How could time only have started with the Big Bang? I understand that before the Big Bang time (as well as dimensions) didn't exist. But how could this be? If there was no time then nothing could change, and so time itself couldn't come into existence.

This is both a physical and philosophical question because it depends what you mean by "time".

From a physical perspective, time doesn't really exist. We know that things change, and we measure a rate of change in relation to other things that also change (like clocks) but how we define time as an absolute concept is not something we have a firm answer to. It may not exist at all. To understand the details fo this you need to learn a whole lot of quantum mechanics, string theory and theoretical physics in general, which will take about a decade, two degrees and a doctorate. Alternatively, I've been reading a great book called "The Order of Time" by Carlo Rovelli. He is a theoretical physicist who has worked for decades to understand this stuff and then written all about it with hardly any maths and some drawings of Smurfs. I would highly recommend it.

Also, from a more philosophical perspective, if the Big Bang started with a singularity in which time and space and all matter were compressed into one single point with no dimensions, then that point contained no information about what was before it. If we can never know what was before the singularity (or even if there was anything before), then there is very little point in discussing it, so we can choose to set that as the zero point of time and call it the beginning because anything that happened before that is irrelevant. Like starting a stopwatch to time a race when the cars set off - there was time before, but that's not important for the race so we call the start of the race a time of zero.


Objection on artificial moon for lighting Some days ago i read about China's artificial moon mission for lighting cities

In my junior classes i was taught the effect of Moon's gravity on tidal waves.
According to me this is a very dangerous mission this can cause floods due to additional gravitational force.
Am I wrong?Please explain.

  I had searched on Internet about this defect of China's artificial moon for lighting but i didn't found any result.Many astronomers are against this mission as this will disturb natural timing of flora and fauna.But no one has raised the point ,that it will disturb natural motion of tidal waves.

This has been called "fake news" However tides are caused by gravity, and the proposal doesn't seem to require very massive satellites, hence no tidal waves.


What would a red giant Sun look like from Proxima b? As of now, Proxima b is the only confirmed planet (or dwarf planet if it didn't clear its orbit - sorry, couldn't resist) around Proxima Centauri, the nearest-known star to the Sun about 4.2 ly away. From that distance, the Sun looks just like an average star in the night sky. Now if the Sun became a red giant, at 256 times its current diameter (if I recall correctly), what would it look like from Proxima b's night sky? On a good telescope, Betelgeuse is recognizable as more than a dot, its surface is visible, that would surely be the case for a red giant Sun too. What would it take to recognize the Sun's surface from the Proxima system? Would the Sun perhaps even cast a visible shadow?

The Sun will not become a red giant for approximately 7 billion years, so there is little chance that Proxima Cen will be anywhere near it.
[EDIT: To answer a comment, the current helocentric radial velocity of Proxima Cen is -22 km/s. The Sun's escape velocity at the distance of Proxima Cen is about 0.1 km/s. So the Sun and Proxima Cen are totally unbound. With a relative speed of 22 km/s (at least - I haven't calculated the additional tangential velocity difference) they will be at least 100 pc apart within 7 million years, let alone 7 billion years.]
The Sun goes through TWO red giant phases. In the first, hydrogen shell-burning phase, the Sun will achieve a peak absolute V magnitude of around -3 at the tip of the first ascent red giant branch. It wil have a temperature of around 2700 K, be 256 times its present size and 2800 times more luminous according to Schroeder & Connon Smith (2008).
From a distance of 0.77 pc (the current distance of Proxima Cen) it would have an apparent magnitude of about -8.5 (about 40 times brighter than Venus).
Its apparent size in the sky would be 1.54 arcseconds, so would have a disc that was resolvable using a small telescope at a good site and would be orange/red in colour.
According to Schroeder & Connon Smith's model, the asymptotic giant branch phase of the Sun, when it has an inert carbon/oxygen core and He + H-burning shells will be slightly smaller and less luminous.
The exact values for both these phases are somewhat dependent on the details of the mass loss model used for the strong stellar winds expected.


The energy density of DM (to be fluid,state parameter=-2)increases with time. Does it violate the concept of accelerating universe? We know that dark energy with value of state parameter $\omega<-1$ is called phantom dark energy model. In this model if we assume dark energy to be a fluid with value of state parameter $\omega=-2$, we can say that the energy density of such dark matter increases with time.

My question is whether the above statement violates the concept of accelerating universe, because both the energy density and matter density turn out to be negative. If we use these values in the acceleration equation, we see the acceleration of the universe (second derivative of the scale factor) is negative.

My derivation is as follows. We have $\omega=-2$, so the equation of state is $p=-2\rho c^2$. From the fluid equation,
$$\dot{\rho}+\frac{3\dot{a}}{a} \left(\rho + \frac{p}{c^2} \right)=0\Rightarrow\rho\propto a^3$$
From the Friedman equations, $a=-k_1 t^{-2/3}$, so the energy density is $\varepsilon=\rho c^2=-kt^{-2}<0$. Hence the acceleration is
$$\ddot{a}=-\frac{4 \pi G}{3} \left(\rho + \frac{3p}{c^2} \right)=\frac{4 \pi G}{3} \times 5\rho = \frac{4 \pi G}{3c^2} 5\varepsilon$$ Since $\varepsilon <0$, this implies $\ddot{a}<0$.

For phantom energy model we have $$H^2 = H_0^2\Omega_pa^{-3-3w_p}$$ such that $w_p < -1$

$$\dot{a}^2 = H_0^2\Omega_pa^{-1-3w_p}$$

$$\dot{a} = H_0 \sqrt{\Omega_p} a^{-1/2(1+3w_p)}$$

$$\int a^{1/2(1+3w_p)}da = \int H_0 \sqrt{\Omega_p}dt$$

Now at this part we should define the integrals upper and lower bounds. When we set time from $t → t_0$

$$\int_a^{1} a^{1/2(1+3w_p)}da = \int_{t}^{t_0} H_0 \sqrt{\Omega_p}dt$$

We get something like,

$$\frac{2} {3(1+w_p)}[ 1 - a^{3/2(1+w_p)}] = H_0 \sqrt{\Omega_p}(t_0 - t)$$

$$a^{3/2(1+w_p)} =1 -  \frac{3(1+w_p)}{2} H_0 \sqrt{\Omega_p}(t_0 - t) $$

Let us take $w_p = -2$

$$a^{-3/2} =1 +  \frac{3}{2} H_0 \sqrt{\Omega_p}(t_0 - t) $$

So

$$a =(1 +  \frac{3}{2} H_0 \sqrt{\Omega_p}(t_0 - t))^{-2/3} $$

here $y$ axis is the scale factor $(a)$ and $x$ axis is the time $(t)$

For $C = H_0 \sqrt{\Omega_p}$ and $a=t_0$

As you can see scale factor goes to infinity

For the acceleration equation

$$\frac{\ddot{a}}{a} = -\frac{4\pi G}{3c^2}\epsilon_p(1+3w_p)$$

For $w_p=-2$

$$\frac{\ddot{a}}{a} = \frac{4\pi G}{3c^2}5\epsilon_p$$

From the graph and also from here its clear that $\ddot{a} > 0$.


Collision of 2 black holes There is a large number of visible Supernovas. Each week - about a 20 Supernovas Type 1a around the Universe.

Is there collisions of Black Holes? What is this collision called?

E.g. 2 black holes come close to each other. There are event horizons for both black holes, will this made such collision super long in Earth's time?

It's called a black hole merger, or coalescence. Here a simulation video.

Even the formation of the event horizons of the two initial black holes takes "super long" in Earth's time. That's similar with the merger. On the other hand we are very close to the completed merger within a short "Earth's" time seen from a distance, as soon as the merger starts. General relativity as well as quantum theory are incomplete with what will happen very close to a presumed singularity or at the presumed event horizon; this will remain disputed until a satisfying theory of quantum gravity is found.

Mergers of black holes are likely to occur, e.g. when two galaxies collide, the momentum of the central supermassive black holes (SMBH) is slowed down by consumption of gas, dust and stars, until the SMBHs merge to the central SMBH of the merged galaxy.
Here a galaxy merger simulation.

Here a simulation of the coalescence of two black holes within a collapsing star.

More on black hole binaries on Wikipedia.


Is there any habitable exoplanet around Tau Ceti? I was wondering.. is there any habitable exoplanet around Tau Ceti?

TLDR version: probably not, and claims for the habitability of planets in this system are on shaky ground.
Long version follows.
Planets
So as of Feng et al. (2017), there are four planet candidates around Tau Ceti:

Planet
Minimum mass ($M_\odot$)
Semimajor axis (AU)

Tau Ceti g
$1.75^{+0.25}_{-0.40}$
$0.133^{+0.001}_{-0.002}$

Tau Ceti h
$1.83^{+0.68}_{-0.26}$
$0.243^{+0.003}_{-0.003}$

Tau Ceti e
$3.93^{+0.83}_{-0.64}$
$0.538^{+0.006}_{-0.006}$

Tau Ceti f
$3.93^{+1.05}_{-1.37}$
$1.334^{+0.017}_{-0.044}$

Note that the designations Tau Ceti b, c and d refer to planet candidates that are no longer thought to exist. The error bars refer to the 1% and 99% percentiles. $M_\oplus$ is the mass of the Earth.
The Feng et al. (2017) paper also notes that the system is dynamically packed, which does not bode well for the prospects for additional planets between the known planet candidates (note that their figure 17 shows the regions where the planets would interfere with each other, not the regions of stability for an additional planet).
The habitable zone
The conclusion of the paper gives the luminosity of Tau Ceti as 0.52 times solar and the effective temperature as 5344 K. Using these values, the habitable zone limits can be calculated from Kopparapu et al. (2013), which assumes that habitable conditions are maintained by the carbonate-silicate cycle with carbon dioxide as the main (non-condensible) greenhouse gas.
Inner boundaries

Boundary
Distance (AU)

