic Pole is the pole towards the hemisphere of the galactic sphere which also contains the celestial north pole.

Dwarf planets, minor planets, their satellites, and comets do follow the right-hand rule mentioned in other answers (see Axial tilt on Wikipedia).

Sources:

Report of the IAU/IAG Working Group on cartographic
coordinates and rotational elements: 2006 - P. Kenneth Seidelmann, B. A. Archinal,
M. F. A’hearn, et al.
Poles of astronomical bodies - Wikipedia


Why does Newtonian physics give the right radius for a black hole? When computing the distance at which the escape velocity is equal to the speed of light, the result is equal to the Schwarzschild radius. Is this just a coincidence, or is there a physical reason why the Newtonian approximation give the correct result?

If this is not a coincidence, then why is it OK to use Newtonian physics here?

As explained in this answer, dimensional analysis indicates that this radius depends on $GM$ and on a velocity squared. However, the fact that the two quantities are exactly equal, rather than there being a constant factor between the two is a pure coincidence.


Mass estimate for cluster NGC2516? The Wikipedia entry on NGC2516 mentions a mass value in the range $[10^5 - 10^6]\; M_{\odot}$. This seems like a rather enormous value for an open cluster.
In Jilinski et al. (2009) the authors state that:

The total mass of NGC 2516 is presently not well known. Values as low as 170 solar masses have been proposed by Pandey et al. (1987) and as high as about 1000 $M_{\odot}$ by Dachs & Kabus (1989). More recently a mass of ∼250 $M_{\odot}$ for this cluster has been quoted by Piskunov et al. (2008)

Anybody has a better/more recent estimate?

NGC 2516 is somewhat richer and more massive than the Pleiades. A careful look at the mass function suggests there is about $1000 M_{\odot}$ in stars $\geq 0.3 M_{\odot}$, within the central 0.9 square degrees (with about a 15% uncertainty), but there is probably a few hundred solar masses beyond this (Jeffries et al. 2001). This agrees with the figures of Dachs & Kabus (1989), who essentially extrapolated from the numbers of high-mass stars using a typical cluster mass function.
New Gaia data will probably provide a more complete census in the halo of the cluster. There will also be some additional mass in lower mass stars and brown dwarfs, but this is unlikely to add more than 10% to the figure.
The lower masses quoted in your question are way too low. In an incomplete spectroscopic survey of the central square degree, a recent paper by
Jackson et al. (2020) found about 500 low-mass members ($0.4-1.2M_\odot$), that alone would add up to about $400 M_\odot$, before considering the many high-mass stars.


How did they decide the length of one year even though it wasn't known that earth revolves around the sun? It takes one year for the earth to go around the sun, but one year was already this long when they didn't even know that the earth revolves around the sun at all. So how did they figure it out?

Originally a year would be noticed as the time between two winters (or two harvests, two annual floods etc), although the exact number of days might not be known with any accuracy.

As people start to observe the sun more carefully, it would be noticed that the position of sunrise and sunset move regularly. Stonehenge and other ancient monuments seem aligned to midwinter sunset or midsummer sunrise. Since this would allow one to predict the seasons, it would have been very useful.

More careful observations led to the geocentric model, in which the sun takes just over 365 days to move around the Earth once relative to the background stars. The length of the year was known to be about 365.25 days since the times of the ancient Egyptians.


Can I measure the moon's gravity? Since I learned about Newton's gravity law, I wonder if I can measure the moon's gravity using (almost) no special equipment. The best I could come up with is a pendulum, which is in a resting position. The moon (at the horizon) will pull on the weight at the bottom of the pendulum and cause it to shift. 6 hours later, with the moon above or below the pendulum, the weight should be back. Maybe we could detect the shift, just like we see the tides.

Running the math for a 5 meter long pendulum and 1 kg mass, I get an amplitude of 0,017 mm. I fear that external forces (wind, unstable surface, ...) will be bigger than this effect.

So my question is: is it possible (again, without specific equipment) to measure or detect the moon's gravitational force? What would be the best way to measure/detect it?

Running the math for a 5 meter long pendulum and 1 kg mass, I get an amplitude of 0,017 mm.

You are off by quite a bit. There is essentially no horizontal deflection when the Moon is at the horizon. The maximum horizontal deflection occurs when the Moon is about 45 degrees above or below the horizon.

