What is the difference between asteroids, comets and meteors?

The objects you are refering to are actually two different objects: asteroids and comets. Meteor and meteorite are other names for an asteroid, at a given time of its interaction with our planet. We'll get to that.

So first, what is the difference between an asteroid and a comet?

A comet is a small solar system body that display a "coma" (an atmosphere of a sort) and sometimes a tail passing close to the Sun. They are mostly made of ice and dust, as well as some small rocky particles. We distinguish two kind of comets, with short or long orbital period. The short orbital period ones originated from the Kuiper Belt, a region composed of small bodies beyond the orbit of Neptune. The long orbital period ones originated from the Oort cloud, a scattered disk of icy planetesimals and small bodies laying around our solar system.

An asteroid is a small body, composed mostly of rocks and metals. In our solar system, they can be originated from the asteroid belt, laying between Mars and Jupiter, or from the orbit of Jupiter (the Jupiter Trojans), or from actually almost everywhere in the Solar System.

An asteroid that enters the Earth's atmosphere becomes a meteor, what we also call a "shooting star".

Eventually, a meteor that was massive enough not to be completely distroyed entering the Earth's atmosphere and hitting the ground is a meteorite.

spectroscopy - Convert axis display in ds9

I have a fits file of an echellogram with the axes showing the pixel indices. However, I would like to convert my horizontal axis from pixel to wavelength given that I have a conversion formula for how much in $mu$m corresponding to 1 pixel. How should I do this so that I could see wavelength rather than pixel index directly in DS9? Thanks!

big bang theory - How do we know the universe's expansion is speeding up?

As a fellow layman, I'll give this my best shot.

The further away a galaxy is from us, the faster it is moving away
from us. But the galaxies we see exist in the distant past because it
takes a long time for their light to reach us. The closer galaxies
are, the more recent their light is, and the slower they move away
from us.

All true. Think of a single point explosion, at any given time, the object twice as far should be moving twice as fast, cause they both started in the same place at the same time, so twice as fast moves twice s far. There are, complications - with the explosion there's air resistance, with the universe well, I'll get to that.

Doesn’t this seem to indicate that the expansion of the universe is
slowing down, because the more recent light from galaxies, appears to
be moving away slower? Does this make sense?

OK, it sounds like you have an incorrect assumption there. Expansion means the far away is moving away faster and the closer is moving away slower, that's true with accelerating or decelerating expansion.

What they look for when studying expansion is measuring the precise speed and comparing that to distance. In steady expansion, you expect to see the galaxy 8 billion light years away to be apparently moving away twice as fast as the galaxy 4 billion light years away. (I say apparently cause we can only observe the relative velocity from 8 billion years in the past).

So, whether the galaxy 8 billion light years is traveling slightly more or slightly less than twice as fast away from us as the galaxy 4 billion light years away - that's what tells us about acceleration vs deceleration.

Imagine a car driving 60 MPH, and the driver puts the ever so slightest pressure on one of the pedals, but you don't know which one, and similarly the car driving 30 MPH does the same, but we can only see how fast the 60 MPH car was driving 6 minutes ago and we see how fast the car driving 30 was driving 3 minutes ago - that gives the 30 MPH car more time to apply the acceleration or deceleration. It's that time differential that gives us the information.

So, like the cars above, the galaxy 4 billion light years away has been in the accelerating expansion of space longer than the one 8 billion years ago and that's what tells us that the acceleration of expansion is happening, the nearer galaxies are moving a bit faster away from us than they would in a steady expansion or a gravitationally slowed expansion. (edited to make a bit more clear)

The newer light is moving slower. The older light moving faster. So
from this it seems that the universe was expanding faster in the past?

light doesn't move slower or faster. it red-shifts when objects are moving away from each other. The faster they move away the greater the red-shift. That's one way relative velocity can be measured.

biochemistry - What are the variables that control/influence the color of oranges(Citrus sinensis)?

