Numbers 80 to 85 in Ancient Astronomy Do any numbers in between 80 and 85 (or thereabouts) hold any relatively important or relatively obvious meaning in ancient astronomy ?

A few clarifications:

By ancient I mean related to human antiquity. (Thus, for instance, although in modern times there are indeed 88 known constellations, almost half of them were unfortunately unknown to the ancients).
The meaning in question could refer, for instance, to the number of time periods in a specific time cycle, or to the number of stars in a certain constellation, etc.
By relatively important or relatively obvious I mean something as self-evident and meaningful  to an ancient sage as the fact that there are roughly 360 days a year, or that the number of constellations in the northern and southern hemispheres are 21 and 15, respectively (as known to the ancient Greeks, for instance).

Some background information:

About a century ago, an archaeological site, located in a clearing in the woods, and dating back to the first two centuries BC, was discovered at 45.62°N and 23.31°E, at an altitude of roughly 1,000 meters.

The structure, oriented on a NNW-SSE axis, consists of four concentric circles, the second and fourth of which (counted from the exterior towards the interior) have a clear calendrical and astronomical interpretation, pointing to a semester of 180 days, divided into exactly six months of thirty days each, and to a number of 21 + 13 constellations in the boreal and austral hemispheres, comparable to the figure given by the astronomer Claudius Ptolemy in his famous Almagest. I was wondering whether the third circle, consisting of a number of no less than 82, and no more than 84 pillars, might not also have a similar meaning. Now, don't get me wrong, interpretations abound, but most of them tend to be either slightly forced, or are outright pseudo-science.

As an interesting aside, there were, initially, only 68 pillars still standing, which just so happened to be double the number of those which constitute the inner horseshoe (as it is called), making many archaeologists speculate that its builders were aware of the fact that after 68 semesters of 180 days, corresponding to a number of 21 + 13 = 34 years of 360 days, the calendrical error would amount to almost an entire semester. All nice and tidy, but this proposed solution suffered a devastating blow when further excavations, performed by the son of the man who initially discovered the site (both were historians by profession) revealed that the number of pillars comprising the third circle was much higher than previously thought. Furthermore, a certain scientist has already started speculating that the number of elements should be about 84 long before the excavation in question even happened in the first place! (He based his ideas on the fact that if the second circle represents the solar year, and the fourth one basically corrects it, then there should also be a refinement to the nice-but-inaccurate 30 day month as well). However, even this little gem of a theory has a small and insignificant scratch: One of the main reasons why 84 year lunar cycles were even considered in the first place was because its value is a multiple of 28, the latter representing the number of years in a perpetual calendar synchronizing the seven day week to the solar cycle... Just one minor glitch, though: The civilization that built the structure had months of thirty days, divided into five six-day weeks, as is evidenced by the clear and uniform distribution of the pillars forming the second circle. (Certainly, it is not completely impossible for them to have borrowed such a time-correcting mechanism from other neighboring cultures, but it's not highly likely either). So, herein lies the dilemma...

The site to which you are referring is Sarmisegetusa in old Dacia, which was a well known royal citadel of the Illyrians in Roman times.

Sarmisegetusa was a fortress, not an observatory. The reconstructed posts there were used to hold up ceilings and walls.

Sarmisegetusa backs up against face of the mountain, so half of the horizon cannot even be seen from the site. That fact alone excludes the possibility that anyone was doing any astronomy there.


How do proto-planetary nebulae gain momentum? currently I am curious about proto-planetary nebulae. At first I was curious about how planets spin but I read in a couple of articles that they got their spin from when they were in a proto-planetary nebula and the momentum stayed because of conservation of momentum. But now a new question arises, where exactly do proto-planetary nebula's get their momentum from? I've searched this up on the internet but I haven't really gotten a clear response.

The angular momentum comes from the chaotic/turbulent collapse of the parent molecular cloud. The collapse is turbulent because the initial conditions in the parent cloud are not spherically symmetric. This leave the proto-stellar clumps with non-zero angular momentum even if the parent cloud started with zero angular momentum. The sum of the angular momenta of all the material of the original cloud after fragmentation is still that of the cloud before fragmentation.

Some other/external triggering events for molecular cloud collapse can impart non-zero angular momentum to the cloud as a whole, but this is not necessary for the the individual fragments to end up with angular momentum.


Angular Diameter Distance The definition of the angular diameter distance is the ratio of an object's physical transverse size to its angular size. However when I was reading my textbook, Astrophysics in a Nutshell by Dan Maoz pp.220-221, I am having some trouble trying to understand the notion of angular diameter distance to the last scattering surface. The text calculates the angular diameter distance to the last scattering surface $D_A$:

  Consider flat cosmology (k=0) with no cosmological constant. We wish to calculate the angular size on the sky, as it appears today of a region of physical size
  $$D_s=\frac{2ct_{rec}}{\sqrt{3}}=140 kpc$$ from which light was emitted at time $t_{rec}$. Between recombination and the present time, the Universal expansion is matter-dominated, with $R\propto t^{2/3}$ for this model
  $$\frac{R}{R_0}=\left( \frac{t}{t_0} \right)^{2/3} = \frac{1}{1+z}$$
  and hence we can write
  $$D_s=\frac{2ct_0}{\sqrt{3}}(1+z_{rec})^{-3/2}$$
  The angle subtended by the region equals its size, divided by its distance to us at the
  time of emission (since that is when the angle between rays emanating from two
  sides of the region was set).

I'm not sure what does the last line actually mean..Can someone please elaborate more on this? I just simply take the $D_s$ as the "physical transverse size".

  As we are concerned with observed angles, the type
  of distance we are interested in is the distance which, when squared and multiplied
  by 4π, will give the area of the sphere centered on us and passing through the
  said region. If the comoving radial coordinate of the surface of last scattering is r, the required distance is currently just $r\times R_0$ and is called the proper motion distance. The proper motion distance can be solved using null geodesic in the FRW metric
  $$\int_{t_{rec}}^{t_0} \frac{c dt}{R(t)} = \int_{0}^{r}\frac{dr}{\sqrt{1-kr^2}}$$
  Setting k = 0, and substituting
  $$R(t)=R_0 \left( \frac{t}{t_0} \right)^{2/3}$$ and integrate
  $$rR_0=3ct_0[1-(1+z_{rec})^{-1/2}]$$

So I take this as the physical distance of the region from us. The next part is what confuse me:

  However, at the time of emission, the scale factor of the Universe was 1 + z times smaller. The so-called angular diameter distance to the last scattering surface is therefore
  $$D_A=\frac{rR_0}{1+z}=3ct_0[(1+z_{rec})^{-1}-(1+z_{rec})^{-3/2}]$$

How does a physical distance $rR_0$ comes into play in the angular diameter distance, because from its definition it is just $$D_A=\frac{\text{physical transverse size}}{\text{angular size}}$$??

How does a physical distance $rR_0$ comes into play in the angular diameter distance, because from its definition ...

The manner you choose to calculate it is explained on Wikipedia's "Angular diameter distance" webpage:

The angular diameter distance is a distance measure used in astronomy. It is defined in terms of an object's physical size, $x$, and $\theta$ the angular size of the object as viewed from earth.

$$d_{A}={\frac {x}{\theta}}$$

The angular diameter distance depends on the assumed cosmology of the universe. The angular diameter distance to an object at redshift, $z$, is expressed in terms of the comoving distance, $r$ as:

$$d_{A}={\frac {S_{k}(r)}{1+z}}$$

Where $S_{k}(r)$ is the FLRW coordinate defined as:

$$S_{k}(r)={\begin{cases}\sin \left({\sqrt {-\Omega _{k}}}H_{0}r\right)/\left(H_{0}{\sqrt {|\Omega _{k}|}}\right)&\Omega _{k}<0\\r&\Omega _{k}=0\\\sinh \left({\sqrt {\Omega _{k}}}H_{0}r\right)/\left(H_{0}{\sqrt {|\Omega _{k}|}}\right)&\Omega _{k}>0\end{cases}}$$

Where $\Omega _{k}$ is the curvature density and $H_{0}$ is the value of the Hubble parameter today.

In the currently favoured geometric model of our Universe, the "angular diameter distance" of an object is a good approximation to the "real distance", i.e. the proper distance when the light left the object. Note that beyond a certain redshift, the angular diameter distance gets smaller with increasing redshift.

See also Wikipedia's "Distance measures (cosmology)":

$$\begin{array}{l}
\text{Comparison of cosmological distance $\qquad\quad\;\,$ Comparison of cosmological distance} \\
\text{measures, from redshift 0 to redshift 0.5. $\qquad$ measures, from redshift 0 to redshift 10K.} \\
\hline
\qquad\text{The background cosmology is Hubble parameter 72 km/s/Mpc, $\Omega_\Lambda=0.732$,} \\
\qquad\text{$\Omega_{\rm matter}=0.266$, $\Omega_{\rm radiation}=0.266/3454$, and $\Omega_k$ chosen so that the sum of} \\
\qquad\text{Omega parameters is 1.}
\end{array}$$

Notice how, even at a small $z$, the choice of cosmological model is important for full accuracy.

The book "Astrophysics in a Nutshell: Second Edition" was published Feb 23, 2016, the first edition was published on Dec 4, 2011. The first edition is old (and 25% of the cost of), the second edition is not new.

Wikipedia explains the Lambda-CDM model:

  The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parametrization of the Big Bang cosmological model in which the universe contains a cosmological constant, denoted by Lambda (Greek Λ), associated with dark energy, and cold dark matter (abbreviated CDM). It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:

  the existence and structure of the cosmic microwave background
  the large-scale structure in the distribution of galaxies
  the abundances of hydrogen (including deuterium), helium, and lithium
  the accelerating expansion of the universe observed in the light from distant galaxies and supernovae

  The model assumes that general relativity is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concordance cosmology, after a period of time when disparate observed properties of the universe appeared mutually inconsistent, and there was no consensus on the makeup of the energy density of the universe.

  The ΛCDM model can be extended [tweaked to fix it, depending on what you are doing] by adding cosmological inflation, quintessence and other elements that are current areas of speculation and research in cosmology.

  Some alternative models challenge the assumptions of the ΛCDM model. Examples of these are modified Newtonian dynamics, modified gravity, theories of large-scale variations in the matter density of the universe, and scale invariance of empty space.