The tidal acceleration at some point on the surface of the Earth due to some external body (e.g., the Moon) is the difference between the gravitational acceleration toward that external body at the point in question and the gravitational acceleration of the Earth as a whole toward that body:

$$\vec a_{rel} = GM_\text{body} \left(\frac {\vec R - \vec r} {||\vec R - \vec r||^3} - \frac {\vec R} {||\vec R||^3} \right)$$
where

$M_{body}$ is the mass of the external body,
$\vec R$ is the displacement vector from the center of the Earth to the center of the external body, and
$\vec r$ is the displacement vector from the center of the Earth to the point in question on the surface of the Earth.

The resultant force looks like this:

Note that the tidal force is away from the center of the Earth when the Moon is directly overhead or directly underfoot, toward the center of the Earth when the Moon is on the horizon, and horizontal when the Moon is halfway between directly overhead/underfoot and on the horizon.

The tidal force is maximum when the Moon is directly overhead, and even then it's only about 10-7 g. You need a sensitive instrument to read that. A simple pendulum or a simple spring will not do the trick.


Sun's apparent magnitude at 2.5 AU? Imagine an astronaut standing on an asteroid 2.5 A.U. distant from the Sun. He is gazing, naked-eye, towards the Sun.

What is the apparent magnitude of the Sun at that distance, and is that bright enough to blot out any of the inner planets? No light blockers and solely viewing with the Eyeball Mark I?

What is the apparent magnitude of the Sun at that distance?

Fortunately, there's a formula known as the Distance Modulus which is defined to calculate precisely this information. The equation is given by

$$m-M=5\log_{10}(d_{pc}) - 5$$

where $m$ is the apparent magnitude of your star, $M$ is the absolute magnitude, and $d$ is the distance from the star, in units of $\mathrm{parsecs}$. The absolute magnitude of the Sun is easily looked up and found to be $M_\odot = 4.83$. The distance, you provide as $2.5\:\mathrm{AU} = 1.2120342\times10^{-5}\:\mathrm{pc}$. Now its simple to solve for $m$.

$$m = 5\log_{10}(1.2120342\times10^{-5}) - 5 + 4.83$$

$$m = -24.75$$

As far as apparent magnitudes go, this is still pretty bright. You can see a table of typical apparent magnitudes for comparison right here. Interestingly, this table lists $-25$ as the "minimum brightness that causes the typical eye slight pain to look at". At $m=-24.75$ (remember higher value = less bright) you'd be just above this threshold and so the Sun would be safe to look at without causing eye strain or pain.

  Is that bright enough to blot out any of the inner planets?

In order to determine the the brightness of the inner planets, we have to do some more math. Unfortunately, people don't really calculate the absolute magnitudes of planets so the form of the distance modulus listed above isn't entirely useful. Instead, we'll use a different form.

$$m_1 - m_2 = -5\log_{10}\left(\frac{d_2}{d_1}\right)$$

This equation relates an object with an apparent magnitude of $m_1$ at a distance $d_1$ to its apparent magnitude $m_2$ at a distance $d_2$. If we look up the apparent magnitude of the various inner systems from Earth, and figure out their distance from Earth at those times, we can figure out the apparent magnitude at the distance of your asteroid.

I'll work this out for Venus since Venus will likely be one of the brightest of the inner planets (given its high albedo). Venus as viewed from Earth, at its brightest, has an apparent magnitude of $m_1 = −4.89$. This occurs when it is an the point of greatest elongation. As determined from this solar system orrery, the distance is approximately $d_1 = 0.75\:\mathrm{AU} = 0.36\times10^{-5}\:\mathrm{pc}$. On your asteroid, you'll be about $d_2 = 2.17\:\mathrm{AU} = 1.05\times10^{-5}\:\mathrm{pc}$ from Venus at the same point of maximum brightness (based on a little trig). From this we can calculate $m_2$ to be

$$m_2 = −4.89 + 5\log_{10}\left(\frac{1.05\times10^{-5}\:\mathrm{pc}}{0.36\times10^{-5}\:\mathrm{pc}}\right) = -2.57$$

From the comparison table listed above, this would make Venus, at its brightest, about as dim as the "minimum brightness of the Moon". This is a rough calculation, but I don't expect the actual answer to vary too much from this value.