Recent Venus
0.551

Runaway greenhouse
0.723

Moist greenhouse
0.729

The moist greenhouse limit is the most conservative inner boundary, it occurs where sufficient water vapour enters the upper atmosphere that water loss begins to occur from the planet. In our solar system, Earth is located close to this limit in the inner part of the most conservative habitable zone.
The runaway greenhouse limit occurs where the positive feedback from water vapour overwhelms the stabilising negative feedback from the silicate-carbonate cycle, driving further evaporation of the oceans and higher temperatures. This is thought to have occurred on Venus, leaving the planet in the state it is in today.
The recent Venus limit is based on the possibility that Venus may have retained oceans for several billion years. This is not known for certain as our knowledge of Venus's evolution is rather incomplete and the conditions on the planet's surface are not favourable for driving rovers around investigating the geology.
From this we see that Tau Ceti e is located close to the recent Venus limit and is closer to the star than the runaway greenhouse limit. This suggests that any oceans that may once have existed would likely have boiled off, leaving the planet in a Venus-like state.
Planets g and h are too close to the star.
Outer boundaries

Boundary
Distance (AU)

Maximum greenhouse
1.279

Early Mars
1.330

The maximum greenhouse limit is the furthest distance from the star that a cloud-free carbon dioxide atmosphere can support conditions compatible with liquid water. Beyond this, the increased scattering leads to increased reflectivity of the planet and the CO2 would begin to condense, removing it from the atmosphere and leading to runaway cooling. This is the most conservative outer habitable zone boundary. Note that by this point, the planet would require several bars of CO2 which would make it toxic for humans.
The early Mars limit is based on the observation that Mars managed to maintain surface water (e.g. various rivers, and a possible northern ocean) in the early solar system when the Sun was significantly fainter than it is today. Tau Ceti f is located right at this limit.
Extensions to the habitable zone
None of the planets fall into the most conservative habitable zone, and Tau Ceti e and f are at the boundaries of the most optimistic estimates for the habitable zone boundaries. There are nevertheless options for extending the habitable zone.
At the inner boundary, a runaway greenhouse effect could be avoided on dry planets, where there simply isn't enough water to evaporate to drive the positive feedback, see Zsom et al. (2013). It isn't clear to me that such a planet can be described as habitable, since such planets may lack the hydrothermal systems that could act as the sites for abiogenesis. Their geological evolution would likely be substantially different to Earth's without water to lubricate plate tectonics.
Another possibility is on slowly-rotating planets, where substantial cloud layers can build up on the day side of the planet and increase the reflectivity, as noted by Yang et al. (2014). On the other hand, Scholz et al. (2018) have noted that there appears to be a universal mass-spin relationship that extends from planets to brown dwarfs. This predicts that super-Earths would likely spin too fast for this mechanism to work unless they have been spun down by stellar tides or a large moon.
On the outer boundary, adding additional greenhouse gases such as methane may work to extend the outer habitable zone, see for example Ramirez & Kaltenegger (2018). This has been suggested as the mechanism for allowing surface water on Mars, which would suggest that the "Early Mars" limit is an observed data point within the methane habitable zone. Another possibility is that a dense hydrogen atmosphere could maintain liquid water, e.g. Pierrehumbert & Gaidos (2011) though the pressure of such an atmosphere may well have implications for the geology of the planet and hence the potential for abiogenesis.
Planets whose climates are stabilised by something other than the carbonate-silicate cycle, or have substantially different atmospheric compositions would have different habitable zone boundaries (if subsurface oceans on icy worlds are habitable, there may be interesting prospects for dwarf planets in the outer debris belt), but this is already getting speculative enough, besides there is another possible objection to the habitability of these planets...
Planetary masses
A limitation of the radial velocity method is that only the minimum masses can be derived. With Tau Ceti, we have a possible means to estimate the true masses: the star is surrounded by a debris disc (this would likely provide a source of impactors onto the planets, how bad the situation is depends on how much material is being perturbed into the inner system). Using Herschel observations, Lawler et al. (2014) give an inclination of 35±10 degrees. Assuming that the planets lie in the same plane as the disc, the true masses would therefore be approximately 1.74 times greater than the minimum masses.
Under this assumption, the true masses of the planets e and f both come out as about 6.85 Earth masses. Taking the 99% lower limit on the minimum mass error bars and a 45° orbital inclination as a low estimate, these would be 4.65 Earth masses for e and 3.62 Earth masses for f.
The nature of the planets
According to Rogers (2014), the transition between rocky and Neptune-like planets is somewhere in the region of 1.4 to 1.6 Earth radii. Using the mass-radius relationship from Zeng et al. (2016) and their core mass fraction of 0.26 for typical terrestrial planets, these radius limits correspond to terrestrial planets of roughly 3.3 to 5.4 Earth masses.
This suggests that Tau Ceti e and f are fairly likely to be sub-Neptunes rather than rocky planets, although the caveats are that in the optimistic case they can have masses below the rocky/Neptune-like transition, and that there do seem to be a few cases of rocky planets above the transition (most of those are likely to be evaporated cores of Neptune-like planets, which wouldn't apply to Tau Ceti e and f as they have much lower levels of stellar irradiation).
Conclusion
Given the current state of knowledge, Tau Ceti does not look like a good prospect for habitable planets. Tau Ceti e and f are rather marginal in terms of their location within the habitable zone, and their masses are sufficiently high that there is a good chance that they are sub-Neptunes rather than rocky planets. The dynamical packing of the system makes it unlikely that there can be a smaller, temperate planet in the habitable zone between the known planets.


Is there an O1 or O0 star? Okay, we've seen the super hot Wolf-Rayet stars, especially WR 102 and 142, and the "slash stars," many of which are early O (O2-4.5/WN). We know the temperatures of these Wolf Rayet stars. So if we know that, what would their spectral types be in the standard Morgan-Keenan spectral classification (i.e. O2V or B0Ia+), and are there known stars with spectral class earlier than O2?

This is what Wikipedia says about it:

When the MKK classification scheme was first described in 1943, the only subtypes of class O used were O5 to O9.5. The MKK scheme was extended to O9.7 in 1971 and O4 in 1978, and new classification schemes that add types O2, O3, and O3.5 have subsequently been introduced.

It references the paper A New Spectral Classification System for the Earliest O Stars: Definition of Type O2

Thus, a new earliest spectral type has been defined.

So unless that information is outdated, there's no such thing as O1 or O0.


What eyepiece to use for moon? I'm using a 95mm f/8.4 telescope. What's the best eyepiece that I can buy for a very close look at the moon or even planets? I'm a beginner in this field so please help me.
Thank you.

Almost all the time, the best eyepiece to use would be the 20 mm lens for seeing the moon. If you want a better view, then you can go for the 10mm. That's what I would do...


Observational evidence for the existence of black holes What is the direct observational evidence that black holes exist? I have read that black holes have been detected through X-ray emission. What is some other observational evidence for black holes?

There are a few different features of black holes that researchers look for:

An accretion disk
Mass transfer from companion star
X-ray emission
Absorption of gas and other matter around it
Gravitational lensing

You mentioned #3 in your question; quite a few black holes, including Cygnus X-1, emit X-rays.

1 is a common feature around black holes. The material can be pulled from surrounding gases, or, in many cases, a companion star. Accretion disks generally emit electromagnetic radiation; the exact type depends on the type of material and the object it surrounds.

2 is related to 1 and 3, but it deserves its own explanation because of the effects on the donor star. Lets take mass transfer on a large scale. Take the Whirlpool galaxy. It is interacting with its neighbor, NGC 5195, via a bridge of dust and matter. What are the effects on NGC 5195? Distortion, as well as loss of structure in the area near the bridge. The same thing happens on the stellar level. A star losing mass can become distorted in the direction of its companion, potentially causing changes in brightness or other features.

4 is, I suppose related to the others, but I should note that if there were merely gas clouds surrounding the black hole, it could also swallow those up. If a black hole is not in a binary system, it may not come in contact with another star, and will instead begin swallowing other bits of matter around it.

5 is the best characteristic; a better way of detecting black holes. General Relativity predicts that massive objects bend light; using Einstein's equations it is possible to determine just how much light will be bent by such an object. This has been used in many cases, such as during the solar eclipse of 1919, to confirm Einstein's theory.

Finally, I should note two things:

These are not the only methods of detecting black holes (other effects, such as frame dragging around a Kerr black hole, offer distinctive descriptions of the black hole), but are rather straightforward
1-4 can also be signs of other compact objects such as white dwarfs and neutron stars, and are often only found in binary systems. Only by using a multitude of different observations, and careful analysis, can an object finally be designated a black hole.


Simple Question about Constellation I am currently self teaching myself some basic astronomy. My book claims, if a constellation is observed for exactly 6 months during a year, then it lies on the celestial equator. I have failed to understand why this must be true. Shouldn't the visible duration depends on the position of the observer? For example, for an observer at equator, wouldn't all constellations (accept those at the polaris) be visible for exactly half a year? Also, is the constellation at the NCP always visible for people in the northern hemisphere? Thank you in advance!

Taken at face value it's not correct that points on the equator are visible for exactly six months.

For example, Orion is on the celestial equator. It is true that Orion will be above the horizon for half the day (12 hours), but during the summer when it is above the horizon, so is the sun, so it can't be seen.

But Orion is visible from  Northern Europe between the middle of August (when it rises shortly before the sun) and the middle of April (when it sets shortly after dusk) That is rather more than six months. Exact dates can't be given as visibility during twilight depends on factors like the clarity of the atmosphere, and stars don't wink off as the sun rises, they fade out.

On the other hand, if you always observe at the same time then points on the celestial equator will be above the horizon for six months of the year, but just being above the horizon doesn't make it visible, when close to the horizon the thicker atmosphere (and more prosaically, trees and buildings) will make a constellation effectively obscured.

It is true that the north celestial pole is always above the horizon, as are many of the constellations around it. From my location that includes Cassiopeia, Ursa minor, most of Ursa major.

More generally, for Northern Hemisphere observers, the further north a point is, the longer it will remain visible.


Can a planet's changing tilt be aligned with the rotation around its star? What I'm asking is if the tilt of a planet can "follow" the rotation around its star so that, for example, its north pole would always lean towards the star, and thus always be under daylight. The planet could have a tilt similar to earth's 23.5°. And can that planet have a rotation around its axis, allowing for day/night cycles closer to the equator? Hopefully this image will explain what I mean. The tilt (red line) stays the same, but the pole is leaning toward the star throughout the whole year, while the planet rotates around its axis.