The reason to nitpick about a tiny difference of opinion is because the distances involved are so enormous, and the difference really isn't so small either. Depending on the distance the amount of time that has passed means that the space through which the light is passing changes somewhat throughout it's lifetime.

See also: "Scale invariant cosmology III: dynamical models and comparisons with observations" (19 May 2016) by André Maeder:

  The basic equations of cosmology are modified, showing an acceleration of the expansion after a certain initial period, the duration of which depends on the mean density of the Universe. Another major consequence of the scale
  invariance is that the laws of conservation of matter-energy show some dependence on the cosmic time. This dependence is very weak for models with a non-zero matter density, but at the conceptual level this is not a minor effect.

  We do think it is worth to undertake the present exploration for two main reasons. One is that the recent cosmological results suggest that a totally unknown form of matter-energy, the dark energy, dominates the energy content of the Universe. This is a major problem. The other main reason is that scale invariance is not a kind of adjusted trick to make things work. But it is a basic physical change, that responds to the fundamental wish (Dirac 1973) that the equations expressing basic laws should be invariant under the widest group of transformations.

The newer paper "An alternative to the LCDM model: the case of scale invariance" (14 Jan 2017), by André Maeder contains the calculations ($d_M = R_0 r_1$, $d_A = d_M/(1+z)$, on pages 13 and 14) and the following graph:

Figure 5. The angular diameter distance $d_A$ vs. redshift $z$ for flat scale invariant models (continuous red lines) compared to flat ΛCDM
models (broken blue lines). The curves are given for Ωm = 0, 0.1, 0.3, 0.99, from the upper to the lower curve in both cases (at $z$ > 3).

Please refer to that paper for details on the derivation of the calculations.


Do gas giants have a core? I have always wondered how Jupiter and the other gas giants worked when it came to having a core(If they have one). Would it be rocky or liquid, or can it be a gas. Every time I have asked this question to my teachers I have never gotten an exact answer.

Gas giants are believed to have a solid core. They first formed as icy planets, and were heavy enough to accrete hydrogen and helium from the protoplanetary cloud they were in.

Saturn, for instance, is thought to have a central dense core of 10  to  25  Earth  masses  that  was  probably  the  seed  of  the  formation  of  the  planet,  before  it  accreted  its  hydrogen-helium  envelope  from  the  protosolar  disk. (see link)


Can Hawking Radiation ever be detected and does it exist? I'm researching black hole Hawking radiation for a contest, and so far I get the overall gist of how the process works. But as far as I've searched, there hasn't been any confirmed observational evidence that it exists, other than laboratory simulations/recreations. Although the theoretical side of it makes sense, how do we know it exists?

How do we know Hawking radiation exists?
Quantum Physics (Quantum Field Theory) and General Relativity are considered as the two main theories in physics, which can explain a broad range of phenomena at the scale of atoms and subatomic particles to the large scales of the universe, beyond the ability/validity of classical, nonrelativistic physics. They also offer a number of extraordinary predictions, many of which have been experimentally confirmed. So, we are sure about the validity of these theories (and we also know their limitations). If we accept the fundamental principles of these theories, the existence of Hawking radiation would be unquestionable, no matter how we interpret this phenomenon.
Hawking, traditionally, obtained it in 1974 by use of the study (quantization) of quantum fields near the event horizon of the Schwarzschild black hole background for different observers in different locations (this subject is called quantum field theory in curved background). Also, using the Heisenberg's uncertainty principle and applying the basic/elementary relations of quantum mechanics and general relativity, one can qualitatively obtain the Hawking temperature without requiring the knowledge of QFT and field quantization (see also Yakov Zeldovich, who first predicted radiation in rotating black holes). Hawking radiation is also predicted by a number of different approaches in physics, so at present there is no doubt about its existence, but the main problem is how to detect it. The are a number different methods for deriving the Hawking radiation such as evaluating thermal partition function of black holes (in zero-loop approximation of quantum gravity path integral formalism), unitary decay of near extremal D-brane states (in string theory) etc, which (I think) are beyond the scoop of this question. By the way, for these reasons, we expect that any quantum gravity theory which combines both quantum physics and general relativity (if exist any) must predict the Hawking radiation as well, undoubtedly.
Is there any confirmed observational evidence for Hawking radiation?
Not yet. The existence of black holes is theoretically possible and now it has been experimentally verified, no doubt (see Reinhard Genzel's works). But, It seems we have serious difficulties for observing Hawking radiation. A straightforward calculation for the Hawking radiation of static (Schwarzschild) black holes results
$${T_{Hawking}} = \frac{{\hbar {c^3}}}{{8\pi G{M_ \odot }{k_B}}}\left( {\frac{{{M_ \odot }}}{M}} \right) = 6.17 \times {10^{ - 8}}\left( {\frac{{{M_ \odot }}}{M}} \right)\,{{\rm{K}}^\circ},$$
where ${M_ \odot }$ is the mass of son and $M$ represents the black hole mass (${k_B}$= the Boltzmann constant, $G$ = Newton constant). The formation of black holes is possible if the initial mass of collapsing object be greater than the so-called Chandrasekhar limit, $1.4$ ${M_ \odot }$ (i.e., $2.765 \times 10^{30}$ kg). This means that a solar-mass black hole ($M \sim {M_ \odot }$) has a temperature of about $60$ ${\rm{nK}}^\circ$, and larger black holes ($M > {M_ \odot }$) have even lower temperatures. Now, compare this extremely tiny value with the cosmic microwave background radiation (CMB, which is faint cosmic background radiation filling all space), i.e. ${T_{CMB}} \approx 2.73\,{{\rm{K}}^\circ}$. In conclusion, the temperature (Hawking radiation) of realistic black holes is significantly lower than the background temperature of the universe. Qualitatively, this argument is also valid for rotating black holes. This is the main reason why it is generally believed that the Hawking radiation cannot be observed, at least with the current technology of our detectors.
Physicists do not stop looking for Hawking radiation
But this is not the end of the story. Until writing this answer, since any direct observational evidence is potentially ruled out, we have to seek indirect experimental evidence, e.g., e.g., by means of simulations or analog systems. The subject of analog gravity and its different models have been invented for this purpose. Analogue gravity is a research programme which investigates analogues of phenomena in general relativity (such as black holes) within other physical systems, typically (but not exclusively) condensed matter systems, with the aim of gaining new insights into their corresponding problems. Naively, the mathematics governing both the black hole and analog systems are similar. So, there exist a number of analog gravity models which share the same essential properties with black holes such as event horizon and Hawking radiation. For example:

In this paper (published in Nature Physics), the author created a narrow, low density, very low temperature atomic Bose-Einstein condensate, containing an analog black hole horizon and an inner horizon, as in a charged black hole, and in this analog black hole model, he's observed the Hawking radiation emitted by the black hole.

In this paper (published in Phys. Rev. Lett.), the authors utilized the analogy between the propagation of fields around black holes and surface waves on moving water and they experimentally (omitting details) confirmed the Hawking process.

In this paper (published in Phys. Rev. Lett.), an (famous) analog of a black hole, known as  sonic black hole, in a Bose-Einstein condensate has been created in which sound waves, rather than light waves, cannot escape the event horizon.

This is a nice link in Physics Stack Exchange about analog gravity which is a water flow analogy with a black hole. It is a discussion about a good (home) experiment with a black hole analog! Also, this one maybe useful for you.

If you search in web about these analog black holes, you quickly find many interesting papers for confirmation of Hawking radiation, especially in Nature Astronomy Journal.
Is there any astrophysical candidate for detecting Hawking radiation?
Well, yes, but we are not sure about the existence of them. As proposed by Hawking, primordial black holes are well-motivated candidates for detecting black hole (Hawking) radiation. These are hypothetical types of black holes that formed soon after the Big Bang (as a result of fluctuations in the early Universe). Studies speculate that, depending on the model, primordial black holes could have initial masses ranging from $10^{-8}$ kg to more than thousands of solar masses. This is an interesting, remarkable result and I explain why.
In fact, a black hole that initially has mass $M$ will eventually evaporate to nothing. According to the Hawking radiation formula of a Schwarzschild black hole, i.e.,
$${T_{Hawking}} = \frac{{\hbar {c^3}}}{{8\pi G{M_ \odot }{k_B}}}\left( {\frac{{{M_ \odot }}}{M}} \right),$$
Hawking radiation further decreases the black hole mass and black holes with very small mass would experience runaway evaporation, creating a burst of radiation at the final phase (The evaporation would actually be pretty catastrophic, as it would release about as much energy as a large thermonuclear bomb during this time). But, the problem is that if we can observe these explosions during our time. Straightforward calculations by implementing the Stefan-Boltzmann law show that the life time of a black hole is as
$${\tau _{{\rm{life}}}} = \frac{{256{\pi ^3}k_B^4}}{{3G\sigma {\hbar ^4}}}{(GM)^3} = (2.095 \times {10^{67}}\,{\rm{year}})\,{\left( {\frac{M}{{{M_ \odot }}}} \right)^3},$$
where $\sigma$ is the well-known Stefan-Boltzmann constant. For the solar-mass black holes this is much greater than the age of the universe (i.e., $13.8$ billion years), so they are not good candidates. On the other hand, by use of the above formula one can show that primordial black hole with mass lower than $10^{11}$ kg would not have survived to the present due to Hawking radiation. But, interestingly, for primordial black hole (if they exist) with mass lower than the solar mass ($2 \times 10^{30}$ kg) and also greater than $10^{11}$ kg, it is possible to detect/observe the final stage of their life, which is a big explosion equivalent to a hydrogen bomb yielding millions of megatons of explosive force! Along these lines, there exist a number investigations, e.g., see these [1], [2], [3] and [4].
Of course, as usual, there exist some technical/fundamental difficulties to experimentally detect Hawking radiation in primordial black holes. This is the beginning of another story (For a good discussion see this link).


Acceleration in Galaxies Collision In the far future the Milky Way and Andromeda will collide.
As far I know direct collision between large dense objects (black holes, stars, planets, etc.) is unlikely due to the relative "low density" of both galaxies.
My naive intuition is it's like two big clouds of dust merging.