Keep in mind, that's the maximum brightness of one of the brightest inner planets. Any other time Venus will be dimmer and all other planets will never be brighter than this. So all in all, the inner planets will likely be outshined by the much brighter Sun. There's a chance, with the right conditions, if you managed to properly block the light from the Sun using some sort of occulting disk or flower starshade, that you could see the inner planets with the naked eye as they still would be pretty bright in their own right. You just need to get rid of the sunlight outshining them.


Could an Earth-sized planet be cold? This question poses the question of why the Earth is still hot after 4.5 billion years, and the primary reasons were:

  (1) heat from when the planet formed and accreted, which has not yet
  been lost; (2) frictional heating, caused by denser core material
  sinking to the center of the planet; and (3) heat from the decay of
  radioactive elements.

With that in mind, would it be possible for a planet of Earth's size and age to have a cold core, mantle, and crust?

If you peruse Google for Earth cooling rates, you might find what you're looking for. Here's one of many sources.  I strongly recommend reading the entire page,as it discusses some of the geology-based estimates as well.

  Kelvin's primary attack on geologic dating was that measurements of
  the rates of geologic processes were highly uncertain, if it was
  possible to measure them at all (Hallam, 110). Accordingly, Kelvin
  sought to apply the knowledge of physics to the problem. Given that
  temperature increases the further one descends below Earth's surface,
  Kelvin concluded that Earth was slowly cooling. He set out to
  calculate the time required for the Earth to cool, and thereby
  solidify, from an initially molten state. The idea that Earth had
  begun as an incredibly hot sphere of liquid dates back to Descartes
  and Leibnitz. This assumed initial condition was the linchpin for
  Kelvin's entire method (Hallam, 110). Bits of material at the surface
  would sink before solidifying, creating convection currents that kept
  the Earth at a uniform temperature until solidification began at the
  core (Hallam, 110; Knopf, 445). Kelvin needed to know: (1) the
  temperature at Earth's core, (2) the temperature gradient with regard
  to depth below the surface, and (3) the thermal conductivity of rocks.
  The gradient was established to be around one degree Fahrenheit for
  every fifty feet. Kelvin made his own measurements of conductivity.
  The problem was determining the temperature at the core. This is where
  Kelvin's theory of solidification enters the picture. Because the core
  was thought to be solid rock, its temperature could not exceed the
  melting point of rocks (Hallam, 110). He constructed the following
  equation:

  dθ / dx = S / h √(π t)

  The temperature gradient is expressed by dθ / dx; h is the thermal
  conductivity; x is the distance below the surface, and θ is the
  temperature (Holmes, 445). In 1862, Kelvin arrived at a likely age of
  100 million years. Because of uncertainties in the data, the lower and
  upper limits were 20 million and 400 million years (Dalyrmple, 26;
  Hallam, 111).

That said, there are plenty of more recent papers which estimate the cooling rates (with and without the help of the radioactive elements) based on the kinds of data now available as to the current and historical makeup of the core, mantle, and outer layer(s), heat transfer cycles, etc.


How do we know if an object is redshifted? I have some questions about redshift. I think that the first two hang on the last two, but feel free to point out anything you think I should know.

How do we know if an object is actually redshifted, and that we aren't just seeing the regular spectrum of the star?

How can we tell the extent to which a star is redshifted?

Do astronomers have a full baseline spectrum that they compare the measured spectrum against? Or do they just use the hydrogen spectrum since all stars are mostly hydrogen?

There are two methods, one more reliable than the other (though both are pretty good.)

Key point: The brighter a star is, the more detail we can see in its spectrum -- you can think of it as being able to magnify the spectrum more so as to be able to see finer details.  This also allows us to see fainter lines (not all spectral lines are equally intense.)

We have very extensive reference spectra of all the elements under a wide variety of conditions, so when a star is bright enough we see many spectral lines and can match them up to reference spectra.  No two elements have similar spectra, so if you can see many lines, you can't easily confuse one for another.

When you can account for nearly all of the lines in a star's spectrum by a plausible set of elements in plausible abundances and all with the same red shift, you have a very, very reliable match and accurately know the object's red shift.

But distant stars (and galaxies) are very faint and so the spectra we get are very low resolution and show only a few of the strongest spectral lines. They can frequently be matched because hydrogen is so common that the strongest lines seen will be hydrogen lines and even if you can only spot two or three of them, if they bear the same relative positions as bright hydrogen lines, you can safely identify them and read off the red shift.  This is less reliable, but still reliable enough that it rarely is a problem.