No, or at least not for a planet of any size. To change the absolute direction of the axis of rotation of a planet needs a large force acting in some way asymmetrically. In the case of the Earth this comes from the gravity of the sun and the moon acting on the Earth's equatorial bulge and it takes 26000 years to rotate the Earth's axis around a cone 46 degrees wide. To rotate the axis in a full circle (a cone 180 degrees wide) in a single year would only be imaginable for a very irregular planet (which means a small one, since big ones collapse into spheres under their own gravity) probably with a very large and close moon to pull on it.


The laws of physics through out the universe How do we know laws of physics are the same throughout the universe? Intuitively I would say they would vary in two natural ways: the constants in the equations may vary or the math in the equations may vary. As a guess they could change over a long time. What is the furthest radius we can prove from earth, with absolute certainty, that the laws of physics do not vary? I am aware this may not be a radius but a more complex shape that cannot be simply described by a radius.

The nearest answer I can think of for a radius is a guess. And that guess is based on the furthest physics experiment we have done from earth. Which I think is an experiment with mirrors on the moon. Therefore if we assume (I don't know if this assumption is totally 100% reasonable) all physics laws hold because this experiment works. Then the radius is to the moon. This doesn't give an concrete answer for the radius, merely an educated guess.

Let's start in the middle:

  What is the furthest radius we can prove from earth, with absolute certaintity, that the laws of physics do not vary?

Zero. Proofs are found in mathematics and court rooms, and are impossible in natural science. The best we can do is have falsifiable theories. This holds for every description of reality - there's no "proof" even for the Laws of Gravity.

So, what could we observe that would tell us that physical constants or relationships between physical quantities are different in other parts of the universe, or at other times during its existence?

Gravity: For galaxy clusters, we have independent mass measurements from several different sources that agree within their (admittedly large) error bars. Gravitational lensing, velocity dispersion of the member galaxies and X-ray temperatures are all in agreement. So the laws of gravity seem to work even at redshifts up to 0.5 or even higher.
Atomic physics: We observe highly redshifted objects. The wavelength of the light emitted by these objects is made longer by the expansion of the universe. Observing redshifted spectral lines of different chemical elements (or molecules) tells us that atomic physics worked the same when and where this light was emitted. If the transition levels between electron orbits had changed over time, we would get different redshifts for the same objects depending on what element's spectral line we observe.
Nucleosythesis: Shortly after the big bang, the temperature lowered such that protons and neutrons were no longer created and destroyed constantly. A free neutron has a half live of about 8.5 minutes before it decays into a proton and an electron. Our theories predict that we'd get a helium (2x proton, 2x neutron) content in the universe of about 25%. (The rest of the "normal" matter being essentially all hydrogen), and that is indeed what we observe. Now, the helium content is dependent both on the matter density at the time this took place and the half live of the neutron. From other observations (BAO come to mind) we are fairly certain that we got the matter density about right. Which leaves only a small wiggle room for the half live of the neutron, and hence for changes in the weak force.
We've covered gravity, electromagnetism, and the weak force. I don't know any good test for the strong force.

For a change of natural laws over time, we can look at the isotope distribution in rocks here on earth. We should be able to tell whether the decay rate of various elements was different at earlier times by looking at how many of each of their decay products are around.

To summarize, we cannot say with "absolute certainty", but what we observe seems to indicate that natural laws are the same throughout the universe.


What is meant by "vastness of space, which now filled a volume of a hundred million light years"? I am reading the book Cosmic biology: How life could evolve on other worlds (citation below) and do not understand the meaning of the following paragraph from page 4 (emphasis mine):

It took 200,000 years or more for the universe to cool to 2700 °C, a temperature at which the protons and neutron-proton aggregates could start capturing the free flying electrons to form the first atoms of hydrogen and helium.  As the dense fog of electrons condensed into newly formed atoms, the opaqueness cleared and photons could stream without interruption across the vastness of space, which now filled a volume of a hundred million light years.

I am under the assumption that a light-year is a unit of measurement for distance and spatial volume is expressed as though it fills a cube (e.g., 100 ly^3).  Even if this practice of denoting volume was unintentionally omitted, the claim does not satisfy my attempt to calculate the spherical volume:
Given 200,000 years of elapsed time since Big Bang -> photons could have traveled a distance of 200,000 ly in any direction.
Formula for radius of a sphere: $$\frac{4}{ 3} \pi r ^ 3 = \frac43  \pi  (200,000 ^ 3) = 3.35\times 10^{16} ly.$$
This result is much larger than "[one] hundred million light years."
Am I misreading this paragraph?

Irwin, Louis Neal, and Dirk Schulze-Makuch. Cosmic biology: How life could evolve on other worlds. Springer Science & Business Media, 2010.

I think this is at best a weird typo, but more likely a confusion by the authors (who are not cosmologists or astronomers, but a biologist and a geologist).
The book is 10 years old, but our view of the timeline of the evolution of the Universe was pretty much the same then. Note that the calculation of the size of the Universe as a function of time is a bit more complicated than you assert, because it expands while photons are traveling.
The three number that the authors give — $200\,000\,\mathrm{yr}$, $2\,700\,^\circ\mathrm{C}$, and 100 million lightyears (Mlyr) — do not correspond to the same epochs, as I will discuss here:
Recombination began at t ~ 200,000 yr
The process the authors discuss is known as the recombination of hydrogen, followed by the decoupling of light from the gas. At an age of $200\,000\,\mathrm{yr}$, the Universe had cooled to $4\,500\,\mathrm{K}$, and atoms began to recombine. At this point, the region that is the observable Universe today had a radius of almost 30 Mlyr, i.e. a volume of some $10^5\,\mathrm{Mlyr}^3$. However, the observable Universe at that time was much smaller, because light hadn't traveled so far — the radius was less than half a Mlyr.
Photons decoupled at T ~ 2,700 ºC
The photons didn't decouple yet, though. Exactly when this happened is a somewhat extended period of time, but can be taken to be the time when the mean free path of a photon is of the order of the size of the observable Universe. This happened around when the Universe was $380\,000\,\mathrm{yr}$, at which time it had cooled to $3000\,\mathrm{K}$, or $2\,700\,^\circ\mathrm{C}$. At this time the radius of today's observable Universe was still only around 40 Mlyr, while the observable Universe at that time was still less than 1 Mlyr.
The diameter of the Universe reached 100 Myr much later
When the Universe was roughly half a million years old, the radius of today's observable Universe had expanded to 50 Mlyr, so its diameter was 100 Mlyr. But firstly, this was quite a lot later than the recombination/decoupling, and secondly it doesn't make much sense to refer to the size of today's observable Universe, since that had no physical significance at that time. The radius of the then's observable Universe didn't reach 100 Mlyr until the Universe was almost 20 million years old
Summary in a figure
The figure below shows how the progression of recombination, from ~100% ionized gas when the Universe was around $200\,000\,\mathrm{yr}$, to ~100% neutral gas when it was $\sim 400\,000\,\mathrm{yr}$. I calculated this by solving the Saha equation assuming a pure hydrogen gas, i.e. neglecting helium, but this is a minor contribution so I think it should be okay.
Along the line you see corresponding temperatures in red, and ratios between the photon mean free path and Hubble distance (~size of the Universe) in green. When this ratio is of order unity, photons decouple. The secondary $x$ axis show the corresponding redshift.


Computing the rate of orbital decay We know that the estimated time until a binary system merges is given by: $$\dfrac{5c^5r^4}{256G^3(m_1m_2)(m_1+m_2)}$$ But what is the formula to determine rate of decay, in some sort of distance unit, per unit of time? Also, what are terms are $r$ and $m_i$ written in?

Here's one way to arrive at ProfRob's answer step by step:
$$t = \dfrac{5c^5r^4}{256G^3(m_1m_2)(m_1+m_2)}$$
If we lump all the constant terms together:
$$C = \dfrac{5c^5}{256G^3(m_1m_2)(m_1+m_2)}$$
then the problem suddenly looks a lot simpler:
$$t = r^4 C$$
$$\frac{dt}{dr} = 4r^3 C$$
$$\frac{dr}{dt} = \frac{1}{4r^3} \frac{1}{C}$$
$dt$ is how much longer the system will live if the starting radius is increased by $dr$. We know that if we watch it decay, the rate of decrease per unit time $dr/dt$ will be negative, so we'll add a minus sign.
Now put it back together:
$$\frac{dr}{dt} = -\frac{1}{4r^3} \frac{1}{C}$$
$$\frac{dr}{dt} = -\frac{1}{4r^3} \dfrac{256G^3(m_1m_2)(m_1+m_2)}{5c^5} $$
$$\frac{dr}{dt} = -\frac{1}{r^3} \dfrac{64G^3(m_1m_2)(m_1+m_2)}{5c^5} $$
$$\frac{dr}{dt} = -\dfrac{64G^3(m_1m_2)(m_1+m_2)}{5c^5r^3} $$
With gravitational constant $G = 6.674 \times 10^{-11} \text{m}^{3} \text{kg}^{-1} \text{s}^{-2}$ the speed of light $c=2.997 \times 10^{8} \text{m/s}$ each body with a solar mass $M_{\text{Sol}} = 1.9885 \times 10^{30} \text{kg}$ and an almost-touching separation of a million kilometers $r=1\times 10^{9} \text{m}$, then $C = 1.0102 \times 10^{-20}$ and the rate $dr/dt = -2.4748 \times 10^{-8} \text{s}^{-1}$ or -78 centimeters per year.


Can information leave the observable Universe? From what I gather, the observable universe is expanding at the speed of light. In addition, information cannot travel faster than the speed of light. It seems as though these two facts would imply that information cannot leave the observable universe. However, if that is true, it would either mean that the universe started spread apart, or that the observable universe is the entire universe. So, which of these explanations is correct?

Good question! I will need to go into some cosmology to answer it, my main source being Davis & Lineweaver (2003).

Nothing traveling through space should be able to leave the observable universe. However, information can and will inevitably leave our observable universe. How is this possible?

The Universe is expanding.

If we lived in a static universe, no objects would leave our observable universe. However, in our accelerating universe, space is being created between objects, with farther objects drifting away faster than closer ones.

Einstein said nothing can travel through space faster than light. However, space is literally being created between objects, so they can be pushed away from each other faster than light. So while the observable universe is expanding at the speed of light, distant objects are moving away from us even faster.