I know at the collision time the Sun will be most like a red star and Earth a scorched dead planet.
For the sake of the next questions let's hypothesise another system with a star resembling the Sun and another small beautiful third rocky blue planet holding some advanced live form.
Also, for acceleration measures, let's use a frame of reference like if someone is observing from far away both galaxies getting close one to another and interacting.

Some questions pop up in my mind.

Can the gravitational interaction sling shot an entire stellar system? How much Km/s2 we can expect these system to accelerate? (In a most extreme plausible case).
How this acceleration can affect the system? Can it de-stabilise planet orbits for example?
How it can affect life? Can it affect magnetosphere? change it's shape? Can solar flares/wind get stronger in some path due particles acceleration?
If another star passes really near (let's say 1 light year at closest approach) but at great speed can its light reach that planet at high energy levels, let's say x-ray and affect that planet life?

The short answer is no. There is no huge accelerations of star systems.

Look at a pair of interacting galaxies  These are the Antenna galaxies (image copyright Star Shadows Remote Observatory and PROMPT/CTIO, from apod)

You will see the long "antennae", which are formed of stars which have been ejected from their galaxies by the interaction. But the accelerations needed are not large, because the interaction takes a long time. The acceleration nothing like $km/s^2$, The force required to accelerate a planet like that would smash it. remember 1$km/s^2$ is about 100g. But small accelerations over long periods can have big effects. The only way to cause objects to accelerate is to apply a force, and the only force that can move planets is gravity. A galaxy has a great big gravitational field, but it is very spread out, and as you note, most of the galaxy is empty space.

Planet orbits should be stable, certainly inner planets would remain bound to their stars. There could be disruption to oort clouds, but the gravitational field around a star would not change much. Similarly the star's magnetosphere would not be changed much. As above there are no large forces applied to stars or planets.

A close-ish approach, to 1 light year, would cause disruption of the oort cloud, but nothing more. Stars may have larger relative motions, but no where near enough to cause blue shifting of light into x-ray, in fact it would be hard for observers on the planet to tell which stars came from which galaxy. Andromeda is approching at 120km/s. But proper motions of stars in the milkyway can be greater than this, Barnards star has a relative velocity of 142km/s

At the end of the interaction, the star and its planet is likely to be scattered to the halo of an elliptical galaxy.


any unique phenomenon when the cores of two planets are aligned with their star's core? Imagine a line passing through the cores of two planets (in the same planetary system) and their star. Have we ever witnessed this - either with both planets on the same side of the star or on opposite sides? If so, was there a unique phenomenon associated with the event?

Referring to your #gravity tag this would only create a peak in the planets tidal forces. But this would be a visible effect in case the planets would be big and close enough... Last night happened that with Sun-Earth-Moon although they were not aligned as you say.

To sum up: a proper alignment would increase the effect of tidal forces.


Does the KBO 2014-MU69 have two numbers and entries in asteroid databases? How did it get promoted to Major Body designation? In this answer I show that the (now pretty famous) Kuiper Belt Object 2014-MU69 has two entries in JPL's ephemeris generating Horizons site; Major Body 3713011 and Small Body 486958. I'm pretty sure these represent the same body, their trajectories differ by about a half-million kilometers only, and that difference is probably only because for one of them the trajectory is only based on a 118 day arc of it's ~100,000 day orbit at ~43 AU back in 2015.

Are both 3713011 and 486958 still official references to the same body, but in different catalogs or databases? Is there a disambiguation page linking the two numbers somewhere? How did 2014-MU69 (unofficially Ultima Thule) get promoted from SB to MB?

The 3713011 object (that is the internal SPICE/SPK id) is a special trajectory computed by the New Horizons team at SwRI which included data which is not in the public domain. The other one for (486958) 2014 MU69 (its official asteroid number and temporary discovery designation) is for the publicly available data.

Generating an ephemeris in HORIZONS for the former produces:

 Revised: Dec 29, 2018            486958 (2014 MU69)                    2486958
 *SPECIAL*

 This pre-computed trajectory is consistent with the New Horizons spacecraft
 Kuiper-Belt extended mission, with the planned 3500 km flyby of Ultima Thule
 on 2019-Jan-1 @ 05:33 UTC.

 Trajectories were provided by the New Horizons mission planning team at SWRI
 and are fits to internal flight-project data that has not been made available
 outside the flight project.

 To use this official mission trajectory to ...

  A) Generate ephemerides with respect TO the mission target:
      Specify the coordinate center in Horizons as "@2486958"

  B) Generate ephemerides OF the mission target
      Specify the target in Horizons as "2486958".

 To instead use the latest JPL ground-based orbit solution (based on the
 publicly available data) and numerically integrate over an arbitrary
 time-span with statistical uncertainties of that public dataset, do a
 look-up in Horizons with syntax "2014 MU69;" or "486958;" or "DES= 2486958;"
 or "DES= 2014 MU69" or "2486958;" (i.e., with a semi-colon).

 Note: the object previously had a provisional SPK ID of 3713011.  It was
 then assigned an IAU number of 486958 such that the primary SPK ID became
 the present 2486958 (2000000 + IAU number).

 Trajectory name                            Start (TDB)         Stop (TDB)
 ---------------------------------------  -----------------  -----------------
 20180601_20250101_od141_tcm30_burn_V0.1  1994-Jan-08 00:00  2033-Dec-21 00:00

(486958) is 2014 MU69's official number and is used at e.g the MPC. 3713011 and 2486958 are the JPL SPK id's for the kernels with and without the extra trajectory information respectively; they are not used outside JPL's software such as HORIZONS, Small Body Browser or the SPICE toolkit. Tutorial 18 of the SPICE Tutorial covers SPK files if you want more details.

The JPL software system handles multiple versions of the trajectory and/or orbital elements by creating multiple "bodies" for the same object. This is most commonly seen with comets which have 1 or more orbital elements for each perihelion passage e.g. this screenshot for comet 46P (Wirtanen):


When Phobos collides with mars (or breaks up), will it have any noticeable effects on Earth? When Phobos meets its predicted doom in a few 10s of millions of years, whether it breaks up or collides with the surface of Mars, will this change have any noticeable effects (permanent or temporary) on the Earth?

No. Phobos is small - just 11 Km across - the size of a small city. Mars (and Phobos) is so far away that a Phobos impact will not affect Earth much. (Mars ranges from 100 billion meters away to nearly 400 billion meters depending on its and Earth's position in their orbits.)

When Phobos hits the Roche limit as it will break up and become a thin light-grey planetary ring around Mars for a few million years.

When it breaks up, (almost) all the debris should stay near Mars because the escape velocity from its orbit around Mars is greater than the velocity imparted to boulders of Phobos as it self-destructs.


Is Cosmic Ray Astronomy a thing? Historically astronomy has been the regime of visible light, looking at distant objects in the visible spectrum and later taking photographs in the visible spectrum.
In the past century radio astronomy, infrared astronomy and exploring other bands in the electromagnetic spectrum became feasible.
Over the past decade we have been able to begin doing neutrino astronomy, identifying distant neutrino sources.
Is there any reason that this cannot progress to other particles, I.E. general cosmic ray astronomy?
One could consider a specialized telescope (it would need to be in a satellite) that detects muons only and forms images from muon detection, or perhaps a proton telescope. The idea being to map incoming particles to pixels in an image, and assign a brightness depending on frequency of particles.

Yes, cosmic-ray astronomy is a thing, and it has been for a while.
More generally, there is multi-messenger astronomy since there are now multiple windows through which we are able to observe the universe via direct observation:

electromagnetic (i.e., light rays, photons)
neutrino
cosmic rays (i.e. high-energy protons and atomic nuclei moving at relativistic speeds)
gravitational radiation

Naturally, we built telescopes for observing light first. Galileo used an optical telescope and it turned out to be very fruitful for him, and it took off from there. Lens crafting became an art that was intimately tied with the progress of astronomy until the 20th century, where the discovery of quantum mechanics opened up the world of particle physics. Neutrinos sourced from nuclear reactions in the Sun, processes elsewhere in the Milky Way, and in other galaxies arrive at Earth and have been detected since the 1960s (although a large fraction of extra-galactic neutrinos are generated in supernovae, it is interesting to note that geoneutrinos are sourced from the decay of radionuclides in the Earth's interior, which helped to confirm the radiogenic theory of Earth's heating).

Over the past decade we have been able to begin doing neutrino astronomy, identifying distant neutrino sources.
Is there any reason that this cannot progress to other particles, I.E. general cosmic-ray astronomy?

There are numerous detectors all over the world designed to detect cosmic rays. There are direct (involving balloons or satellites in the atmosphere making measurements) and indirect (involving ground-based detectors searching for the shower of particles that cascade from the decay of cosmic rays in the atmosphere or searching for photons that are created from that cascade moving through the atmosphere) detection methods. I am generalizing, there are other methods and it is an active area of research (as Benny listed many examples in their comment).
For example, muons were originally discovered in cosmic rays shortly after antimatter was discovered.   Muon detectors are of many types (i.e. Cherenkov-radiation water-tank detector) and can be used for all kinds of interesting purposes. For example, exploring the insides of pyramids and volcanoes without people getting hurt.
The recent direct detections of gravitational radiation by the LIGO/Virgo collaboration reveals that parts of the Universe we used to think we closed-off from observation are now see-able (or may soon be), for examples, at the early Universe prior to the cosmic-microwave-background radiation, and inside of compact objects such as white dwarves and neutron stars.
There could be other undiscovered windows into the Universe, for instance, if there is a "dark force" and thus a "dark photon" associated with dark matter, but that is speculative. We generally need reasons to suspect that something exists before we start making detectors to see them, but the early bird can get the worm, or sometimes it doesn't (like Joseph Weber!!).
Before the advent of large particle accelerators, i.e. 1950s, particle physicists relied on cosmic ray observations. These large accelerators, like at Fermilab or the LHC, are built to discover particles, and they have had varied success which also helped in the development of modern cosmic-ray detections that you could consider as being "general cosmic ray telescopes."


How do planets retain momentum? I'm watching this YouTube video, and in it, the lecturer explains a model of planetary orbit. At 1:55 he shows how a marble will naturally orbit the center object, and he briefly claims that planets will not lose energy like the marble does. But I cant see how that is the case. Surely there must be meteors, asteroids, comets, including general space debris, that will over the course of millennia, diminish this energy/momentum.