In the very dimmest cases you may only see a single line. You have a very rough idea of the redshift from the object's brightness and all you can do is assume it's the strongest hydrogen line and see if it's in roughly the right position given the distance deduced from the object's brightness and type.  This works too, but is still less reliable.  (Much of Hubble's original work relied on just a single line for the more distance objects, but proved to be correct when observed later with dramatically better equipment.)


What does Sa and Sab mean for spiral galaxies? I have learned that the notation to classify spiral galaxies in the De Vaucouleurs system goes like "SA for spirals without bar, SB for spirals with bar and SAB for intermediate spirals". But in some places I've seen galaxies classified as Sa or Sab for example. What it means and what is the difference between a Sa and a Sab spiral?

Capitalization is critical here. (As is knowing which classification system is being used.) The traditional spiral stages (going back to Hubble) are Sa - Sb - Sc; this was a sequence from more centrally concentrated (more dominant central "bulge") + smoother disk + more tightly wrapped spiral arms (Sa) to less centrally concentrated (smaller or even nonexistent bulge) + less smooth disk + more open spiral arms (Sc). Later, S0 (for lenticular galaxies, which are not spirals but seem to have significant or dominant disks) was added at the beginning and Sd (and sometimes Sm) were added as stages beyond Sc.

Hubble also specified that clearly/strongly barred galaxies should be labeled SB0 - SBa - SBb - SBc (with a later extension to SBd), creating a parallel sequence to the nominally unbarred sequence S0 - Sa - Sb - Sc - Sd.

De Vaucouleurs emphasized the existence of intermediate stages: thus, Sab is in between Sa and Sb, Scd is in between Sc and Sd, and so on. (There is also a stage intermediate between S0/lenticular galaxies, which are not spirals, and the Sa spirals: "S0/a".) He also applied this to bar classifications, arguing that there were weakly barred galaxies in between unbarred and strongly barred galaxies. To do so, he changed the Hubble classifications so that "SA" mean unbarred, "SAB" mean weakly barred", and "SB" meant strongly barred. These precede the lower-case Hubble-sequence labels, so you end up with SA0, SAB0, SB0 - SA0/a, SAB0/a, SB0/A - SAa, SABa, SBa - SAab, SABab, etc.

To add to the confusion, de Vaucouleurs also recognized that some spiral galaxies had an unclear bar status (especially true for edge-on galaxies). His famous and widely used RC3 catalog uses "S" for those cases, so "Sa" in RC3 actually means "Hubble stage a, unknown bar status". This, of course, looks exactly like the traditional Hubble classification (continued by other classifiers such as Allan Sandage) meaning "Hubble stage a, unbarred), which has confused people over the years.

To directly address your question: the "a" and "ab" mean what you said in your comment: "Sa galaxies tend to have significant bulges, and tightly-wrapped and relatively smooth spiral arms. Sab galaxies are similar to Sa galaxies, but show more obvious resolution of the arms." Loosely, people will often use "Sa", etc., to refer to spirals regardless of their bar status, as in your quoted text (or in something like, e.g., "Sa galaxies tend to have lower star-formation rates than Sc galaxies."). If it's a specific classification of an individual galaxy, then it might mean "also unbarred" or even "bar status unclear".


Do star remnants actually burn? As we know, some stars can fuse heavy elements to produce carbon and oxygen after using up hydrogen if they are massive, and the remnant of stars are usually hot, my question is, if a star fuse to produce carbon and oxygen, does it also burn to produce carbon dioxide?

Stars don't "burn", they undergo nuclear reactions that do not involve atoms and chemistry at all. The temperatures in the interiors of stars, and certainly in the interiors of stellar remnants like C/O white dwarfs, are far too hot (millions of degrees) for electrons to bind to nuclei and far too hot for molecules to survive. The energy required to break up carbon dioxide is 5.5 eV, which is easily provided unless a gas is cooled well below 10,000K.

The only parts of a star where chemistry can occur is in the outer atmospheres where temperatures can drop to thousands of degrees and where atoms and partially ionised atoms can exist. Here, yes, then it is possible for carbon atoms and oxygen atoms to interact, but that would mostly produce carbon monoxide. This molecule is produced and can survive between temperatures of about 1100K and 3500K in the atmospheres of cool M-dwarfs and brown dwarfs and the atmospheres of red giant stars.