And the result? Take a look at this image:

This describes how the observable universe will evolve. The Hubble sphere defines the area in which objects are receding from us at or below the speed of light. Beyond this, objects are far enough to recede from us faster than light.

The light cone is the region of the Universe capable of influencing us today. Essentially, it is the observable universe, and its boundary is clearly marked. It is, as you mentioned, growing at the speed of light.

The light cone does not contain the entire Hubble sphere, since photons from many objects receding faster than light cannot reach us yet. Conversely, the Hubble sphere doesn't contain the entire light cone. This is because photons emitted by objects outside of the Hubble sphere can crawl into regions of space that are receding from us a bit slower than the one from which they were emitted. They can then crawl into regions that expand slower than the last one, and so on. Eventually, the photons will reach regions of space that aren't expanding faster than light, and they can reach us.

Now, there is a distance beyond which space expands faster than the light can traverse it. This distance is called the cosmic event horizon. Light from beyond the event horizon will never reach us. Our observable universe grows because more photons come into our view. However, the observable universe will infinitely approach the event horizon, since light from beyond there can never reach us.

Thus, after an incomprehensibly long time, the observable universe would stop growing. At this point, it may finally be possible to travel through space beyond the observable universe.


Why does Sirius proper motion "wiggle" with a 1 year period, when Sirius A and Bs binary orbit is a 50 year period? Some stars, if observed repeatedly over time, show a perturbation or "wobble" in their proper motion. If this is a periodic occurrence we can infer that the perturbation occurs due to the gravitational influence of an unseen companion.

In Sirius Matters, Noah Brosch describes a secondary wiggle,

"The trajectory described by the two components of Sirius shows an additional component of motion as tiny wiggles super-posed on the wider modulations of the proper motion by the orbital motion of the Sirius pair. The wiggles have a period of one year. "

What causes this second wiggle?

Your vantage point changes throughout the year as the Earth moves around the solar-system barycentre (close to the centre of the Sun). That means the positions of nearby stars "wiggle" with respect to more distant background stars, with a period of one year; the amplitude of this wiggle is how you determine the parallax distance to the object.

In the case of Sirius AB, this wiggle is superimposed on a motion caused by the binary orbit of the two components in the Sirius AB system and by the motion of the Sirius system with respect to the Sun projected onto the plane of the sky - the proper motion.


Is there an all sky meteor watch with spectroscopy? I assume performing spectroscopy on meteors would give us information about the composition of the outer layers of meteoroids, which we can't study on finds because it has already burned up. This would increase our knowledge on the small bodies of the solar system.
There are programs, like CAMS or FRIPON, that watch the entire sky to spot meteors. These are just regular cameras.
We can perform spectroscopy for many points in the sky simultaneously, like with MUSE, so it would be possible to monitor most of the sky continuously to get spectroscopic data of meteors.
Has this been done? If not, why not?

You can do this kind of thing reasonably easily, even as amateur astronomer. See e.g. this link. There also have been programmes by the Americal Meteor society and there are a lot of published papers to that end, e.g. here
Two reasons it has not been done more widlely:
It's a difficult and very costly endevour to make high-resolution spectroscopy at very short time intervals - at the time you have for the meteor to show. There is no reasonable technique to justify a setup which points a large telescope within sub-second time to an arbitrary location as identified by a full-dome camera scanning the whole sky - to which you will have to attach the spectrograph.
At the same time there is little reason to believe that the outer material of meteorites which ablates in the upper atmosphere is different to what we find as meteorite on Earth. The surface is altered, and the processes are well-understood. Thermal conductivity and inertia are very small so that below this very shallow crust the material is unaltered. That said, missions like the Apollo missions as well as StarDust and similar did in-situ analysis of interplanetary material which has not been thermally altered in Earth's atmosphere.
General statistics on type of meteorites, including their chemical composition and origin can also be done with the finds from Earth's surface.
So in summary: the cost to gain ratio for such endevour might be much smaller than you seem to anticipate.


Do black hole singularities actually merge? new questioner here so please be gentle.

Do the singularities of merging black holes actually merge together?  I mean there are 2 infinitely small objects (singularities) that are trying to find each other but for them to merge they have to join at the EXACT same point in space.  I know they can get close, but to expect them to align perfectly with zero tolerance seems impossible.

Infinities are hard to bend the mind around, but in this case, the merge is not impossible. Yes, the distance between them must reach zero in order to make the black holes merge, but the rate of which energy is lost to gravitational waves also increases when they get close to each other.

We are therefore dealing with a $\frac{\mathrm{infinity}}{\mathrm{infinity}}$ problem, where a finite limit may, and in this case does exist.

Do not forget your $\lim$'s!


If I look beyond (about same region, higher redshift) a galaxy, will I see its progenitors? Is there a range of redhsift dz, such that if I look at z+dz from a massive object at redshift z, I will see its progenitors?
(in a LCDM scenario of halo assembling, with smaller halos evolving towards larger ones across the cosmic time)

I am looking for a detailed explanation of this (maybe naif) question.

I think I understand what you mean and the answer is: specifically no; but generally yes.

If we look out into space, we can divide up what we can see into redshift slices of arbitrary thickness. The light we see from galaxies in each slice has been travelling for a certain amount of time, so we are seeing that "piece of space" at a particular cosmic epoch corresponding to its redshift.

If we look past that galaxy to a higher redshift slice, then what we are seeing there is a different patch of space at a younger cosmic epoch. i.e You cannot see the same galaxy as it was at a different time. We see each and every galaxy only once.

But in general you will be seeing younger galaxies at higher redshift. In an LCDM model then smaller galaxies build up into larger ones, so there will be a higher density of galaxies at higher redshifts (even after accounting for cosmic expansion), but the galaxies they will produce by merging etc. are not yet visible to us. It is possible that we will see them in the future (depending on the exact values of the cosmological parameters and what redshift we are talking about) as that distant patch of space recedes from us and becomes older (in cosmic terms).


When (yyyy-mm-dd) does the north pole of uranus most nearly point towards the sun? When (yyyy-mm-dd) does the north pole of uranus most nearly point towards the sun?
The information I've found suggests this happened in 1944 or 1945, but would like to find a more precise date or alternately what the heliocentric longitude is.
The "Poles of Astronomical Bodies" article on Wikipedia lists the RA and Dec, but doesn't include the Geocentric distance (otherwise, I think I could just translate between geocentric and heliocentric coordinate systems and have my answer).
Thanks
Tim

I have made an interactive simulation of Uranus and its seasons at https://ecliptiqc.ca/UranusEN.php. Playing with it, I get the north pole of Uranus pointing sunwards in early 1946 (my steps are 6 months, so I can’t be more precise for now).
The actual date may be slightly different, as I use a “fixed” orbit instead of the osculating elements, but it would be a few days or weeks off at most.


Data to "check" Kepler’s first law I want to "check" Kepler’s first law by using real data of Mars. From the equation of the ellipse, I derived
$$\frac{1}{r}=\frac{a}{b^2}+\frac{a}{b^2}\cdot\epsilon\cdot\cos(\varphi),$$
where $a$ is the major semi-axis, $b$ is the minor semi-axis and  $\epsilon$ is the eccentricity of the elliptic orbit. I'm looking for the following kind of data:

Mars' distance from Sun $r$
the angle $\varphi$ between Mars, Sun and the principal axis of the elliptic orbit.

Then, I want to check, whether $r$ and $\varphi$ fit the measured values of $a$, $b$ and $\epsilon$.
If there is no such data (perpendicular view on Mars' orbital plane) available, how can I transform data given in other coordinate systems to the ones I need? On a NASA website (https://omniweb.gsfc.nasa.gov/coho/helios/heli.html) I found data in "Solar Ecliptic", "Heliographic" and "Heliographic Inertial" coordinates, but I don't know which come closest to my plan.
Update:
I tried it with uhoh's recommendations. Unfortunately I failed.
With the following python code, using the Horizons x, y, z data stored in an xlsx file,
from __future__ import division
import numpy as np
from statsmodels.regression.linear_model import OLS
from statsmodels.tools import add_constant
from statsmodels.tools.eval_measures import aicc
import pandas as pd
import matplotlib.pyplot as plt
horizons = pd.read_excel("horizons2.xlsx")
horizons = np.array(horizons)
horizonsxyz=horizons[:,2:5]
horizonsxyz=np.array(horizonsxyz, dtype=np.float64)
hx=horizonsxyz[:,0]
hy=horizonsxyz[:,1]
hz=horizonsxyz[:,2]

horizonsr=np.sqrt(hx**2+hy**2+hz**2)
horizonsr=horizonsr*6.68459*(10**(-9))

phi=np.arctan2(hy, hx) * 180 / np.pi
phi2=np.mod(phi+360, 360)
phia=np.mod(phi-286, 360)
phiganz=add_constant(phia)
horizonsdurchr=1/horizonsr

horizons_regr=OLS(horizonsdurchr, phiganz).fit()
print(horizons_regr.params)
print(horizons_regr.summary())
y_pred_horizons=np.dot(phiganz, horizons_regr.params)
print(horizons_regr.params)

I get a value of $7.1349\cdot10^{-1}$ for $\frac{a}{b^2}$. This is bad but at least in the right order of magnitude. However for $\frac{a}{b^2}\cdot\epsilon$ I get a really bad value of $-2.89228\cdot10^{-4}$. Deviding the two result yields an estimated excentricity of $0.00044$ which is really far away from the true $0.0934$.
I also tried another approach, using the heliographic data mentioned above. Here, I get closer, but only if I add 35 degrees to the angles, which doesnt make sense, since I should add 74 degrees or subtract 278 degrees, to get the angle relative to the perihelion.