How then, can planets retain their energy, when there are almost only forces that would slow it down? Slowly increasing the energy wouldn't help either, as it would offset the balance. How can there be stability, especially over the course of millions of years?

Such forces do exist.

They are utterly negligible in most circumstances. If you imagine a planet "running into" matter whilst travelling in its orbit. Let's say that on average that matter is at rest with respect to the star the planet is orbiting. Then in order to make a very significant change to the linear momentum of the planet, then it must accrete a significant fraction of its own mass.

Such a thing might be important in the very early history of a planetary system when the system is full of gas and debris (e.g. the formation of the Moon), but later on (and bear in mind that the IAU definition of a planet includes the specification that it has "cleared the neighbourhood around its orbit") this just isn't an issue.

This popular science article suggests that 37,000-78,000 tonnes of material hits the Earth every year. Sounds a lot, but in comparison to the mass of the Earth ($6\times 10^{21}$ tonnes) it is very small. If the material was at rest with respect to the Earth's orbit, then an order of magnitude estimate for how long such impacts would take to significantly affect the Earth's orbit would be $\sim 10^{16}$ years.


Calculating the time a star is at my local meridian based on its right ascension I've been watching an astronomy course on YouTube and I'm struggling to calculate stars' positions based on their right ascension.
What I'm trying to achieve: Calculate when a star (Sirius in this example) will be exactly on my local meridian.
What I know: The star's right ascension and the "noon" time (=when the sun will be exactly on my local meridian).
Let's assume we are on March 21st: According to https://stellarium-web.org/ The sun will be on my meridian at 12:10. Sirius's right ascension is 6h46m, which means Sirius should be at the meridian 6h46m later which is 18:56. According to Stellarium Sirius will indeed be at the meridian at 18:52 (I suppose that 4 minute difference is because the sun is already 4 minute behind due to Earth rotation).
But when I try to do the same calculation for today (Feb 10th) I get a 20 minute error.
The "noon" on Feb 10th where I live is at 12:18. We add Sirius' right ascension to get 19:04. But this time we also have to take into account the fact that we are 41 days away from March 21st. Each day the sun falls behind by ~4 minutes, so that's 2h44m. If we add that to 19:04 we get 21:48. So that's the time Sirius should be at my local meridian on this particular day. But Stellarium shows that Sirius will actually be at the meridian at 21:26. So there's 22 minutes error in my calculations for some reason.
I think the root of the error is the 2h44m that I calculated for the sun's position. According to Stellarium the sun's right ascension on that day is 21h38m. Meaning it is 2h22m behind not 2h44m. And that's why I get that 22 minutes error. But I don't understand how it can be 2h22m because Feb/10 is 41 days away from March/21. That means 41x4 = 164 minutes = 2h44m.
What am I missing here?

The sun's position is irrelevant to when a star will be in its meridian; the Sun's coordinates in the RA/dec grid does change over the year. A star's position is fixed in that system and it will be always at the exact same sidereal time that it culminates (as that's the definition of sidereal time).
The difference of the sidereal day to the mean solar day is ~3:56 minutes (366 earth revolutions in a sidereal year, 365 in a solar year), thus a star culminates (and rises and sets) that much earlier each day.
If you compare it to the true solar time (which determines when the Sun is in the meridian) as you try, you also have to account for the difference of the mean solar time and the true solar time due to the eccentricity of Earth's orbit; this phenomenon visible as the analemma (which basically visualizes the equation of time) accounts for a difference of the true noon which varies by about +-20 minutes throughout the year - and can explain the differences you see.
This means that the Sun culminates at different times throughout the year. On March 21st it may be 12:00h. But that is not exactly true 2 month earlier or later, it might be 11:40h or 12:20h.
I think the explanation in the video as linked in your comment as "hours behind the sun" can be a bit mis-leading, and is only exactly true for that one exact date (and defines how the two coordinate systems align with respect to eachother) - but he ignores the equation of time and assumes the mean solar time to be used while his words "behind the sun" imply true solar time. For the task at hand, where to visually find a certain constallation, that is good and accurate enough, though - so not wrong, just mathematically you will have to consider effects he graciously left out.


Why dimmer high-redshift supernovae means the expansion is accelerating, if the dilated region pertains the distant past? I must be seeing this wrong, because it seems to me the data indicates faster expansion in the past, contrary to Adam Reiss' study that led to the birth of the notion of 'dark energy'.

In Reiss' seminal study, [https://arxiv.org/abs/astro-ph/9805201], which was followed by others [https://www.researchgate.net/publication/231060958_Measurements_of_O_and_L_from_42_High-Redshift_Supernovae] that confirmed the measurements (and earned him the 2011 Nobel), high redshift (very distant) Ia supernovae are 15-25% dimmer (i.e more distant) than the current Hubble constant (circa 74 km/s/megaparsec) would predict from their redshift. This lesser luminosity (or greater distance) in the distant region was concluded to signify the universe's expansion is accelerating, rather than slowing down as would be expected from the effect of gravity, as a ball thrown upwards by hand will rise more slowly each second until it stops rising and falls back down. Thus, that some effect must be accelerating the expansion of the universe, referred to by the placeholder name 'dark energy'.

This measurement generates a graph where low redshift (closer) supernovae seem to follow a straight line along the Hubble constant, and then in the more distant region the plot goes up from this straight line, as they are further than their redshift would predict, forming what I call for the purposes of this question a 'shallow V' shape.

[pages 267-269, How Old Is the Universe?, by David A. Weintraub, available at http://93.174.95.29/main/3FF82B0C945C31FF63E4388ED31AB7F9]

The standard answer is something along the line "The argument is pretty straightforward, and can easily be understood with a real-world example. Consider two cars leaving your house. They start out going at the same speed. But over time, one car speeds up, while the other slows down. After some time, which care will be farther away from you? The one that’s speeding up, of course. That’s obvious.  And something that’s farther away looks dimmer (at least if they have the same intrinsic brightness)."

This explanation - that the universe currently expands at a faster rate than in the past - does not seem to explain the “shallow V” curve we see. It would explain a “shallow A”, with a higher Hubble constant in the present and a lower one in the past. We see a curve (or a line with a bend on it) that - it seems to me - cannot be interpreted other than the greater increment being at the point of departure, most distant from us, not nearer to where we are, ie. with a higher Hubble constant in the distant past, say around 80-90 km/s/Mp.

How can we be seeing this curve we see with the accepted interpretation? Should not the curve be bending the other way? Obviously I must be seeing this wrong, but where is my error?

They are further away than they "should" be according to a decelerating universe model (one without dark energy). That is because the expansion has accelerated.

The Hubble parameter isn't a constant, it was larger in the past and is getting smaller. The Hubble parameter does not equate to the expansion rate of the universe. It is defined as the rate of change of the scale factor divided by the scale factor. A Hubble constant would imply exponentially accelerating expansion. e.g. Evolution of the Hubble parameter and Is hubble constant dependent on redshift?

More detail

The light travel time distance to a distant supernovae is measured by the time it takes light to travel from the supernova (when it went off) to us, now. A relatively nearby supernova is barely affected by any acceleration/deceleration of the expansion. It's distance is given approximately by a straightforwad application of a "coasting universe", one that is expanding at a constant rate  - the flat line on your top plot.

If the light has to travel further across the universe then the effects of the cosmological parameters start to become apparent. In a decelerating universe the rate of expansion slows, so a simple application of a "coasting universe" would result in an underestimated distance (the dashed line curving down in your top plot).

I attach a better plot, from the Riess et al. (1999) paper that you reference, with lots of lines representing different combinations of $\Omega_M$ (matter density, a decelerating influence) and $\Omega_\Lambda$ (dark energy, an accelerating influence). Thus a coasting universe has neither and that is the flat line in the middle, representing a universe that has always been expanding at a rate that can be measured locally.

In a decelerating universe (e.g. a flat universe with $\Omega_M=1$, $\Omega_{\Lambda}=0$), the expansion rate was much faster in the past. If however we lived in an "empty" coasting universe, the rate of expansion would have been constant and we would now see the supernovae as further away. If the universe is accelerating (e.g. $\Omega_{\Lambda}=1$, $\Omega_M=0$), then this effect becomes more extreme; the supernovae would be much further away and even fainter.

We appear to live in a universe somewhere between coasting and extreme acceleration (well we know there is some decelerating matter in the universe right!). This is the $\Omega_M=0.28$, $\Omega_\Lambda=0.72$ curve. This universe has been accelerating for the last few billion years, which covers the distances to the supernovae on this plot. The distant ones suffered a lower rate of expansion than those closer to us and as a result are further away than predicted by a coasting model.

However, in such a universe, if you go even further back in time to even more distant supernovae, then the expansion was being decelerated, because whilst the dark energy density stays the same, the matter density was much higher. That is why you can just see the $\Omega_M=0.28$, $\Omega_\Lambda=0.72$ turning down again at the highest redshifts on the plot.

And here indeed is a more recent plot (from Riess et al. 2007), which appears to show this turn-down at higher redshifts quite clearly and delineates the turnover from a decelerating to accelerating universe at $z \sim 0.8$ (e.g. Daly et al. 2008).


can i use heliocentric velocity as a rotation speed? In the research of the galaxies, does heliocentric velocity involves space's expanding velocity? and can i use heliocentric velocity by galaxy's rotation speed?

It's a little unclear what you're asking for, but...
"Heliocentric velocity" means measured radial velocity of an object relative to the Sun. (Which basically means relative to us, except you take out the variations due to the Earth's motion around the Sun.) For galaxies more distant than, say, the Local Group, the heliocentric velocity is the combination of a) the Sun's motion in our Galaxy; b) the local peculiar motion of our Galaxy; c) the local peculiar motion of the other galaxy; and d) the cosmic expansion of the universe ("cosmological redshift"). The first three never vary that much, but the fourth increases with distance, so for distant galaxies, it's (almost) all due to the cosmic expansion.
"Rotation velocity" for a galaxy generally means the speed of stars and gas clouds about the center of that galaxy; it is not one single number but a function of distance from the galaxy's center -- though in the outer parts of the galaxy it often settles to a nearly constant value, which may indeed be referred to as "the" rotation velocity.
The two have nothing to do with each other, though. For example, the rotation velocity in the outer part of M31 (the Andromeda Galaxy) is about 230 km/s, while its heliocentric velocity is about $-300$ km/s. If it were 100 megaparsecs away in the Coma Cluster, its heliocentric velocity would be something like 7000 km/s, but its rotation velocity would be the same.