I hear that Oranges cultivated in tropical areas of the world tend to be greener when ripe, is that correct?
Even the same type of Orange differs in color if cultivated in California or Florida. I hear that's because of the climate (colder nights == oranger oranges)

But, at the same time, oranges tucked in between the tree leaves tend to be greener, for they need more chlorophyll to make the most use of less access to sun rays.

Could someone correct my assumptions? Also, if possible, list the pigments and processes involved?

cosmology - Evolution of the Hubble parameter

The solution to the Friedmann equation in a flat universe is
$$H^2 = frac{8pi G}{3}rho + frac{Lambda}{3},$$
where $rho$ is the matter density (including dark matter) and $Lambda$ is the cosmological constant.

As the universe expands, $rho$ of course decreases, but $Lambda$ remains constant.

Thus the Hubble "constant" actually decreases from its current value $H_0$ and asymptotically tends towards $ H = sqrt{Lambda/3}$ as time tends towards infinity.

As $Lambda = 3H_0^{2} Omega_Lambda$, and measurements suggest that $Omega_{Lambda} simeq 2/3$, then $Lambda simeq 2H_0^2$, and the Hubble parameter will therefore decrease to approximately $sqrt{2/3}$ of its present value if the cosmological constant stays constant.

Of course if $Lambda = Lambda(t)$, (ie not the basic $Lambda$-CDM model) then the behaviour will be different.

EDIT: Another useful form of the solution (for the case of a constant vacuum energy density) is

$$H^2 = H_0^2 left( frac{Omega_r}{a^4} + frac{Omega_M}{a^3} + frac{Omega_k}{a^2} + Omega_{Lambda}right),$$
where $H_0$ is the Hubble parameter now, $a(t)$ is the scale factor of the universe, $Omega_r$ is the current (i.e. $a=1$) ratio of the radiation density to the critical density and $Omega_M$, $Omega_k$ and $Omega_{Lambda}$ are the equivalent densities for the matter (baryonic and dark), curvature and (constant) vacuum energy densities.

As $a$ increases you can see that all three of the leading terms get smaller and the Hubble parameter decreases at all times. When $a$ is very large, $H$ approaches $sqrt{Omega_{Lambda}} H_0$ as before.

expansion - What exactly is meant by "expanding universe"?

When we say the Universe is expanding, we really mean that space is expanding. The Universe could be infinite in size, but there continues to be more and more space between objects. Essentially, objects are moving away from each other because more and more space is being created between them.

In the early Universe, matter was much closer together than it is now; this density caused extreme temperatures and no hadronic matter could form. The first expansion is thought to have occurred because of how hot and energetic everything was, and spacetime itself was expanded in an event we call the Big Bang.

As objects spread out from each other during the inflationary epoch, the Universe began to cool down. Now, dark energy is the main culprit for its accelerating expansion.

To answer your question, yes, dark energy is making all particles move away from each other, although farther objects move away from each other at a faster rate. Why is that?

Well, the only thing holding all atoms, stars, planetary systems and galaxies together are the four fundamental interactions — the strong force, weak force, electromagnetic force, and gravity. In space, the main attracting interaction is gravity. As such, dark energy will cause farther objects (which are less affected by our gravity) to move away at a faster and faster rate.

Think of it like you are holding a dog with a leash, and the ground begins to spread out from below you. You and your dog are being moved away in opposite directions, but you both stay close together because of the strong leash.

Now, your mention of atoms being torn apart is actually the basis of the Big Rip hypothesis. It states that dark energy will become more and more abundant until even closeby objects separate from one another. First, galaxies will be disbanded as the stars move away from each other in all directions.

Much later, the gravity of planetary systems won't be enough to hold them together. Later still, planets and stars will be disbanded into their molecules. This will eventually continue as the amount of dark energy increases, until not even atoms can be held together by the electromagnetic force, and the subatomic particles will be moved apart.

By the time the expansion of the Universe exceeds lightspeed at the subatomic scale, no particle will ever be able to interact with one another. The Universe would dissolve into countless lonely particles that won't be able to do anything. Now, the Big Rip hypothesis is only one of the three most known fates of the Universe. Currently, the most accepted theory is the heat death of the Universe.