Great project! and welcome to Stack Exchange. I'll post a short answer but I think someone can add a more detailed, thorough and insightful answer.
I think that website is not well suited, so I'll answer based on you switching to Horizons. If you like Python then it's more fun to use Skyfield.
If you want apply an equation based on a Kepler orbit model, you'll need to use data where the Sun stays in one place and Mars orbits around it. That would be Heliocentric with the Sun at (0, 0, 0).
That there are three zeros raises the issue of the number of dimensions; proper Kepler orbits are sort-of in 3D i.e. they have an orbital plane that can be tilted to a reference plane, but the orbits are planar. Two problems; your equation assumes 2D flat orbit because of the way $\varphi$ is defined. Ideally you'd like data in the plane of Mars' orbit and you may need to transform NASA/JPL Horizons data into Mars' orbital plane yourself because there are only two main "official" planes, no real planet remains perfectly in a plane.
So what you do depends on how far down the rabbit hole of pretending orbits are planes that you want to go.
Zeroth order approximation
Go to Horizons
Use this tutorial and set it up to match the following:
Current Settings
Ephemeris Type:      VECTORS
Target Body:         Mars [499]
Coordinate Origin:   Sun (body center) [500@10]
Time Span:           Start=2020-10-04, Stop=2020-10-05, Step=1 d
Table Settings:      quantities code=2; output units=KM-S; CSV format=YES
Display/Output:      default (formatted HTML)
             -- OR --
Display/Output:      download/save (plain text file)

Here's a sample line for Mars for today using the Sun as origin (I've truncated some decimal digits). You see right away that Mars is about 201 million km from the Sun, it is also about 4 million km below the J2000.0 ecliptic.
2459126.500, A.D. 2020-Oct-04 00:00:00.00,  2.036231544E+08,  5.355405115E+07, -3.872888712E+06...

From here you can approximate
$$r = \sqrt{x^2 + y^2 + z^2}$$
and
$$\varphi = \arctan2(y, x) - \text{286.502°}$$
Since you are going through all four quadrants it's better to use a computer's arctan2(y, x) or atan2(y, x) with two arguments, not $\arctan(y/x)$ which only works in two quadrants (i.e. 1/7 = -1/-7).
First order approximation
You see right away that Mars is about 201 million km from the Sun, it is also about 4 million km below the J2000.0 ecliptic.
If you want to correct for Mars' orbit's tilt with respect to the ecliptic, you can just find the best plane fit to one Martian year's of data and make your own Mars ecliptic.
But I recommend you do the zeroth order first and see how well or poorly it works, then you can decide if you want to tilt.


What is the maximum distance measurable with parallax? What is the furthest star or celestial object whose distance has been calculated with parallax and how does it compare to the theoretical limit using today's telescopes? And how exactly does telescope aperture relate to the maximum distance measurable (other than the bigger the aperture the bigger the distance)?

Quick Google reveals a couple simple analyses.  For example,

  The Andromeda Galaxy, M31, is the nearest major galaxy to the Milky
  Way. The distance to M31 has been measured using other techniques to
  be
  2.5⋅10^6 light years , or 7.6⋅10^5 parsecs. Using the slightly modified parallax formula, we can find the necessary parallax angle to
  measure the distance to Andromeda. $ p = \frac{1}{d} =
> \frac{1}{7.6*10^5} parsec = 1.3 *10^{-6} arc-seconds $

  This is an incredibly small angle. For comparison, the resolution of
  the Hubble Space Telescope is 0.05  arc-seconds, so even Hubble would
  not be able to detect the necessary angular shift of the nearest
  galaxy to effectively use parallax as a measure of its distance.


Is there a radius inside of which objects are (doppler) blue shifted? The Andromeda galaxy is about 600,000 light years away and is doppler blue-shifted.  Are there objects closer to us than Andromeda which are red-shifted?  Are there objects farther than Andromeda that are blue-shifted?

I'm curious as to whether there is a more or less uniform radius from earth outside of which objects are generally all moving away from us, and inside of which objects are generally all moving towards us.

No, there is no spherical volume of space within which objects all tend to approach us and thereby show blue-shift. The fact that the Andromeda galaxy is blue-shifted is because at these relatively small distances the cosmological red-shift is much smaller than further away. Andromeda's own (non-cosmological speed) is larger then the cosmological speed away from us and it happens to move towards us and is therefore blue-shifted. It could also have been moving away from us, and be red-shifted as a result, but that red-shift would not be cosmological.

I'd expect that the chance that a nearby (Local Group) galaxy is either moving away from us or moving towards us is 50%.

Furthermore, the Andromeda galaxy, and all other galaxies belonging to the Local Group, are gravitationally bound and would therefore not show any cosmological red-shift anyhow.

NB. The Andromeda Galaxy is actually 2.5 million light years away from us.


Any simple experiment with an H-alpha telescope? Is there any simple experiment that can be done with an H-alpha telescope, for example to estimate the Sun's mass, size, distance, temperature or intensity?

I give lessons about renewable energy and it would be nice to somehow integrate a telescope (PST Coronado + double stack) to the chapter about photovoltaics and solar thermal energy.

Right now, the only "experiment" I could come up with was to show that there's often nothing to see because of the solar minimum. But we also wouldn't see any feature if the telescope was not focused or not well calibrated.
With some luck, it should be possible to follow the movement of a sunspot over a few days and estimate how fast the sun is rotating, possibly at different latitudes.
I suppose that in order to calculate many sun characteristics, it is mandatory to know the average distance between Earth and the Sun. It seems to be relatively hard to estimate 1 AU.

Is it possible to use the telescope for any experiment and estimate an order of magnitude for any of the Sun characteristics, assuming that the distance to the Sun is approximately 150 000 000km?

If you have the right filters and equipment you can make doppler measurements of the $H_\alpha$ line from the sun. Since an H-alpha telescope directly detects this you can use this to measure the doppler shift. Using this you can measure the rotation rate of the sun. This has been done before with a different telescope and the paper is here.

It should also be noted that if you don't find an adequate experiment just seeing the sun thru your telescope makes a profound impact on the viewer. One writer wrote that " I watched with a mix of awe and fear. Ever since that time, I've seen the Sun not so much as a sunny companion but as a star to be reckoned with."
Reference is here. That link and this one discuss viewing the doppler effect using an H-alpha telescope.


Smallest body that can be observed from Earth? What is the minimum size of an object that can be observed from Earth with our most powerful telescope?

I understand that the answer depends on how far the object is from Earth. For the sake of  discussions let us consider distances less the orbit of Neptune.

The smallest natural object that I know of that has been detected from an Earth-bound telescope is 2011 CQ1, a one-meter asteroid observed while specifically looking for NEOs.

As DeerHunter mentions in a comment, smaller artificial objects are identified and tracked, mostly by NORAD and some other national defence centers.


What might some examples be of radio telescope interferometric arrays made from "cheap components relying on massive computing power"? This answer mentions that there are some interferometric radio telescope arrays

  ...consisting of very cheap components relying on massive computing power to retrieve the signals from noise...

The radio interferometers that normally come to mind for me are the VLA and especially ALMA type, where there are only dozens of dishes, each one extremely high-tech and chock full of analog and digital electronics, often linked by high speed fiber optic cables.

What might examples of arrays made from "cheap components relying on massive computing power" be?

I'm going to compare the Murchison Widefield Array (MWA) to the Green Banks Telescope (GBT) just to pick two rather big projects.

The first phase of the MWA featured 256 128 tiles and cost A$ 51 million.
About the MWA: http://www.mwatelescope.org/telescope
It saw first light in 2013.

edit: the first phase comprised 128 tiles only but I could not find out if the 51 million were the price for the first or the first and second phase.

The GBT cost US$95 million and saw first light in 2003.

To make it compare better: US$ saw an inflation of 1.27 within 10a making a total of USD 120 million. AUD is 0.68 USD bringing down the cost of the MWA to USD 34.5 million.

both telescopes got a lot of upgrades later.

It is difficult to compare but the GBT has a much higher receiver area while the MWA has a vastly greater baseline. They serve different purposes. From this point of view they don't seem to differ in an order of magnitude in pricing.

But the question was about "cheap" parts. Here the costs of the MWA are broken down (page 8). Only 12% of the total costs are related to the front end (i.e. antenna and beam steering electronics), the rest goes in equal parts to the infrastructure and the back end. Considering that in a design like the MWA a lot of signal processing is already part of the design it might even be cheaper in total when considering costs for later upgrades.


How to convert luminosity at rest frame wavelength of 1450 A to absolute magnitude at 1450 A? How do I convert the luminosity (erg sec$^{-1}$ Hz$^{-1}$) of a quasar at a rest frame wavelength of 1450 Angstroms to absolute magnitude at the same wavelength?

I know that the bolometric luminosity is related to absolute magnitude via this relation from Bolometric magnitude:

$$M_{bol, ★} - M_{bol, ☉} = -2.5 log_{10} \left( \frac{L_★}{L_☉} \right)$$

Should the same relation be valid for the 1450 A rest frame luminosity and I just used that luminosity instead of the bolometric luminosity?

The absolute magnitude of an object is defined as the brightness of the object observed at a distance of $d = 10\,\mathrm{pc}$. With this distance, you can convert the luminosity density $L_\nu$ in $\mathrm{erg}\,\mathrm{s}^{-1}\,\mathrm{Hz}^{-1}$ to a flux density $f_\nu$ in $\mathrm{erg}\,\mathrm{s}^{-1}\,\mathrm{cm}^{-2}\,\mathrm{Hz}^{-1}$:
$$
f_\nu = \frac{L_\nu}{4\pi \times (10\,\mathrm{pc})^2}.
$$

From there, you use the definition of the AB magnitude from Oke & Gunn (1983):
$$
M_\mathrm{AB} = -2.5\log f_\nu \,\,–\,\, 48.60.
$$
Note that there's an error in the original equation, as the authors write plus 48.60 instead of minus.

If you want Vega magnitudes or Johnson magnitudes or whatever, you use a slightly different zeropoint. But you don't want that, just stick with the AB magnitudes.

Or you just use astropy's tools for converting between fluxes and magnitudes.


How can a galaxy in-between our view and the galaxy behind it have a 'lensing effect'? In this article, the author writes:

  This galaxy is so distant that it would have been invisible without the gravitational lensing effects of a large galaxy cluster called Abell 1689, located nearly 2.2 billion light years away in the constellation Virgo. The cluster’s enormous mass acts as a natural telescope by bending and amplifying light from objects behind it, like A1689-zD1.

To me this doesn't quite sound the same as what a telescope is doing.

My question is: How can a galaxy in-between our view and the galaxy behind it have a 'lensing effect'?