Why does the Hertzsprung–Russell diagram's x-axis go from large temperatures to lower? In my textbook, the H–R diagram’s y-axis is $\log(L/L_{\odot})$ and values are higher as we go higher on the scale, but the x-axis is $\log(T_\text{eff})$ and gets smaller as we proceed to the right.

This confuses me. Why not let the x-axis go from lower values to higher values? This will also help visualising the “linear” relation between the luminosity and the temperature of a star in the main sequence.

Originally, what was plotted was luminosity against colour, and by colour I mean the wavelength of the peak intensity. Short wavelengths on the left, and long on the right, as you would expect.

Now since stars emit (nearly) black body radiation, there is a close relationship between colour and temperature. I suspect that the reason that the x axis isn't inverted when temperature is used is just inertia:- We have always plotted out H-Z diagrams like this and we will keep doing so.


Distance to Proxima Centauri (Gaia VS New Horizons parallax program) The current best parallax measurement for the nearest star to the Solar System, Proxima Centauri, has been given by the European Space Agency's Gaia mission. This is $768.5004\; \pm \; 0.2030 \; mas$ (milliarcseconds) as for Gaia Data Release 2. This puts Proxima Centauri at a distance of $4.2441 \;\pm\; 0.0011\; ly$. Therefore the uncertainty is so small that the error spans $141.8 \; AUs$, which is more or less the size of the orbit of the Dwarf Planet Eris. The precission is staggering, but if we want to send one day a light-sail mission to this system and explore its planets we will need two orders of magnitude greater precission in the distance estimates (to at least start talking on how to aim at the $AU$ level).

NASA's New Horizons team has launched an interesting proposal to measure the parallax of Proxima Centauri and Wolf 359 by using the Long Range Reconnaissance Imager (LORRI) onboard of the New Horizons probe. Gaia was made to perform these astrometric measurements with high accuracy (less than a milliarcsecond) and New Horizons was not. But while Gaia has a $\sim 2 \; AU$ baseline for the parallax measurements, New Horizons is at $\sim 47 \; AU$ from Earth (as for the 6th February, 2020). The team wants to get this new measurement for Proxima's parallax on April 22, 2020, using simultaneus observations from Earth and the Kuiper Belt.

I guess that the real baseline for the measurement can't be the entire $47\; AU$ between the spacecraft and Earth but something less (since the probe is not moving in the plane perpendicular to the Proxima - Earth line), but still it will be a huge increase with respect to Gaia's baseline. Still LORRI is not as prepared as Gaia to measure small angles.

So, my question is, How these two things (larger baseline but lower ability to measure small angles for New Horizons) balance out? Will the distance to Proxima Centauri get more accurate with New Horizons parallax program, or is Gaia going to still hold the record for that measurement with its $2\; AU$ baseline? And if New Horizons gets a more accurate parallax measurement, how large we should expect the error in the distance to be compared to the current $141.8 \; AUs$ uncertainty measured by Gaia?

LORRI will be used in 4x4 mode, which yields 4-arcsec pixels.  The error in positions is unlikely to be better than 1%, or 40 mas, about 200x larger than Gaia's error.  NH has a baseline ~20x larger, but this means it still misses Gaia by ~10x.

The date was selected for New Moon to help Earth observers find the two targets.  There is no Earth analogue for LORRI, but it should be readily matched by amateur rigs.  The project will use professional ~0.5 - 1.0m telescopes to get Earth obs.  Simultaneous Earth obs are not strictly required, but the simultaneous times are offered to conduct the aesthetically purest demonstration of instantaneous parallaxes.


Where is the center of the Milky Way located? I have downloaded a star database from this page (The HYG Database):
http://astronexus.com/node/34

And all the stars have (among other parameters) their XYZ coordinates in parsecs according to this definition:

  X,Y,Z: The Cartesian coordinates of the star, in a system based on the
  equatorial coordinates as seen from Earth. +X is in the direction of
  the vernal equinox (at epoch 2000), +Z towards the north celestial
  pole, and +Y in the direction of R.A. 6 hours, declination 0 degrees

The problem is: I cannot figure out how to calculate the XYZ coordinates of the center of the galaxy (the Milky Way). So the question is: What are the coordinates of the Milky Way center? (Or is it not possible to calculate it just with that information?). This is an example of the data:

Distance estimates to the center of our galaxy vary around $r \approx$ 8000 $\pm$ 200 parsecs.
Its spherical equatorial coordinates are $\alpha$ = 17h45m40s, $\delta$ = -29$^\circ$00'28" (J2000).
Converting those to rectangular form, we have:
$$\begin{align}
X &= r \cos \delta \cos \alpha \approx -437 \pm 11 \ \mathrm{pc} \\
Y &= r \cos \delta \sin \alpha \approx -6983 \pm 175 \ \mathrm{pc} \\
Z &= r \sin \delta \approx -3879 \pm 97 \ \mathrm{pc}
\end{align}$$
As with most celestial objects, its direction is known much more precisely than its distance.
We can't pinpoint its 3D position, but we can narrow it down to a long, fuzzy ellipsoid pointing away from the Sun.


How well do planetary orbits fit with Johannes Kepler's in- & circumscribed Platonic solids? In Mysterium Cosmographicum (1596) Johannes Kepler proposed that the relative distances between the orbits of the six ancient planets (six because heliocentrism had recently added Earth as one of the planet) correspond to the geometry of the five Platonic solids. Each planetary orbit was assumed to be the grand circle of a sphere. Each Platonic solid would circumscribe an inner planet's orbitally defined sphere, and in same position inscribe the next outer planet's "orbital sphere".

How well does it fit?
Is it somehow mathematically related to the equally spurious Bode's law?
I would appreciate some hints or links to the geometric calculation itself, for me to compare with my own exercise trying to solve part of it.

Johannes Kepler proposed this order of matching planets with Platonics (I suppose because this order gives the best fit):

Mercury <-- planet

octahedron <-- Platonic solid

Venus

icosahedron

Earth

dodecahedron

Mars

tetrahedron

Jupiter

cube

Saturn

It is easy enough to do the calculations, formulae for the in and circum radii of the Platonic solids can be found here which give ratios of circ to in radii of (note formulea for the radii have dropped common factor of the side length, which we don't need as we are interested in the ratios):

>ri4=sqrt(6)/12,rc4=sqrt(6)/4
     0.204124
     0.612372
>
>ri6=1/2,rc6=sqrt(3)/2
          0.5
     0.866025
>
>ri8=sqrt(6)/6,rc8=sqrt(2)/2
     0.408248
     0.707107
>
>ri12=sqrt(250+110*sqrt(5))/20,rc12=(sqrt(15)+sqrt(3))/4
      1.11352
      1.40126
>
>ri20=(3*sqrt(3)+sqrt(15))/12,rc20=sqrt(10+2*sqrt(5))/4
     0.755761
     0.951057
>
>rho4=rc4/ri4
            3
>rho6=rc6/ri6
      1.73205
>rho8=rc8/ri8
      1.73205
>rho12=rc12/ri12
      1.25841
>rho20=rc20/ri20
      1.25841

Which may be compared with the orbital radius ratios from here (radii in km)

>RMecury=57.9e6;
>RVenus=108.2e6;
>REarth=149.6e6;
>RMars=227.9e6;
>RJupiter=778.3e6;
>RSaturn=1426.7e6;

Now we can compare the corresponding radii ratios:

>[RVenus/RMecury,rho8]
      1.86874       1.73205
>[REarth/RVenus,rho20]
      1.38262       1.25841
>[RMars/REarth,rho12]
       1.5234       1.25841
>[RJupiter/RMars,rho4]
      3.41509             3
>[RSaturn/RJupiter,rho6]
       1.8331       1.73205

Which, as these things go, is not bad.


Why do massive rapid-rotating stars move bluewards off the zero-age main sequence (ZAMS)? I'm reading a well-cited paper by Szecsi et al. 2015 titled "Low-metallicity massive single stars with rotation". The paper can be found here. I was surprised that figure 5 depicted an HRD in which rapid rotators of 500 km/s evolved bluewards on the HRD. I didn't know any star could move anything but rewards when leaving the ZAMS. Other rotators below that 500 km/s move in a more typical fashion. Can anyone explain what is going on here?

The blueward evolution is a simple consequence of the homology relations for main sequence evolution.
If the star is rotating very fast, then this induces strong mixing of the interior, such that the star can be treated as chemically homogeneous. As main sequence hydrogen burning proceeds, the entire star is gradually turned into helium, with a consequent increase in the mean molecular weight $\mu$.
Therefore, the evolution can be thought of as a sequence of models with similar mass, but increasing $\mu$.
The luminosity evolution is
$$L \propto \mu^{7.5} M^{5.5} R^{-0.5}\ .$$
The strong $\mu$ dependence comes about through the strong dependence of opacity on $\mu$ for stars in radiative equilibrium.
On the other hand, the radius is only weakly dependent on $\mu$. That is because the central temperature depends on $\mu M/R$ (from hydrostatic equilibrium), but the strong temperature dependence of the CNO cycle, means the central temperature hardly increases as burning continues. As a result
$$ R \propto \mu^{2/3} M^{4/5}\ .$$
If we assume a blackbody, then $T_{\rm eff}\propto L^{1/4}R^{-1/2}$ and thus
$$ T_{\rm eff}\propto \mu^{1.54} M^{0.98} R^{-0.12}\ .$$
If we start off with 10% He by number, then $\mu=0.56$. But if we end with 80% He, then $\mu=1.2$.
On the face of it, this would appear to more than double the surface temperature during the main sequence evolution. The effect will be mitigated by mass loss and the disproportionate effect on opacity contributed by whatever metals are present (these are not zero metallicity stars).


How do we know a star's age based on its spectrum? A star's nearby environment may give clue to its age.

Different stellar type have different spectral features. If we just have its spectrum, how do we know its age?

For example, a star may be born with a M3-type(I know it is more difficult for M-type compared with OBAFGK) and stay here for a long time.
How do we know it was born with a M3-type?
How do we know its age?