Life without DNA? - Biology

To follow up what mbq said, there have been a number of "origin of life" studies which suggest that RNA was a precursor to DNA, the so-called "RNA world" (1). Since RNA can carry out both roles which DNA and proteins perform today. Further speculations suggest things like a Peptide-Nucleic Acids "PNA" may have preceded RNA and so on.

Catalytic molecules and genetic molecules are generally required to have different features. For example, catalytic molecules should be able to fold and have many building blocks (for catalytic action), whereas genetic molecules should not fold (for template synthesis) and have few building blocks (for high copy fidelity). This puts a lot of demands on one molecule. Also, catalytic biopolymers can (potentially) catalyse their own destruction.

RNA seems to be able to balance these demands, but then the difficulty is in making RNA prebiotically - so far his has not been achieved. This has lead to interest in "metabolism first" models where early life has no genetic biopolymer and somehow gives rise to genetic inheritance. However, so far this seems to have been little explored and largely unsuccessful (2).

edit

I just saw this popular article in New Scientist which also discusses TNA (Threose nucleic acid) and gives some background reading for PNA, GNA (Glycol nucleic acid) and ANA (amyloid nucleic acid).

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(1) Gilbert, W., 1986, Nature, 319, 618 "Origin of life: The RNA world"

(2) Copley et al., 2007, Bioorg Chem, 35, 430 "The origin of the RNA world: co-evolution of genes and metabolism."

amateur observing - What are the stars/constellations a beginner/enthusiast can easily identify?

It varies throughout the year. A book or a website with maps will help.

In Spring, Leo and Boötes dominate the southern skies, with Coma Berencies between them

In Summer, the summer triangle of Deneb, Altair and Vega is seen, with Cygnus flying along the Milky Way, and the rich star fields of Saggitarius closer to the horizon.

In Autumn there is the square of Pegasus, with Andomeda riding, past Perseus

And in Winter, Orion dominates the southern skies, with his dogs following.

In the North, Cassiopea and the Ursa Major, are on opposite sides of the Pole star.

zoology - What's the name of this bird?

From what I understand of the flight description you give, and given the size and habitat, I would suggest to have a look at woodpeckers. Dryocopus martius is large and black.

Another idea (my favourite, actually): a bird of the genus Tetrao: they can be black and large, live in the forest, and the tail widens towards the end.

Other suggestions, but I really doubt it's relevant:
- cormoran (Phalacrocorax for the size, dark color, and I've seen some perched in trees, and ther's a lake in Zürich);
- Accipiter (for the flight and habitat):
- Milvus (for the size, the tail, and the dark colour):
- cuckoo (Cuculus canorus);
- magpie (Pica pica, black, makes nests on top of high trees, but I suppose you would have recognised it without hesitation).

The yellow stripe on the back matches none of the above suggestions.

physiology - Are ectopic beats considered sinus rhythm for pNN50 purposes?

No, the beats originating outside of the sinoatrial node are not considered for pNN50. Moreover, this metric cannot be applied to the rhythm featuring any type of ectopic or non-sinoatrial activity.

NN50 has its name from an acronym "normal-to-normal", this acronym is used instead of RR ("from R to R") to emphasize that only the normal, e.g. sinoatrial beats are considered for evaluation.

cosmology - Are objects in the universe moving away from each other at the same acceleration?

I assume you mean is $frac{dv}{dt}$ the same for all objects and/or is it constant for all objects, where $v$ is recessional velocity (and $t$ is cosmic time)? The answer is no it is not the same for all objects and it is not constant for all objects.

$$v=frac{dD}{dt}=H(t)D$$

Where $D$ is proper distance and $H(t)$ is the Hubble parameter. If we take the Hubble parameter as a constant, then:

$$D = D_0e^{Ht}$$

Where $D_0$ is the proper distance at the present time. So,

$$D''(t) = frac{dv}{dt} = D_0H^2e^{Ht}$$

So the "recessional acceleration" of an object depends on its present proper distance and is exponentially increasing with time.