It's called gravitational lensing. Here's a link to the wikipedia article on the subject: http://en.wikipedia.org/wiki/Gravitational_lens.
Gravity affects everything, including light. A massive object such as a star, a galaxy, or in this case, a cluster of galaxies, bends the path of photons that pass very close to the massive object. Bending light is the basis of the lenses in an optical telescope.
The behavior of a gravitational lens is different from that of an optical lens., but the end result is the same: Gravitational lenses enable astronomers to see more distant objects than they would without them. Gravitational lenses create multiple images of the remote objects behind the lens. Oftentimes these multiple images are in the form of streaks. See the below image of gravitational cluster Abell 1689, which is the cluster that let those astronomers see A1689-zD1.

(source: hubblesite.org)
The cluster magnified the remote galaxy A1689-zD1 by a factor of 9.3. Without that magnification, that remote galaxy would be invisible to current technology.


Binary Orbit around the Earth? Is a orbit possible where 2 objects going in opposite directions can intersect repeatedly with minor course corrections?

I'm not sure I see the point to this question, but if one of the orbiting objects is hollow and you allow for course correction, then yes, one object passing through the other is possible.

I don't see what force would keep the object with a hole in the middle properly positioned so it was in effect perpendicular to the movement of the other objects.   There's also problems with the orbits lining up just right rather than missing and giving each other a gravitational push, and with gravitational perturbations from the sun and the moon.   A system like that would be a lot easier and require less adjustment if the Sun and Moon weren't there.

You'd probably want both orbits to be over the equator to reduce fluctuations, but eliminating fluctuations would be impossible.  Every orbit would probably require some adjustment, and while it's theoretically possible, I'm not sure I see why anyone would want too - apart from perhaps it would look cool.


How close to a host star can a tidally locked planet be and its dark side still maintain a moderate temperature? So, imagine an atmosphere-less planet, tidally locked to a sun-like star. How close to the star can the planet be before its dark side becomes too hot?
I imagine that at some point the rocks on its sunlit side will melt and evaporate so that the dark side would experience rocky precipitation. Would this be true?
Also, at some point the atmosphere of the star itself would engulf the planet.
But at which point would these effects make the conditions on the dark side unbearable?

Your general idea about this process is correct. At close semimajor axis distance, rock can evaporate and will form a Silicate-oxygen atmosphere.
For low-mass rocky planets, the condensation flow from day to night-side, as it necessarily is very hot, will have to compete with the possibility of instead escaping vertically from the nightside, instead of precipitating. For higher-mass planets, vertical escape will be too difficult, and the hot Silicate-Oxygen gas will recondense on the nightside and therefore heat via thermal radiation and condensation latent heat.
This is a problem on which current research is in progress, and not many groups have worked on this, with the exception of one fantastic article that came out this year. They glue four different 1-D models together to represent vertical and horizontal for each day and night-side of catastrophically evaporating planets together, in order to create a sort of fake-2D model of the planetary Silicate-atmosphere.
Their nightsides are very hot in general (500-1000K), but they sadly do not give silicate densities or pressures. Hence, without the density, it is difficult to estimate how much the heat transfer between the Silicate gas and a human would be, i.e. how much a human would 'feel'.
If you are very curious though, I am sure you can construct this effect, by assuming Silicate saturation pressures, which are given in this article.


How can the Advanced Composition Explorer (ACE) warn of incoming solar storms? How can the Advanced Composition Explorer (ACE) warn of incoming solar storms when is is invested with radiation?

Discovery.com article Solar Storm Warning Satellite on Last Legs states that:

  Until the sun's free-flying and highly energetic outbursts, known as
  coronal mass ejections, hit the ACE spacecraft, forecasters don't know
  the orientation of their embedded magnetic fields.

I read that it can give 15 minutes in advance warning to Earth of the presence of an incoming solar storm. However to do that, it sends a radio signal which goes at the same speed of the solar storm so it will presumably take 15 minutes as well?

Solar flare X-rays travel at light speed, but the solar wind from CME's travels at merely 600 to 2000 kilometers per second. It's the wind that causes aurora and solar storms, depending on the orientation of its magnetic filed.
Here's a SOHO view of a CME. It's clear the gas is moving slower than light. You can tell if the earth is in the path of an ejection by how near to symmetrically the gas cloud expands around the sun.

So, to answer your question, the satellite measures magnetic field direction, and can give 15 minutes warning because the CME gas is moving much slower than light.


2002 Planetary alignement In april 2002 the inner planets had aligned and this event was captured in this beautiful photo:

But, according to this website simulations for the date, Jupiter was pretty much away. Is that possible? Can Jupiter saw as a straight line even be so far from the other planets?

Below is an image of the solar system from that date. You can imagine drawing lines from the Earth to the various planets. You will see that Saturn, Mars, Venus and Mercury are quite closely aligned. And Jupiter is about 25 degrees out of that alignment. This matches with the photo that shows Jupiter further from the other planets.

Note that my image, derived from Nasa shows the orbits of the planets are not equally spaced. Your image does not represent reality.

The photo shows four planets quite close, and Jupiter a little way from them, just as the model of the solar system suggests. Of course the planets are in a straight line in the sky. They always are in a straight line, because they all are on the ecliptic. The alignment was significant because the planets appeared close together.

All the planets move around the sun in (almost) the same plane. The Earth also moves in this plane. The plane that the planets all move it is called the "plane of the ecliptic". Imagine a circle drawn on a piece of paper. If you look at the circle from above you see a circle. If you look at it from an angle you see an ellipse, and if you look at it from the side you only see a line. The Earth is in the same plane as the other planets, so all the planets appear to be moving in a line. This means that the positions of the planets in the sky will "always" be in a line, even when there is no alignment. The plane of the ecliptic looks like a line, because Earth is on the plane.

However when there is an alignment with the Earth (as there was in 2002) the planets will appear to be not only on the line of the ecliptic but close together in the sky.

Of course the planets are not actually close together, and there are no gravitational or other malevolent influence of planets being in a line


Has a “white hole” theory been advanced to explain anomalous star formation in Sagittarius A? In 2008, the European Southern Observatory reported, upon the end of a 16-year study described here http://www.eso.org/public/usa/news/eso0846/, that the 28 stars nearest the very large black hole in Sagittarius A included 22 in varied orbits compared to a "swarm of bees", and six (all slightly farther from the BH) in a disc of very fast orbits. As the stars were "too young" to have migrated far, and as the tidal forces in black holes had apparently been felt to leave star formation in that region unlikely, further research was planned. I'm asking whether there might have been any results, given the torsion-based cosmology which pairs black holes with white ones and is most concisely described at arXiv.org > https://arxiv.org/abs/1510.08834.

The spin of smaller celestial bodies may affect the spin of the larger systems of which they're a part to an extremely great extent, according to a version of inflationary cosmology developed by physicist Nikodem Poplawski since 2009. The simplest statement of his cosmology is at https://arxiv.org/pdf/1007.0587.pdf, but, in spite of its title as an "alternative" to cosmological inflation, it actually describes a version of that theory, as pointed out in the Wikipedia article "Inflation": Poplawski's version uses an extension of Einstein's General Relativity that's usually referred to as the Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity, and was developed, partly in consultation between Einstein and the French mathematician Cartan, to incorporate particulate spin (the rotation of subatomic particles) into relativity, since GR had been formulated several years before such spin was discovered.

Partly because ECSK made an assumption that fermions (loosely describable as "matter particles") have a spatial extent (tiny, but about 37 times the Planck length) that's incompatible with a renormalization technique useful in quantum mechanics (which generally requires all subatomic particles to be pointlike), and perhaps partly because its application to cosmology allows a universe that's eternal to the past and to the future rather than one that's eternal only to the future, the ECSK theory has not been widely utilized in cosmology until recently, when physicists exasperated with the failure to discover any specialized subatomic particle that would cause inflation began turning to it. As you can see on p.7 in the piece I've linked you to, Poplawski's torsion-based cosmology may be falsified if there's no evidence for any prevalent direction of rotation, whereas inflationary cosmology that's based on a field of hypothesized "inflaton" particles cannot be falsified at all, leading to many recent objections to it by theoreticians.

I'd also like to know (if possible) whether the direction of the orbits of the stars concerned is the same as the direction of rotation of the super-massive BH itself, assuming that the latter was not inferred from the former: This would help me to assess the plausibility of this BH cosmology, as one of its leading proponents (Nikodem Poplawski) feels the arrow of time to derive from the direction of matter's passage across the event horizons of BHs, and has also felt the torsion-based theory to be falsifiable by the lack of a prevalent direction of rotation in the universe. (These are details to me, but might appear in whatever conversations or observations might contain the answer to my question.)

I'm going to say that the answer to the main question is "no", for two reasons.

The Introduction to this recent paper by Naoz et al. mentions a variety of different suggested models and explanations, none of which is based on anything like alternate cosmological models. (The paper itself argues that the apparently problematic distribution of stellar orbits may be an artifact of failing to account for the presence of binary stars, so that the system isn't really anomalous at all.)
It's not at all clear to me how an alternate cosmological model like the one you link to would be even remotely relevant to the details of star formation in the Galactic Center. In other words, I wouldn't expect anyone to be trying to explain star formation near Sgr A* using alternate cosmologies or extensions to GR (the star formation took place mostly well outside the region where GR becomes noticeably different from Newtonian gravity, so modifications to GR would be even less relevant).

As for the second question: we simply don't know the direction or amount of the central supermassive black hole's spin (yet).


$\eta$ and $\xi$ coordinate system Is there a standard definition for $\eta$ and $\xi$ in terms of Ra and Dec, as used in an astronomical coordinate system? I'm used to working with Ra and Dec, and am not sure how to precisely interpret this spatial graph from de Boer et al. 2013.

$\xi$ and $\eta$ are just arbitrary names of coordinates, used because the actual position on the sky doesn't matter in this context, i.e. only the relative position in the plot is important. An analogue would be to label the coordinates of your living room $x$ and $y$, instead of using Earth's longitude and latitude.
If you really want to transform, you can use the information given by the authors that an "over-dense feature" is located at $(\xi,\eta) = (0.25,0.06)\,\mathrm{deg}$, which they say corresponds to $(\mathrm{RA},\mathrm{dec}) = (2^\mathrm{h}21^\mathrm{m}2.2^\mathrm{s}, -34^\circ 27'17.6'')$.
This transformation requires that positive $\xi$ and $\eta$ values point toward east and north, respectively. This is not explicitly written in the reference you give, but is seen to be the case in the paper they quote (de Boer et al. 2012). Thanks to @planetmaker for digging this up!