It is better to talk about different stellar types and give reference papers.

There are two separate issues when you talk about a star's age.  Are you talking about its absolute age, in years, or its age in terms of how far along is it within its own evolution?  The difference is, massive stars go through their evolutionary phases very quickly, and low-mass stars very slowly, so essentially all very low-mass stars are older in years than essentially every very high-mass star.   Also, you can know more than the "spectral type" from a spectrum, you can also know the "luminosity class"-- that's the roman numeral that tells you if the star is, for example, a main-sequence dwarf or not.  So if you pick an M spectral type main-sequence star, and an O spectral type main-sequence star, as two stars at random, it is extremely likely that the M star is much older than the O star, and you can know that purely from the spectral type and luminosity class.  But if you want to know the age of the M star, or the O star, in years within their evolutionary stages, then it gets more difficult because there is rather little main-sequence evolution in the spectrum.  There is some evolution though, especially late in the main sequence, so you could tell its age if there is evidence of main-sequence evolution in the spectrum (for one thing, the luminosity rises with age, within a spectral type, but that's pretty hard to tell from the spectrum).  If the star is both low-mass and early in its main-sequence evolution, the best way to tell its age is to look at the rotational broadening of its lines, as low-mass stars spin down rapidly as they age (due to strong magnetic fields and weak winds).

Another good way to tell the age of stars is if they are in clusters that all formed together, you can look at what is called the "main sequence turnoff", which basically means you look for the lowest mass star that has gone supernova, and you know how long that takes for that mass of star.  You tell this from the spectrum because the turnoff is in the "Hertsprung-Russell" diagram, which you make from the spectra, but it requires a lot of stars in the cluster, so it's not really a property of a single spectrum.

So the bottom line is, you need a suite of different techniques for assessing the ages of stars, it is not always easy or straightforward but you can take each case individually and look for ways to infer age.  Much easier is determining which evolutionary class a star is in, because stars change dramatically in one phase or another, and the spectrum alone can tell you if you have a dwarf or a giant, etc.  (Basically, the lines get much narrower as a star puffs out in radius, because the pressure drops.)


What is the difference between the way light travels in a gravitational field and the way it travels through an expanding universe? A photon is travelling through space. As it travels, the space through which it travels is expanding

Does this describe

A - a photon travelling from a distant galaxy to earth
B - a photon travelling from a point of higher to a point of lower
gravity
C - either

If like me you think the answer is C, can you explain why light should travel differently through a gravitational field to how it travels through an expanding universe? In other words, why in one case does the speed of the photon vary, while in the other case it doesn't?

Alternatively can you explain why you don't think it's C?

I have asked a similar question on the Physics Stack, but I probably worded it badly, so I just got a load of down votes and no answers. I hope I haven't offended anyone here with this wording.

If like me you think the answer is C, can you explain why light should travel differently through a gravitational field to how it travels through an expanding universe? In other words, why in one case does the speed of the photon vary, while in the other case it doesn't?

I think the reason is, we can take the Cosmological redshift as a Doppler redshift, where the speed of the photon does not change but only the wavelength changes due to the expansion of the universe.

Meanwhile, in Gravitational redshift, its the "redshift" is purely caused by GR and it's possible that the light loses its speed due to this effect.

Here is the link why I think cosmological redshift can be thought as Doppler redshift.

Here


How can we estimate if a certain astronomical object will be visible from a place on earth? If we have the RA/DEC of an object that we want to observe, how can we tell if that object is visible from our place on earth (at a particular time of the year)?

Given that the part of the sky we are observing is changing throughout the year, it seems fairly complicated.

A simple estimate can give you a rough idea what area of the sky will be visible at different times of the year, using only a bit of mental arithmetic.

I just remember one number, the right ascension (RA) at (or nearest to) the meridian (between due S and the zenith) at midnight on Jan 1st. This is (roughly) equivalent to local sidereal time. Actually, I just remember the hour, 06h, at my longitude of just under 72 degrees E. This changes very slowly from year to year due to precession (I may have to use 05h by around 2050 or so, if I am still alive!). Since the difference between sidereal time and UTC is about 4 minutes per day, RA on the meridian at midnight shifts about 2 hours later per month. Now around Jul 15th, about 19h RA is on the meridian at midnight here. Latitude determines what range of declination can be seen. At ~42 degrees N, I usually cannot see much below -30 degrees declination, depending on the horizon.

Knowing what RA is near the meridian (I can easily subtract or add hours corresponding to time before or after midnight), by looking at a sky chart I can easily estimate what objects should be visible, or well placed for observing. I used this simple technique for many years, before digital everything! Now I can just use SkySafari on my iPad. :-)


Images of gravitational lensing I will expect that gravitational lensing should turn an object into a ring image. But I saw in some situations that instead multiple images are formed. For example, the Einstein-cross in the image below, consisting of four images:

Why is it so?

As mentioned in the comments, a ring will (ideally) only occur if you have perfect alignment of source, lens, and observer. This is true for point sources, for extended sources things get more complicated.

Double and quadruple images occur when the source is small and not in perfect alignment - typically a quasar, as in your example. For the sake of completeness, this would actually be triple or quintuple, but the third / fifth image is very close to the centre, overpowered by the lens, and highly demagnified (faint).

There are examples of rings and almost-rings, but these tend to be extended sources, i.e. galaxies. It is more likely that some part of an extended source happens to be aligned with lens and observer than it is for a point source.

(Image of the Cosmic Horseshoe)

In your example, if the host galaxy of that quasar could be seen, it might be an Einstein ring (or an oval, as the lens seems to be somewhat asymmetric).


What does forward modeling mean? In my research on exoplanets, I have heard many people talk "forward modeling of exoplanet atmospheres".  I don't know what the "forward" means in "forward modeling" and how it compares with "reverse modeling", if that's even a thing.

What is forward modeling, and why is it so special that it needs to be distinguished from just plain ol' regular modeling?

There are different ways to model something. From what you're asking, there are two main types of modeling: forward modeling and inverse modeling.

Forward Modeling

In this type of modeling, you have a specific model that defines the "current" state of your system. In the case of exoplanet atmospheres, it'd likely be something that defines the molecular content, ionization level, density, etc. of your exoplanet atmosphere. Then, you use the known physics/math of your system to decide how it will behave. In this setup, what you've created is a system for predicting system states from a predetermined physics model.

Such an example would be someone creating their own atmosphere of an exoplanet in a model and then saying, okay what happens when I shine light through this atmosphere. What observations might I record?

Inverse Modeling

In some sense this is the opposite of forward modeling, albeit it doesn't really mean you're running a model to see into the past. Instead, what happens with this setup is you know a particular state or result, and you want to construct a model of your system which can produce said state. Essentially, you want your model to arrive at a certain state when it is done calculating. If it does, you have a reasonable confidence that your model was some indication of what your system is actually like.

In this situation, you'd measure components of the atmosphere, e.g. the radius of the planet as a function of wavelength, and then create a model of the atmosphere which can hopefully reproduce your observations. If you can, then the hope is that the model accurately represents what your system is.


Moon orbits crossing each other Some planets, such as Mars, have 2 or more moons. Giants, like Jupiter of Saturn have a lot of moons!

How likely the orbit of one crosses another one's orbit? Is it possible for two moons to collide? If yes, what would exactly happen?

There is one known pair of moons in the solar system that seemingly swap orbits every couple of years. That's Saturn's Epimetheus and Janus. Their orbits are so close together that they interact gravitationally every couple of years (when the inner moon catches up to the outer moon), so that the outer moon is slowed down, and the inner moon is accelerated.

Each moon changed direction from prograde to retrograde and vice-versa in two co-orbital horseshoe orbits, never crossing paths as they exchange a bit of momentum when closer but Saturn's gravitational pull prevails and pulls each of these two moons back in the opposite direction where they came from, swapping from lower to higher orbit. It's a bit tricky to explain in words:

[From: The Rotation of Janus and Epimetheus - Tiscareno, Matthew S. et al. Icarus 204 (2009).]


What is the brightest star (relative magnitude) in M31? I am wondering what the brightest individual star is in M31, the Andromeda Galaxy.  Specifically, brightest as seen from Earth (so relative magnitude).

The Variable stars that Hubble studied in M31 when he showed that it was a galaxy are among the most luminous. They include Var-A1, a luminous blue variable, and magnitude about 16.5. Var A-1 is one of the most luminous stars known.

Nasa has a catalog of stars in the m31 field, The brightest star in this catalog is an 11.4 magnitude star. But I think that database needs careful interpretation.


Term for a momentary geometric pattern formed by astronomical objects Few days back, the Pleiades, the Sun and the Moon were forming an almost perfect equilateral triangle.

Is there a term that describes such momentary geometrical patterns? Asterism and conjunction are close, but not exactly applicable here.

Momentary events in general (comets, supernovae, solar flares, etc.) can be lumped under the general heading of "transient phenomena". 'Transient asterisms' may be a candidate term for the concept you are describing.

Then again, we now know that on a large enough time scale all asterisms are eventually transient in nature. So one might justifiably take the point of view that the adjective "transient" is redundant. So perhaps calling the patterns you describe simply as "asterisms" is not as bad of a candidate term as you might suspect.


Resources on planetary stability I am a fifth (and last) year undergraduate student in Physics with good level of Mathematics formation and basic Astrophysics formation. I recently read some theories about Solar System formation and evolution and became interested in planetary stability, but I couldn't manage to get a good introduction to the topic.

I was wondering if there is a standard book or resource that approach this topic with precision that you could recommend. Any advice will be welcome.

The book by Dvorak et al. 2006 "Chaos and Stability in Planetary Systems" is a good place to start (as with many titles by Dvorak), but reviewing and studying recent(ish) published work about the topic can greatly enhance understanding of the topic.  For example:

Malhotra et al. 2011, Chaos and stability of the solar system, PNAS (full text online) - this article explores the notion that there may be a significant element of chaos in the planetary orbits. A small snippet from the abstract:

  Over the last two decades, there has come about a recognition that chaotic dynamics is pervasive in the solar system. We now understand that the orbits of small members of the solar system—asteroids, comets, and interplanetary dust—are chaotic and undergo large changes on geological time scales. Are the major planets' orbits also chaotic? The answer is not straightforward, and the subtleties have prompted new questions.