Now the Hubble parameter isn't a constant and in LCDM cosmology is currently asymptotically decreasing to a constant. In the current epoch though it is fair to say that the "recessional acceleration" of an object depends on its proper distance and is increasing with time.

Warm and Hot dark matter density profiles

For cold dark matter, density profiles are well known and easy to find information about - eg. NFW, Burkert, Einasto, and others.

But for some reason I couldn't find explicit expressions for the density profiles for Hot and Warm dark matter.

I need to know what are $rho_{_{HDM}}(r)$,$rho_{_{WDM}}(r)$.

I'm interested in the differences between cold/hot/warm dark matter and why do we use Cold dark matter ($Lambda$-CMD model) and not Hot or Cold dark matter. I need to back my claims with formal quantitative analysis and not just a qualitative explanation.

If you can recommend about other aspects which differentiate the models, or a good review paper on the subject, I would welcome it.

gravity - Concerning fate of Milky Way Galaxy

The Milky-Way does not orbit the Andromeda galaxy, they both move under the influence of all the members of the local group. Even if one were orbiting the other the orbit need not be near circular but could be a very eccentric (elongated) ellipse.

The projected merger is because the tangential component of Andromeda's velocity with respect to the Milky-Way is small compared to its radial component That is Andromeda galaxy appears to be moving almost directly towards the Milky-Way (which is what it says in the Wikipedia page you link to, but it is not too difficult to find primary sources using Google, here is an arXiv paper reporting a proper motion study of Andromeda and reporting such).

evolution - Is there evidence that some non-human species perform sexual selection based primarily on intelligence? How do they do this?

Very intresting question. The problem is that animal intelligence is hard to measure not only for scientists, but probably also for the potential mate. Paradoxically, that is why selection for intelligence, if it occurred, may be very strong. One has to be smart in order to recognise smart behaviour, so preference and preferred feature are strongly connected. But that's only my opinion.

Boogert et al., 2011 1 reviews the current knowledge about animal preferences for cognition skills. They conclude that there is very little data on this subject. The given examples are:

1) Preference for elaborating birds songs (as songs are not inborn and have to be learned)

2) Spatial abilities:

In meadow voles (Microtus pennsylvanicus), males with better spatial learning and memory abilities were not only found to have larger home ranges and to locate more females in the field (Spritzer, Solomon, et al. 2005 2) but were also preferred by females in mate-choice tests, even though the females did not observe males’ performance on spatial tests (Spritzer, Meikle, et al. 2005 3).

In guppies (Poecilia reticulata), males that learned faster to swim through mazes to gain a food reward were found to be more attractive to females (Shohet and Watt 2009 4). However, females were not able to see the males’ performance in the mazes. Although male learning ability was weakly correlated with saturation of the orange patches on his body (a sexually selected trait (...)), orange saturation surprisingly did not correlate with female preferences. Thus, the cues leading female guppies to prefer faster learners are unknown.

It is possible, that females base their choose on some factors that correlates with cognitive skills or on total wellness, what may depend on intelligence.

3) bowerbird's abilities to build bowers (courtship constructions):

Comparative studies across bowerbird species have shown that relative brain size is larger in species that build bowers than in closely related nonbuilding species (Madden 2001 5). In addition, relative brain size increases with the species-typical complexity of the bower (Madden 2001 5), and a comparative study on the relative size of specific brain regions showed that species with more complex bowers have a relatively larger cerebellum (Day et al. 2005 6).

4) foraging performance

A recent experiment by Snowberg and Benkman (2009) 7 using red crossbills (Loxia curvirostra) showed that, after observing 2 males extracting seeds from conifer cones, females associated preferentially with the more efficient forager of the 2. The authors were able to exclude female choice for correlated traits by experimentally manipulating foraging efficiency, such that fewer seeds were available in the cones of one of the males. The males were also swapped between treatments (i.e., slow vs. fast forager) so that male identity could not explain the females’ preferences for the most efficient forager.