Galactic revolutions relative to the age of the universe If the universe is only 40 to 50 galactic revolutions old, how has it acquired its present state so "quickly" relative to this time scale?

Gravitationally bound dynamical systems evolve towards their equilibrium states on a dynamical timescale of $\sim (G \rho)^{-1/2}$, where $\rho$ is their average density.

If we assume the Galaxy started of with $10^{12}$ solar masses in a sphere of radius $10^5$ pc, then the dynamical timescale is 1 billion years.

If we consider an object at the "edge" of such a system, Newtonian gravity and a bit of rotational mechanics, we find that the fastest possible bound orbital period is also of order $(G\rho)^{-1/2}$. The Sun is not at the edge and the average density inside the solar orbit is much higher and so the orbital period can be a bit shorter than this (a factor of four).

Thus what we see is exactly what is expected for a $>10$ billion years old universe - a relatively settled dynamical system.

You could extend this argument to the timescale for major galaxy mergers. The distance between galaxies is of order ten times their size and thus the mean density of galaxy systems is 1000 times lower than for an individual galaxy. This increases the relevant dynamical timescale to $1 \times 1000^{1/2} \sim 30$ billion years. That the Milky Way and Andromeda will collide some 17-18 billion years post big-bang is also therefore not an unexpected event.


Distance to Sun at Perihilion and Aphelion at max and min Eccentricity Title says it all. I'm putting together a presentation on Milankovitch Cycles, and I would like to bring up the difference in distance to the sun (km) at aphelion and perihelion when the earths orbit is at maximum and minimum eccentricity. The numbers I've found are that the maximum eccentricity of Earth's orbit is 0.0679, and the minimum is 0.000055.

I like the math of ellipses cause there's enough parts to keep it interesting, but it's not super complex either.   The answer to your question as you put it, is remarkably simple.  I've bolded the letters that represent distances for easier reading.

Eccentricity or $e = c/a$, where $a$ is the semi major axis and $c$ is the distance between the focal point (sun's location) and the center of the ellipse. $ea$ is the distance between the center point and the focal point.

So, the answer to your question is simply $a$ plus $ea$ and $a$ minus $ea$.   For the Earth and sun, the semi major axis or $a$, is $149,600,000\:\mathrm{km}$, then simply add and subtract $ea$ to both.

When $e = .0679$, $ea = 10.15\:\mathrm{million\:km}$. So $149,600,000 \pm 10,150,000$. $159,750,000$ and $139,450,000\:\mathrm{km}$ at furthest and closest.

When $e = .000055$, $ea = .008\:\mathrm{million\:km}$, so $149,680,000$ and $149,520,000$ at most circular.

Simple picture

More detailed picture

Maths and sources of pictures, here and here

footnote:  I hope this wasn't a homework question.


Can a rogue planet neither orbit around a star nor a galaxy? As we know, rogue planets don't orbit around a star, how about galaxy? Can a rouge planet not orbit around a galaxy?

They would be enormously difficult to observe, but with a big enough gravitational assist a rogue planet certainly could be ejected from a galaxy and become a "double rogue" so to speak, or intergalactic rogue planet is probably a better term.  Rogue (or intergalactic) stars have been observed.  Here and Here.  The same gravitational forces that create intergalactic stars absolutely should create inter-galactic rogue planets and in fairly significant numbers.  The merging of 2 galaxies should create millions of them.


How do we get to know the total mass of an atmosphere? Since atmospheres don't end abruptly but gradually get thinner the higher you go, I wonder how we can get the total mass of an atmosphere if we don't know where exactly it ends. E.g. the Earth's atmosphere's mass is defined as 5.1480 × 1018 kg. Does this value include the exosphere (which doesn't have an abrupt end either)? Or is it up to the exobase only? Or is it even the significant part only, up to the mesopause or to the Kármán line or something?
Also, if we mention the mass of a celestial body, does this value (e.g. in case of Venus 4.867 × 1024 kg) include its atmosphere's mass or not?

There is a simple$^*$ way to know the total mass of the atmosphere: measuring the pressure it exerts on the surface, which necessarily integrate all of the atmosphere above ground level.
If you take an atmospheric pressure of $1\cdot10^5$ Pa, it is equivalent to a force of $1\cdot10^5$ newton over one square meter. Multiply by the area of the planet in square meters, you get the total weight of the atmosphere: $1\cdot10^5 \times 5.1\cdot10^{14} = 5.1\cdot10^{19}$ N. Divide by the acceleration of gravity to convert this weight to a mass: $\frac{5.1\cdot10^{19}}{9.8} = 5.2\cdot10^{18}$ kg. There you go!
$^*$Well, I guess it is simple on Earth, but could be more challenging on other planets...


By putting a mirror in space, would we be able to see into the past? I only ask this because of how fast light travels. The question remains in the title. Why, or why not, would this work?

I think the question is referring to situating a very large mirror in space facing earth.  If we were to put it several light minutes away, then events occurring opposite the mirror could be reviewed de novo with more preparation upon the warning we received upon the first light of the event arriving at earth.

For example, a supernova going off in M31 might not be under observation at the moment its light first arrives, and so the initial observations might be lost.  However, with a mirror facing M31, we would be able to observe that mirror as the event unfolded, having been warned that there was something worth watching, in advance.

Nice idea!  But it would likely be much less expensive to simply have multiple telescopes always watching "prime" starscape for unexpected events.


Formula to calculate B-V index? Is there a formlua or equation to calculate a star's B-V index based on it's observed frequencies in the B and V spectrums ? I have unfortunately not been able to find anything...

I found :

$$B-V = -2.5 \log_{10} \left(\frac{f_B}{f_V}\right)$$

From this question. It works for my purposes.

Those are magnitudes on the left. Five magnitudes are a factor of 100, so 2.5 magnitudes are a factor of 10. So if $f_B/f_V =$ 100 (i.e. 10$^2$) then $B-V =$5.


Is there another habitable planet in our galaxy? I have wondered, what'll happen when we destroy our planet or it becomes uninhabitable for human life? Is there another option than the complete extinction of the human race? Can anyone give me a logical response?

what'll happen when we destroy our planet or it becomes none-habitual for human life?

Very pessimistic idea.

We lack the technology to tell if a planet orbiting another star could be lived on by humans.  We barely have the technology to detect some planets orbiting a small number of other stars (compared to the number of stars in the galaxy).

The term for these planets is exoplanet and Wikipedia says we have detected about 3750 to date orbiting about 2800 stars.  As there are somewhere between 100 and 400 billion stars in the galaxy, we only know a tiny fraction of what's out there.

We have a very limited basis for listing some planets as possible candidates for supporting some form of life, but, with all respect to the serious scientists doing this work, this is nowhere near knowing if they really can support life at all, let alone humans.

So your question's answer is : we don't know.

We cannot travel fast or far enough at present to reach another star in a reasonable time frame and we also could not do it with enough people.  We do not currently have any reasonable expectation that we will be able to do that in the future.

So even if we knew of a suitable planet, it would be unlikely we could ever travel there to e.g. colonize it.

So we're stuck here so keep recycling. :-)


Star density in- versus out- of the arms of the galactic pattern? What is the density difference in our galaxy (or in a typical spiral),
at A, B, C versus at a, b, c?

Consider the yellow track.
Do astronomers have a graph like this...

...which shows the shape of the density through and between the arms?
In short,
Do we roughly know the density between-arms versus in-arms ... is it 10%, 50% or 90%?
(Perhaps at the "corotation radius", which is about where we are.)

Further issues arising:
= I understand that one of the reasons the arms "appear real" is just that there are more bright young stars forming in the arms (due to the higher pressure). Perhaps the actual density difference is very low?
= Perhaps the density variation is dependent on the type of star, or other material - what about things like gasses?
= Let's say the percentage I am asking about is X% - at our radius. Is it X% at all radii?  How does the "strengthiness" percentage vary with radius? This is not immediately intuitive from looking at images.
(original galaxy arm pattern diagram courtesy wikipedia)

I'm afraid there is no answer, yet... The problem is that you would have to know the star densities in the different regions (in the spiral arms and outside of the spiral arms). While it is certainly possible to have an accurate estimate of the density of massive stars because of their brightness, the density of low mass stars in different regions of the galaxy is much more difficult to estimate. And since low mass stars make up the vast majority of stars (see for instance the initial mass function which is a measure of the distribution of stars over the different masses), estimating the density of stars in different regions becomes very uncertain.

But, at the moment the Gaia satellite is measuring the position and distances of about a billion stars and other objects. A much more detailed three dimensional map will be created with that data, including distance data for dim stars whose distances we were as yet unable to measure. So there is hope ;-)

NB. The first data release of Gaia has been published in September. I haven't found any papers that were able to answer your question (my search was not extensive though), but they might be forthcoming. Of course if you have some programming skills, you might determine the density differences from the data (available here) yourself.

EDIT - Just took a look at the data, the parallax (and therefore the distance) is still lacking for many stars. Hopefully this will change with future data releases.

  = I understand that one of the reasons the arms "appear real" is just that there are more bright young stars forming in the arms (due to the
  higher pressure). Perhaps the actual density difference is very low?

I would expect that the density difference of stars is quite small.

  = Perhaps the density variation is dependent on the type of star, or other material - what about things like gasses?

The density variation is certainly different between different types of stars. High mass stars only occur near star forming regions (i.e. in spiral arms). Their lifespan is so short that they do not have the time to get very far from the region in which they were formed.

I'd expect that the density variation for gas and dust will be higher (but I have no knowledge to support this).


If a black hole does not emit light, how can one take a picture of the black hole itself? There's some discussion that the image composed by the Event Horizons Telescope is really just an accretion disk. To "take an image" of something, you need the light reflecting off of the surface of the object within frame. The "light" in the image is really just color-mapped gases within the accretion disc. Since black holes do not allow light to escape, is this actually an image of a black hole?

The analogy I've heard is that it would be like taking a picture of an object in a completely dark room, showing someone the photograph taken, and saying, "Hey look at this picture I took of this object." The other person could ask, "Where is the object in this entirely black photo?" to which the other person might respond, "It's somewhere in the picture."

Was a picture of the object really taken if you can't even see it? If you photograph the sky, have you "captured an image of air molecules?"

The picture is of the central region of M87, taken at a wavelength where the gas is "optically thin".