In a similar vein, the article: Barnes and Quinn, 2004, The (In)stability of Planetary Systems, The Astrophysical Journal (full PDF online),

  present results of numerical simulations that examine the dynamical stability of known planetary systems, a
  star with two or more planets.


Can quantum entanglement cause nucleosynthesis to happen in stars? Even if there isn't enough heat and energy in the star to cause nucleosynthesis, could atoms quantum entangle to create a new atomic nuclei? Or would it be quantum tunneling - if this is possible?

You are referring to pyconuclear reactions - these are reactions that are initiated even when the temperature is effectively zero. They are caused by zeropoint oscillations of particles that are trapped in a deep potential well and hence are purely a quantum mechanical effect.

This is far from just of theoretical interest. It may be that pyconuclear reactions occur in the condensed matter of white dwarfs; possibly even initiating the carbon burning that can destroy the star in a type Ia supernova.


Do sungrazing comets leave a field of meteoroids near the Sun? A large fraction (a third?) of all comets found (with observational bias thanks to SOHO) have been sungrazers, breaking up with perihelion of a few of Sun's radius. Is there reason to believe that this replenishes some kind of vulcanoid population of small objects? Or would they evaporate and be blown away by the Solar wind, or continue in their comet's orbit, or be ejected by Mercury's eccentricity? Would the constant replenishment, even now, not billions of years ago, help keep a population there in spite of all above?

The SOHO image you attached, provides some evidence, that most of the debris continues the trajectory of the original body.
Most of the debris hence won't replenish the Vulcanoid population.
But due to the disruptive event you get an additional delta-v, which may change the orbit a bit, however insufficient to slow down to a Vulcanoid orbit; compare the velocity of the comet near perihelion with the speed of sound as an order of magnitude estimate of the upper limit of the delta-v for debris.
Dust may either be slowed down in this or in future orbits in the solar corona to end up in the Sun, or blown away by solar radiation pressure, again no Vulcanoids.


How to map moon phase number + "lunation" to moon phase name? I am querying an API (weatherbit) which returns a moon phase number which looks like this:
0.9594168
For the 16 days I look at the numbers vary from 0.006 to 0.99.
I have 8 "moon phase" icons for the full, crescent, gibbous, etc. phases.  Filenames are the phase names.
How can I map the moon phase number to the phase names so I can use images with those names appropriately.
Final Update: Use moon_phase_lunation (instead of moon phase number) only
Here is the final js-react code which seems to be working well so far:
import React from 'react';
const Moon = ( data ) => {
  const lunation = Number(data.moon_phase_lunation);
  let imageToUse;
  if (lunation <= .06) imageToUse = 'new';
  if (lunation > 0.06 && lunation <= .19) imageToUse = 'waxing_crescent';
  if (lunation > 0.19 && lunation <= .31) imageToUse = 'third_quarter';
  if (lunation > 0.31 && lunation <= .44) imageToUse = 'waxing_gibbous';
  if (lunation > 0.44 && lunation <= .56) imageToUse = 'full';
  if (lunation > 0.56 && lunation <= .69) imageToUse = 'waning_gibbous';
  if (lunation > 0.69 && lunation <= .81) imageToUse = 'first_quarter';
  if (lunation > 0.81 && lunation <= .94) imageToUse = 'waning_crescent';
  if (lunation > 0.94 ) imageToUse = 'new';
  const imageURL = `/moonIcons/${imageToUse}.png`;
  return (
    <>
      <img src= { imageURL } width="20px" height="20px" />
    </>
  );
};

export default Moon;

The WeatherBit 16-day forecast documentation gives these output field descriptions:

moon_phase: Moon phase illumination fraction (0-1)
moon_phase_lunation: Moon lunation fraction (0 = New moon, 0.50 = Full Moon, 0.75 = Last quarter moon)

The illuminated fraction doesn't help you distinguish waxing and waning phases, so moon_phase_lunation is the value to use.
One possible mapping is:
0.0  0.06  0.19  0.31  0.44  0.56  0.69  0.81  0.94  1.0


What is needed to break through the surface of Europa? How big does a satelite we send have to be to be able to chrush through the ice layer and dive into the ocean on Europa? If a mission should head there, is this a better way of examining the ocean than landing on the surface and drilling through?

There is no feasible way for a human-made probe to crush through Europa's ice layer.

"It is predicted that the outer crust of solid ice is approximately 10–30 km (6–19 mi) thick." (Wikipedia)

It's not even known, whether there is a liqud ocean at all under Europa's ice layer.

Instead of drilling one could try to slowly melt trough the ice.


What will succeed the Arecibo Observatory? Just a few minutes ago, I got a notification from Space.com stating that the Arecibo Observatory will be, sadly, decommissioned due to extensive damage to its structure. So, with the loss of one of the world's largest telescopes, we will be put at a setback in space exploration and astronomy. So, what will succeed Arecibo and when will this happen?

There's no simple answer. In the immediate future, different radio telescopes around the world will pick up the slack in various ways; how that happens will depend on the needs of individual observers and collaborations. Unless someone was to build an identical observatory at the same latitude as Arecibo, with the same frequency range, receiver options and field of view . . . we'll have to spread out the observing. Given that we didn't really expect to lose Arecibo for more than about a year$^{\dagger}$, there are a lot of things up in the air. Insert "probably" and "maybe" into this answer wherever you please.
I do pulsar timing, so I'll talk about what a future without Arecibo might look like from our perspective. My collaboration's two main instruments were Arecibo and the 100-meter Green Bank Telescope (GBT), with roughly half of the observing time at Arecibo and half at the GBT. There aren't firm plans in place for the exact strategy we'll take going forward, but we'll have to decrease our observing cadence at the GBT (i.e. how often we observe certain pulsars) so we can use some of the time to observe pulsars we'd normally observe using Arecibo. So the GBT can take some of the load, but as we only have a finite amount of observing time, that impacts our other observations. We'll likely have to decrease the cadence of observations and the number of pulsars we monitor regularly.
Pulsar timing arrays will also have options with other existing instruments in the immediate future. A key one is the Canadian Hydrogen Intensity Mapping Experiment (CHIME) in Canada. The folks at CHIME will actually be able to observe all of our northern hemisphere pulsars (CHIME Pulsar Collaboration, 2017), which is excellent. In the short-term, CHIME will slightly lessen the burden of losing Arecibo. We've also done a little bit of timing with the Very Large Array, although I don't think that'll be a major player in the future.
That brings us to telescopes currently in the planning stages or under construction. The DSA-2000 (Hallinan et al. 2019) will hopefully see first light in the late 2020s and would likely become a major part of our ongoing observations. The Square Kilometer Array will also be extremely important for radio astronomy as a whole - I don't know whether we in particular will be using it a lot. The SKA should also reach completion in the next decade.
These are just the current potential options from my corner of the astronomical world - and they're quite tentative. Arecibo was our most-used screwdriver in the toolbox, so we've certainly been hit. We'll hopefully be able to somewhat supplement the GBT with CHIME and ideally DSA-2000 a decade from now - so in that sense, those will effectively succeed Arecibo for our observations. In reality, all that means is that we won't lose quite as much of our observing capacity - but it doesn't come close to making up for the loss. Other collaborations and astronomers will presumably increase their usage at the observatories that are best equipped for their observations, depending on frontend/backend requirements and field of view.
It's not going to be fun. We'll be set back. But science will go on. We'll figure it out.

It's worth updating this answer now that the white paper for the proposed Next Generation Arecibo Telescope (NGAT) has been released. The Arecibo Observatory has proposed a phased array of small dishes mounted on a circular platform ~300 meters in diameter (or potentially multiple smaller platforms) which would be angled in various directions to provide reasonable sky coverage. One variant involved 1,112 9-meter dishes, as smaller dishes provide a higher packing efficiency and therefore maximize collecting area. Regardless of the precise configuration, the sinkhole that housed the former 305-meter dish would ideally be the new array's home.
The aim is for frequency coverage from 200 MHz to 30 GHz via four broadband receivers and a frequency-dependent field of view ranging from 6 degrees at 300 MHz to 3.5 arcminutes at 30 GHz, a significant field of view increase over its predecessor by a factor of 500. The dishes would also be equipped with transmitters for radar observations.
Whether the NGAT will be built is a question for which nobody has any answers just yet. It would cost roughly $450 million, which could take money away from other projects unless it received special Congressional funding or support from private sources. Additionally, the setup has not been tested on such a large scale, so there are some technical and engineering concerns (the group did consider but reject single-dish and classical array designs). All that said, the design was put together in an impressively short amount of time, and even if the NGAT isn't build, the scientific considerations that went into it may inspire future designs for replacement telescopes at Arecibo.

$^{\dagger}$ This isn't totally true - a scenario where we lose Arecibo had already been studied in detail. But . . . I think a lot of folks felt that it was more likely that it would be out of commission for a bit but could be salvaged in some way, and hopefully brought back online before too long. This was not the Thursday we were expecting.


Is it possible that the Sun has a binary partner (the Nemesis Theory) that has eluded detection? I just recently learned about the theory that our Sun has a small companion star with a 26 million year orbit. This theory came about when it was realized that mass extinction events happened approximately every 26 million years. My question is not whether or not this is possible as that has been asked before; my question is how could we have missed it?

When we look for exoplanets in the Universe, we are sometimes able to detect a slight wobble in the parent stars. Along those lines, if the Sun had a companion star, how would we not notice the effects on its rotation/orbit? If the sun and this companion star were locked in a 26 million year orbit, would we be able to notice the orbit?

Finally, when you have a star system like ours, with so many planets, is it possible to tell which planet is causing which specific motion in the Sun? For example, let's say we traveled to a different star system a few hundred light years away, and we were studying our solar system. Would we be able to look at the way the Sun wobbles and determine how many planets were in orbit around our Sun, or would we only be able to say that there was one, or simply that there may be several? I guess, the root question is how accurately can we judge the contents of a star system based on the perturbations in the star's orbit? Thank you kindly for your time.

The first part of your question has been asked before:  Is Sun a part of a binary system? and the current (lack of) evidence for such a companion is discussed on the relevant wikipedia page about "Nemesis".