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Another way that intelligence may be favored by sexual selection is "cheating" during courtship. For example most frog species call to attract females. But this signal may also attract aggresive rivals or predators. Some males, especially the weaker ones, do not call but stay near calling individual. This allows them to avoid confrontation and wait for approaching females [8]. The successfulness of this strategy may depend on how "smart" the individual is (only my opinion).

[1] Boogert, N. J., Fawcett, T. W., & Lefebvre, L. (2011). Mate choice for cognitive traits: a review of the evidence in nonhuman vertebrates. Behavioral Ecology, 22(3), 447-459.

[2] Spritzer MD, Solomon NG, Meikle DB. 2005. Influence of scramble competition for mates upon the spatial ability of male meadow voles. Anim Behav. 69:375–386.

[3] Spritzer MD, Meikle DB, Solomon NG. 2005. Female choice based on male spatial ability and aggressiveness among meadow voles. Anim Behav. 69:1121–1130.

[4] Shohet AJ, Watt PJ. 2009. Female guppies Poecilia reticulata prefer males that can learn fast. J Fish Biol. 75:1323–1330.

[5] Madden J. 2001. Sex, bowers and brains. Proc R Soc Lond B Biol Sci. 268:833–838.

[6] Day LB, Westcott DA, Olster DH. 2005. Evolution of bower complexity and cerebellum size in bowerbirds. Brain Behav Evol. 66:62–72

[7] Snowberg LK, Benkman CW. 2009. Mate choice based on a key ecological performance trait. J Evol Biol. 22:762–769.

[8] Bateson P. 1985. Mate choice. Cambridge University Press. 181-210

What visible star is closest to the ecliptic?

HIP 76880 = $kappa$ Librae (V=4.72) has an Ecliptic latitude of -0.019 degrees.

This is the winner amongst all stars in the Hipparco/Tycho catalogue with a Hipparcos magnitude <6.

If you mean physical distance, rather than angular distance, then the sine of the ecliptic latitude must be multiplied by a distance estimate for the star. This cannot be conclusive, the distances to many naked eye stars are very uncertain, a small fraction of Hipparcos parallaxes are too uncertain to be useful in this regard.
However, from those with decent parallaxes then HIP 3765 = HD 4628 (V=5.72) has an absolute distance of 0.036 pc above the ecliptic plane.

tidal forces - What places on Pluto and Charon are facing each other?

As New Horizons past through the Pluto system, it travelled so that the spacecraft was on the far side of Pluto, as seen from Charon. It did this so both Pluto and Charon were roughly in the same direction, so the space craft would not have to rotate 180 degrees between imaging Pluto to imaging Charon.

It means that in images of Charon, the face that you can see is roughly the face that faces Pluto, However the it is the far side of Pluto (the side with the "whale" and the "dots" that faces Charon.

Tidal locking is pretty stable. See our own moon: it is locked, and has been for a long time. There is likely to be some wobble, just like the libations of the moon, but no overall rotation of either Pluto or Charon.

How small a star can provide Sun-level illumination to its planets?

What you need is a mass-luminosity relation combined with an expression for the tidal radius in terms of the stellar mass. The latter also depends on the mass of the planet, so when you say earth-sized, I'll assume that means mass and radius.

So going through the calculation.

Flux at the planet is $L/4pi r^2$, where $L$ is the luminosity and $r$ the orbital radius (assumed circular).

Let's next use an approximate relation that
$$frac{L}{L_{odot}} = left(frac{M}{M_{odot}}right)^3$$
A more accurate numerical relationship could be obtained from evolutionary model calculations. There is a complication that the luminosity of very low mass stars and brown dwarfs does depend on age.

For a rigid body the tidal radius (Roche limit) is
$$ r_tsimeq 1.4 R_Eleft(frac{M_{odot}}{M_E}right)^{1/3},$$
where $R_E$ and $M_E$ are the radius and mass of the Earth.