These chemical reactions are utterly negligible in terms of their energetics compared with the fusion reactions that power a star.


Trajectory: What would happen if the sun disappeared one day? So, let's just assume, to no aspect explainable to humans, the sun just magically popped out of existence on January 1st next year (2022), that'll never happen, this is just a scenario to explain my question. If the sun disappeared, regardless of life on Earth, where would the Earth float off to? If it would come close to a gas giant, then a gravity assist would affect the Earth's path through space. Where would it go?
In an answer, I want a feasibly explained way to calculate where Earth would go, not giving much thought to Gravity assists, since I got their calculations from this question, the first answer, and the answer in the link embedded in it.
Also, in the comments section, I've seen comments claiming that my question is a possible duplicate of others. One other addresses what would happen here on Earth, while the other one is about how long it would take for us to stop orbiting the sun after its sudden disappearance. In contrast, I'm wondering about where the Earth would float off to, and where it would go.
Now, this question can seemingly be applied to any celestial object, whether the sun is there or not, I want to figure out trajectory in space. I want to know about trajectory, and how it affects the motion of celestial bodies.
Assuming this can be answered theoretically by the use of equations and mathematics, thanks in advance!

On the first of January, the direction of the sun from Earth is towards Sagittarius, with an ecliptic longitude of 280.  The velocity of the Earth around the sun is perpendicular that that, and towards Virgo, in particular, it is close to the direction of Gamma Virginis (Porrima), with an ecliptic longitude of 280-90 = 190.  The Earth will move in a straight line in that direction.  (Conveniently Jan 1st is very close to perihelion, so elliptic corrections are needed even less than normal)
It won't actually get near to Gamma Virginis because that star is 38 light years away and at the Earth's speed of 30km/s it would take 400,000 years to get close and by then the star will have moved away from its current location.
It wouldn't come close to a gas giant (none are in a position in which they would come anywhere near the trajectory of the Earth, even without checking, they are all on the "wrong" side of the sun)
It would be very unlikely for the Earth to come close to a gas giant.  If it did then the gravity of the giant planet would change the direction of the Earth, it could go in almost any direction.
For another date, the equation is simple enough: find the ecliptic longitude of the sun on that date and subtract 90.  That gives the ecliptic longitude of the Earth's velocity.
You can now use a star map to find the direction that the Earth will travel in.  On January 1st the Earth will travel in a direction toward an ecliptic longitude of 190, but remain in the plane of the ecliptic.  On the map below, the ecliptic is the line through the middle of the map and you can find where 190 is by looking at the numbers at the top and bottom.
Because in the absence of the sun, there would be nothing to cause the Earth to orbit, it would travel in a straight line towards that point.


In Orion, how close in local distance are the closest of the member stars? All the members of Orion are within the Milky way, and some of them look pretty close to a neighbor. And could the bow* be an effect similar to the Radcliffe Wave?

*shield

The three stars in Orion's belt, along with Sigma Orionis and the Orion Nebula cluster, along with several other young clusters and star forming regions in the central Orion region are all part of the Orion OB1 association at a distance of 350-420 pc.

A review of Orion OB1 can be found in Bally (2008). The three belt stars are probably a similar age and distance and form the brightest stars of the OB1b sub-association. Measured distances to these stars are individually rather uncertain, but better estimates come from the low-mass, co-moving stars around them. It is therefore true to say that the individual distances to each star are not known well enough to be sure that they are close together in distance.

The other bright stars in Orion - Betelgeuse, Rigel, Bellatrix, Saiph are significantly closer than this by 150-300 pc and probably not at a common distance. It has been speculated in the past though that these stars and the Orion OB1 association are part of one, large star forming complex, extending 200-300 pc along the line of sight (Bouy & Alves 2015).

The recent paper, claiming the discovery of a "Radcliffe wave" gas structure in the solar vicinity, does include the young stars in Orion as part of this structure.

So to spell it out: The belt stars are within 70pc of each other in terms of distance. If they are at a similar distance of 400pc, their angular separation on the sky of around 3 degrees, translates to a tangential distance separation of about 20 pc. Other members are more separated than this.