To summarise: if it were a small companion star, or even a brown dwarf that had been cooling for 4.5 billion years and it had a 26 million year orbit, then Kepler's third law tells us how far away that object would be. It turns out that this is not far enough away that the object would have eluded detection in all-sky surveys. The recent WISE survey in the near-infrared should have been capable of detecting even a very cool brown dwarf (and indeed it has detected some very cool brown dwarfs, just not that close to the Sun - e.g. a 250K brown dwarf only 6 light years away Luhman et al. 2014) that was close enough to the Sun to be a Nemesis candidate.

Since the details do not appear to be on the wikipedia page, I'll fill some in. If we take a very low mass brown dwarf - say 20 Jupiter masses - in a 26 million year orbit, then Kepler's 3rd law tells us this will be about 90,000 au (1.4 light years) from the Sun (assuming a circular orbit). According to the evolutionary models of Saumon & Marley (2008), such an object has an intrinsic luminosity of $10^{-7}$ times (1 ten millionth) that of the Sun and a temperature of 400 Kelvin and would appear to have a spectral type of late T or early Y.

From the calibration of absolute magnitudes versus spectral type for cool brown dwarfs in Marsh et al. (2013) we know that at 90,000 au, such a brown dwarf would have magnitudes of $H=14$ and $W2=8$. The former is bright enough to have been seen in the 2MASS all-sky survey and the latter is easily detected by WISE. The combination of data would also easily have revealed the large parallax of such an object. We can conclude that an object would have to have much lower mass than this to remain undetected.

Now the middle part of your question: A star will "wobble" in response to its companion with exactly the same period as the orbit. So, if you are prepared to wait for an appreciable fraction of 26 million years, then yes, the presence of the binary companion might be revealed in a net small oscillation of average proper motions over the whole sky, with a period of 26 million years! Otherwise not. Measuring the "wobble" by doppler methods is currently capable of detecting Jupiter-mass objects in orbital periods of 10-20 years. Measuring the wobble "astrometrically"  - that is measuring the position displacement of the star due to an unseen companion is more sensitive to distant companions, but still, one is limited by the fact that the wobble period will be the same as the orbital period of the companion. An assessment of the performance of the Gaia astrometry satellite by Perryman et al. (2014) suggests detection of planets with orbital periods out to 10 years might be possible.

For the final part of the question - yes, the motion/wobble of a star can be decomposed (using Fourier techniques) into components that are due to each planet. There are numerous examples of multiple planetary systems that have been discovered by the radial velocity technique in this manner. Similar techniques can and will be employed to analyse any astrometric wobble. An interesting plot is to show the motion of the Sun in the plane of our solar system, in the rest frame of the solar system centre of mass. The Sun executes a complicated trajectory in this plot due primarily to the influence of Jupiter (on an 11 year orbit), but with superimposed "epicycles" due to the influence of the smaller planets on different orbital periods. See below.

Motion of the Sun around the solar system centre of mass (from http://commons.wikimedia.org/wiki/File:Solar_system_barycenter.svg )


Motion of rogue planets Two Questions:

1) Are rogue planets in motion, i.e. are they just wandering freely in space or stationary?

1) Do rogue planets have defined path or a one which can be anticipated? I understand that they cannot be at absolute rest as they are moving along with the galaxy.

2) Do rogue planets rotate around their axes?

If they are in motion, and they outnumber the stars in our galaxy, why our solar system never had a guest?

On the numbers

Rogue planets are thought to be more abundant than stars in the milky-way and depending on where you make the cut-off, rogue dwarf-planets for example, are expected to enormously outnumber the number of stars.   older article quoting the MOA survey.

This article - OGLE survey, or, Portland's Optical Gravitational Lensing Experiment estimates:

  Based on a statistical analysis of more than 2,600 microlensing
  events, drawn from six years of observations on about 50 million
  stars, the OGLE team estimates that there is perhaps one Jupiter-mass
  rogue planet for every four stars in the galaxy.

It's not an experiment it's a survey, but I guess they couldn't resist the name OGLE, so they went with that, so, props on the name, but I digress.

There's still some disagreement between MOA and OGLE, though I think the consensus is that OGLE gives a slightly better estimate of 1 Jupiter-mass rogue for every 4 stars.

Due to the nature solar-system formation, we expect that a number of planets get cast out during the early period and larger orbiting objects are good at casting out smaller ones when they pass to close, but it's almost impossible for smaller objects to cast out a larger one.    We expect that the number of smaller rogue planets should increase significantly, perhaps even exponentially.  But the OGLE survey had difficulty locating smaller planets, 1-10 Earth masses.   That may be because they are more difficult to see, or they might be less common than expected.

Binary star systems, for example, with two or more much more massive than Jupiter objects could cast out larger objects like Jupiter-mass planets fairly easily, so there are significant unknowns on the number of smaller than Jupiter rogue planets.  Estimates are high, observations are low.   NASA's WFIRST might be powerful enough to resolve this after it's launch in 2020.

This article a study by the Kavli institute, suggests an aggressive estimate of 100,000 rogue-planets (or Nomad planets) for every star in the Milky-way, based on the 2011 MOA estimate of two Jupiter-Mass objects for every star and extrapolating based on how common Pluto sized objects are thought to be relative to Jupiter sized (about 50,000 to 1).    If we adjust for the 1 to 4 instead of 2 to 1, that estimate is shaved down to about 12,000 pluto or larger rogue planets per star.

Whatever the real numbers are, if we count all the way down to dwarf planet size, Rogue planets should significantly outnumber stars and an estimate of 3-4 magnitudes isn't unreasonable.   For planet sized, say Mercury to Neptune, better observations would help with this estimate a great deal, but a bad estimate of Mercury and up Rogue planets outnumbering stars 10 or 20 to 1 isn't crazy.

I'm fussing on the numbers because it's relevant to how many pass through the solar system.   Using this question/answer as an approximation and because the escape velocity from a solar system is usually tiny compared to the escape velocity from a galaxy or the orbital speed around the galaxy, generally speaking, rogue planets should have star-like orbits around the Milky-way.    If a star passes within one light-year of our sun about once every million years, even if you set a relatively high estimate of 100,000 rogue planets (pluto size and up), that's still one every 10 years, and that's within 1 light year.   If you want to estimate within the Kuiper Belt - where we might expect to observe a pluto sized rogue planet passing through.   The target area of the Kuiper belt is about a million times smaller than the 1 lightyear radius, so a rogue planet passing through the Kuiper belt - by this math, once every 10 million years.

The reason why it's never been observed is that they are usually very far away and too small to be noticed.  Even with today's best equipment, it's nearly impossible to see a Pluto sized rogue planet passing through a lightyear or half a light year away and if they only pass through every 10 or 100 or more years, well, that's why we've never seen one.

It's possible, in our lifetime, someone might see one or two rogue planets pass within 1 light year of us, or inside the Oort cloud just past 1 light year, but we'll almost certainly need an upgrade in telescopes first.

on capture

In a two body system, gravitational capture is impossible and a rogue planet to our solar system is very much like a two body system.   The problem is the rogue object accelerates towards the larger object (the star) and it adds velocity.   That added velocity means it flies away just as fast.    In a two body system, objects are either already in orbit or they fly past.

In a loose sense, all the stars in the galaxy create an N-body system where capture becomes possible, but the problem is that the stars are so far apart that any secondary body gravitational effects from other stars is close to negligible.  The chance of Alpha Centauri (for example) slowing down an object so our Sun can catch it, is close to zero.   If it happened at all, it would be a very distant and very tenuous capture.   That's not to say it never happens.  Over 4 billion years of our solar system, capture may have happened several times, but I wanted to point out why capture is difficult and likely rare.  Most Rogue planets that got close enough would likely just pass through.

Capture becomes statistically more likely when a massive 3rd body is close.

If a Pluto-sized rogue planet passed close enough to one of our 4 large planets, or, the theoretical planet X, then it's direction and velocity could be significantly changed, and the odds of capture way up.   Needless to say, those 4 planets and the theoretical "Planet Nine" make very tiny targets in the vastness of space, but that's one way capture could happen and over the 4 plus billion years the solar system's been around, capture probably has happened from time to time.   The trick is getting a close enough look at distant orbiting objects to see if their chemistry indicates they aren't from our solar-system.

In addition to Rogue planet capture, when two stars pass close enough to each other, two stars exchanging Oort cloud objects probably happens too and might be the more common method of object exchange.  Oort cloud objects already have a relatively slow orbital speed around their star which makes striping them away from one star and being captured by another, somewhat more likely.   It would also depend on the relative velocity of the two stars also and how close they passed.   But this method of exo-object capture might be quite a bit more common than rogue object capture.

If an object like Sedna is eventually identified as not being from our solar-system, it would be hard to know if it had been a rogue planet or a "stolen" object from the Oort or Kuiper belt from a close passing star from long ago.


How dense would planet earth have to be to have the same gravity as Jupiter? I was reading this question about how small could a planet be while having earth-like gravitational pull.

This got me thinking, how dense would planet Earth have to be to have the same gravitational pull as Jupiter while all the other factors staying the same (even if it is impossible in the real world)?

If there are any formulas could you please explain them so I understand them please?

Edit

Sorry about some of the confusion but I meant keeping everything but the mass the same.

There are at least two interpretations to this problem:

Per Wikipedia, Jupiter's surface gravity is $2.528$ times Earth's. Thus,
if the Earth were $2.528$ times denser, it would have the same surface
gravity as Jupiter. The Earth's current density is $5.514$ grams per
cubic centimeter, so the new density would be $2.528 \times 5.514$, or about
$13.9394$ grams per cubic centimeter. This assumes we change Earth's mass, but not its radius.

@Rob_Jeffries answer assumes the Earth's mass remains constant and the radius changes. If the radius shrinks by a factor of $2$, the volume decreases by a factor of $8$, and the planet becomes 8 times more dense. The surface gravity increases by $4$, since it depends on the radius squared. In general, shrinking the planet's radius by $x$ will increase the density by $x^3$ and the gravity by $x^2$. If we want the gravity $2.528$ times higher, we choose $x = \sqrt{2.528}$ or right around $1.590$. This makes $x^3$ equal to about $4.019$. Multiplying that by Earth's current density of $5.514$, we get $22.16$ grams per cubic centimeter, pretty close to what Rob got.

So, you can't really change the density without changing anything else: either the mass or the volume must change.