So setting $r=r_t$, the flux to $1400$ W m$^{-2}$ and replacing $L$ in terms of mass, we find
$$frac{M}{M_{odot}} = left[frac{4pi times 1400}{L_{odot}} (1.4 R_E)^2 left(frac{M_{odot}}{M_E}right)^{2/3}right]^{1/3}.$$

All that remains is to put the numbers in and I get $M = 0.026 M_{odot}$.

So, a small brown dwarf - but there are caveats. First, and most importantly, as I said, the luminosity-mass relation is a bit rough and ready, and is certainly age dependent for something as low mass as this. Second, the expression for the Roche limit depends a bit on structural properties of the planet, but I think this introduces relatively little uncertainty.

EDIT: If you use that mass and the tidal radius formula, you find that the orbital radius is only $5R_E$. As the minimum size of a brown dwarf is about a Jupiter radius, it appears that tidal breakup would not be the limiting factor for an Earth-like planet.

How the watches are showing perfect time?

The actual time for one day is 23hrs, 56mins, 4.1secs right? Then how can the clocks and watches can show perfect time?
I mean, if I observe the sun rise at 6:00am this day, tomorrow I should observe it before 6:00 or I can say at 5:56 approximately as our measuring devices follow 12+12 i.e., 24hr day. But in practice again it will be 6:00am when the sun rises. How it is possible?

star - What's in the center of a Galaxy?

At the center of our galaxy is a powerful radio source named Sagittarius A*, which is believed to be a super massive black hole (SMBH). This blackhole would contain far more mass than your run-of-the-mill supernova remnant. Our galaxy is believed to contain a SMBH containing the mass of likely a bit above 4 million times the mass (Gillessen) (2) (Ghez) of our Sun. For reference, I don't think we've ever discovered a star more massive than 600 times that of our Sun.

It's also important to understand that while many people look at blackholes as mystical or all-consuming, they actually have to follow the same rules as everyone else in the stellar neighborhood. The stars that make up our galaxy don't fall into the black hole for the same reason our planet doesn't fall into the Sun. Our star orbits black hole, our star system's velocity in equilibrium with the attractive force of the galaxy's center of gravity. This should hopefully resolve point 3.

For point 1, we should make clear that the 'black' part of the black hole is only true once you cross the event horizon. This is the case because at this point the escape velocity to escape the gravity of the black hole because greater than the speed of light. The light that isn't within the event horizon and is moving away from it is free to escape. So we can see light around it. But why is there so much light? Well, as it happens there are a lot of rather young and large stars in this area. It is not completely understand why this is the case. Lots of stars, lots of light! There are other factors that can contribute to this too, such as there simply being lots of stars between us and the center, not just in the center itself. The accretion disk of a black hole can also be exceptionally bright. Hopefully that clears up part 1.

Now for part 2. As far as I know, we don't really have any way of determining exactly where our SMBH came from originally. Black holes aren't necessarily formed just from a supernova event, there are a handful of other ways they can be created in nature. What is apparent, however, is that SMBHs contain far too much mass to be from a single star. It has probably consumed plenty of other black holes to grow to what it is now.

One interesting and notable difference between the comparison of a star system and a galaxy is the distribution of mass. While our Sun is believed to contain 99.8% of the mass of our solar system, the SMBH at the center of the Milky Way is not nearly as massive as the total mass of the Milky Way. The ratio can vary a lot, and there are some galaxies which are believed to host no SMBH at all.

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Gillessen, Stefan et al. (23 February 2009). "Monitoring stellar orbits around the Massive Black Hole in the Galactic Center". The Astrophysical Journal 692 (2): 1075–1109.

Ghez, A. M. et al. (December 2008). "Measuring Distance and Properties of the Milky Way's Central Supermassive Black Hole with Stellar Orbits". Astrophysical Journal 689 (2): 1044–1062.

cosmological inflation - Looking back in time by looking further away

Before the advent of telescopes, we could only look back in time from a few years (for nearby stars) to a few thousand years (for the most distant stars visible to the unaided eye). In addition to this, a handful of galaxies are visible without binoculars, letting us look back a few million years.