The ring of bright light is pretty much exactly where it is expected to be for the synchrotron radiation emitted by the hot gas to have been gravitationally lensed by a black hole with the same mass as deduced previously from the motion of stars close to the centre of M87.

It is a "picture of a black hole", though all you see is the way it warps the light around it.

Your analogies are poor. It isn't like taking a picture of someone in a dark room. The room here is illuminated and the effects of the black hole on that light have apparently been seen quite clearly. That, by the way is the only method by which you can see someone in an illuminated room, unless you have eyes that detect the mid-infrared light they emit. Of course that option is not available for a black hole, since they emit no light at all.

Your other analogy is also curious. A cursory glance at the sky reveals it is full of air molecules. That is why it is blue. Your view though lacks the angular resolution to see individual air molecules, so you would not be able to see them.

Here, the resolution of the "telescope" is just good enough to reveal the essential structure and size of the photon ring.

Finally, why isn't it a picture of an accretion disk? As I said, it is expected that the disk is optically thin and actually much bigger than the imaged area. Emission from the disk would not be expected to show anything but a haze with a vague central concentration. Given the spatial resolution of the image, what has actually been seen is a sharp, bright ring.

The accretion disk around a black hole should be terminated at or slightly beyond the innermost stable circular orbit. This is at 3 times the Schwarzschild radius, but gravitational lensing would make it appear to have an inner radius of 3.7 times the Schwarzschild radius. The bright ring has a radius of 2.6 Schwarzschild radii; correct for a lensed photon sphere explanation, incorrect for the inner wall of the accretion disk (unless the black hole is 70% of the mass previously determined from stellar motions).

The orientation might be just about ok for an accretion disk explanation. If the rotation axis is aligned with the jet of M87, the disk should be about 17 degrees from face on. However, in order to see the inner parts having such a circular shape and well defined structure would require a geometrically thin and optically thick disk, the opposite of what is deduced from the physical conditions in the plasma.

To see more context, here is a wider view of M87 taken by Chandra, and from the Chandra team's blog post:

  Chandra was used to observe M87 and other targets during the EHT campaign. While Chandra can’t see the shadow itself, its field of view is much larger than the EHT’s, so Chandra can view the full length of the jet of high-energy particles launched by the intense gravitational and magnetic fields around the black hole. This jet extends more than 1,000 light years from the center of the galaxy.


What are six different methods to measure distances in Astronomy? What are six different methods to measure distances in Astronomy in regards of their respective range in terms of astronomical objects?

So far I can name 4: Parallax method, radar ranging, main-sequence fitting, cepheid variables.

Using type Ia supernova light curves.

The RR Lyrae period-luminosity relation.

Moving cluster statistical parallax.

Surface brightness fluctuations.

Redshift-distance relation.

Using merging gravitational wave sources as standard sirens.

These and more can be pursued following this link. https://en.m.wikipedia.org/wiki/Cosmic_distance_ladder


Is there a upper limit to the number of planets orbiting a star? Our sun has 8 planets orbiting as well as a number of dwarf planets. Are there any calculations that hint as to whether this number is close to some theoretical maximum value or are we simply an average solar system in this particular way?

I could imagine that if you have many planets, they will likely interact with each other. Can you calculate any theoretical value for the maximum number of planets which have long-term stable orbits around their own star?

There do exist somewhat trivial configurations, which are stable in the long term and which include arbitrarily many bodies. Consider, for example, a set of $N$ circularly moving bodies of the same mass $m$, which obeys the constraint $mN\ll M$, where $M$ is the mass of the star. So long as $mN\ll M$, the bodies move dominantly in the gravitational field of the star and are hence moving stably over long term period. However, as $N$ is arbitrary, one concludes that there is no upper limit on the number of planets, provided that their total mass is small.

A more physical example would be a protoplanetary disc, or an accretion disc, which is a limit $N\rightarrow \infty$ of an arbitrary planetary system (not not necessarily circular) of a given mass. A yet more physical example is an asteroid belt, consisting of a large number of bodies on, roughly, stable orbits. Finally, during planet formation process the star goes through stages, when it is surrounded by sets of pebbles and asteroids, which keep their structure constant over a large number of orbits (roughly, of order $10^5$). And these all are real physical examples of planetary-like systems.

The answer to your question would start to alter, though, if you start imposing additional conditions apart from $N\rightarrow \infty$. For example, if you require that bodies do not collide in the long term, some of the above named systems would not work (for example, accretion disc model), but some other would (sets of concentric particles). If you additionally require that the object should obey the definition of a planet, that is have some range of masses, then interesting things will start happening when the total mass of the planets will start being comparable to the mass of the star. So the limit would certainly exist. Finally, you might be more strict about what do you really mean by stability here, and that could also have a bearing on the answer.

To summarize, unless you impose any constraints, there do exist N-body systems orbiting a star in a stable fashion and having arbitrarily large $N$.


Astronomy Calculations Tool I took many images like the following:

As many of you may recognise, this is a picture of Jupiter and its four Galilean moons. Using these images, I am aiming to calculate the mass of Jupiter by finding the orbital distance and orbital period of each of these moons, and then plugging those values into Kepler's Third Law.

However, this requires a seemingly tedious process of the following sort:

1) Locate the centre of mass of Jupiter

2) Measure the distance to each of the planets

I have a lot of data (many, many pictures). I am hoping that there is a relatively easier (or even more accurate) method of doing all of the above than using software like Gimp to do everything for each image manually. Can anyone recommend anything?

Try WinJupos. It can be used to measure Jupiter (as well as other planets)


Why is the moon phase not in sync with the moon's illuminated fraction? I am using the following R script to plot the moon phase and the moon's illuminated fraction:

library(oce)

X11()

t_start <- as.POSIXct("2017-02-23", tz='UTC')
t_end   <- t_start + 75 * 24 * 3600  # 35 days

tm <- seq(from = t_start,
           to  = t_end,
           by  = 10000
        )

moon     <- moonAngle(t=tm, longitude=-8, latitude=47)
fraction <- moon$illuminatedFraction
phase    <- moon$phase - floor(moon$phase)

plot (tm, fraction, type="l", col='blue')
lines(tm, phase   , type="l", col='red' )

grid()

# wait for mouse click or enter pressed
locator(1)

This is plotted:

The red lines indicate the phase (0 = new moon, 1/4 = first quarter, 1/2 = full moon etc.), the blue curve indicates the how much of the moon is illuminated.

I have expected the illuminated fraction to be zero exactly then when also the phase is zero. However, this is not the case.

So, is there something I am missing, am I doing something wrong in my script or is the implementation of oce inaccurate?

This is a partial answer since your question is still unclear.  I would recommmend finding an astronomy package for tools like this rather than using what's basically a "bonus feature" from an oceanographic package.

From the help pages for package oce,

  illuminatedFraction
   fraction of moon’s visible disk that is
   illuminated
  phase
   phase of the moon, defined in equation 32.3 of Meeus
   [1982]. The fractional part of which is 0 for new moon, 1/4 for first
   quarter, 1/2 for full moon, and 3/4 for last quarter.

Perhaps you are missing the fact that marginally more than 50% of the moon is illuminated, and thus at first/last quarter marginally more than 50% of the visible disk is illuminated?  I would also recommend looking up the referenced "equation 32.3" to see what the definition is and how it applies to a zero-altitude viewer.


How did the Archimedes crater fill with lava? This is the Archimedes crater, on the moon, near the Apollo 15 landing site.

It is located in Mare Imbrium, a plain filled with lava.
The strange thing is that the interior of the crater looks flat, as if it had been also filled with lava, but there is no passage for lava to come inside the crater. All the walls appear to be intact.
So how could lava have possibly entered the crater?
Could it have had such low viscosity that it infiltrated as seepage?
The interior of the walls appears to be broken as if they suffered a landslide.
(The image source is this video, apparently a Lunar Reconnaissance Orbiter image)

Great question! The mare lava bubbled up through fractures in the floor of the crater, burying its ring system and central peak.


Would a spaceship have to evade interstellar clouds? Apparently, there are clouds of "dust" between the stars. Would a starship have to fly around those clouds, trying to find "tunnels" between clouds, or are the interstellar clouds harmless for a spaceship?

I'm mainly thinking in terms of abrasion or (micro)collisions, not radiation, but would welcome information on the latter also.

Yes.

As has been commented, the amount of damage taken by an interstellar spaceship depends on its velocity $v$, as well as the number of gas and dust particles that it encounters on its way. This number is usually measured per area, in which case it's called column density $N$, and is equal to the total distance $d$ traveled times the particle density $n$, i.e. $N = nd$. For instance, if a spaceship travels 1 lightyear ($10^{18}\,\mathrm{cm}$) through a region with a density of $10\,\mathrm{cm}^{-3}\!$, each square centimeter of the spaceship will encounter $10^{19}$ particles.

That is, the faster you go, the farther you go, and the more dense regions you go through, the more your spaceship is damaged.

The Breakthrough Starshot project aims to reach our nearest-neighbor stellar system $\alpha$ Centauri in ~20 years, with a gram-sized satellite reaching $0.20c$ by means of a light sail. Today, there was a paper by Hoang et al. calculating the amount of damage taken by such a satellite. The total column density of gas from Earth to $\alpha$ Cen is $\sim10^{17.5\mathrm{-}18}\mathrm{cm}^{-2}$, and assuming (fairly) a dust-to-gas ratio of 1% and a carbonaceous/silicate dust grain population with a Weingartner & Draine (2001) size distribution, they calculate that this journey to $\alpha$ Cen will erode the surface of the spacecraft to a thickness of the order of 1 mm.

Most of the damage is caused by dust, not gas, but in principle gas may slowly heat up the spaceship. However, at $v=0.2c$, as long as the density is $\lesssim10\,\mathrm{cm}^{-3}$, the temperature is insufficient to cause any melting.

Molecular clouds — the dense clouds where stars are born — have densities from $10^2\,\mathrm{cm}^{-3}$ and even up to $10^6\,\mathrm{cm}^{-3}$, i.e. many orders of magnitude higher than the roughly $1\,\mathrm{cm}^{-3}$ found in the more dilute interstellar medium. To reach even more distant stars in a tolerable time, you would have to go faster than $0.2c$, and thus it seems that it is in fact a good idea to evade these clouds.