The first telescopes allowed us to see much farther, like hundreds of megaparsec, so we could look back hundreds of millions of years. As technology improves and our telescopes become better, we are able to observe more and more distant objects, and thus look further and further back in time.

The farther away an object is, the less light we receive, and hence the bigger telescope and better detector we need in order to see it. So, being able to look further back in time than previously is not about the light from more distant objects eventually reaching us, but simply a matter of developing the tools necessary to see it.

However, even the most distant galaxy we will ever see (which are at earliest a few hundred million years after the Big Bang, i.e. roughly 13.5 billion years ("Gyr") ago), are not farther away than the cosmic microwave background, which was emitted 380,000 years after Big Bang, i.e. ~13.8 Gyr ago, and which we have been able to detect since the mid-1950's. If we ever manage to build an efficient neutrino detector, we may be able to look back to seconds after the Big Bang, when these particles decoupled from matter and began traveling freely through space.

space time - How was all the matter curled up inside a singularity during big bang ?

Ahh, yes, I suggest you watch this short video of mine on YouTube: https://www.youtube.com/watch?v=o-LbvFB33fw
I talk about the beginning of the Universe in it.
Basically, space and time didn't really exist at the time of the Big Bang. A single point in space is called a zero-dimensional entity because it has no length, no width, and no height, nor does it have any other dimensions.
SO no space. Also, since the Big Bang was the origin of time, you can't have anything "before" it.
SO no time.
And these two completely contradict your question itself: there was no spacetime. Nor was there any matter.

You see, Einstein once wrote on some black board in 1905 this very particular equation: E = mc^2

This stated that mass and energy are interchangeable. Mass requires space, but energy does not. Where all this points to is:

all the mass in the Universe was energy at the Big Bang, and since energy doesn't need space in order to exist, it was the Universe.

Also, the term "singularity", though used by many, isn't really the right word to call the original universe. But that's ok, as long as everyone knows what you're talking about.

To answer your question directly, there wasn't infinite mass in the beginning of the Universe; there was zero. There was a lot of temperature, but not infinite. And density . . . if the Universe had been infinitely dense, it would have been a black hole, and we wouldn't exist in any possible way. And there was no space-time to start with in the first place; space-time only became a later concept. A concept originating in the first 10^-35 of a second.

amateur observing - What is the first recorded reference to the Moon being a satellite of the Earth?

From before the dawn of history people naturally assumed that the sky was a solid dome above the flat earth. The dome was assumed to rotate once a day, so the stars were assumed to be lights attached to the dome.

Anyone who assumed that the sky dome was opaque had to assume that the sun and the wandering planets were nearer than the sky dome. I think that it was usually assumed the sky dome was opaque and colored blue, thus making the sky seem blue when it reflected the light of the sun during the day, thus making the sun closer than the sky dome.

Those who kept records of astronomical observations soon noticed that the moon occulted or passed in front of stars, planets, and the sun (solar eclipses), and thus was closer.

Everyone assumed that the sun and the moon were tiny, until traveler's reports showed that they had the same apparent diameters every place that as visited, and so were about equally far away from every place that was visited. Thus as the size of the known world grew larger and larger, the minimum possible size and distance of the moon and the sun grew larger and larger.

The idea of a spherical earth was proposed and gradually accepted by Greek philosophers between the sixth and third centuries BC. Thus the earth became known as Earth, a sphere instead of a flat disc, and the dome of the sky became a hollow spherical shell around it.

In Hellenistic times the diameter of the Earth was calculated with reasonable accuracy, as well as the distance to the moon and thus its diameter. So it became known that the moon was about a quarter the diameter of the Earth and over sixty Earth radii distant.

Because of solar eclipses, it had been known since prehistoric times that the moon was closer than the sun, and keepers of astronomical records of events when the moon occulted (passed in front of) stars and planets knew that the moon was closer than planets and stars.

Anyone who assumed geocentrism, that the Earth was the enter of the universe, naturally assumed that every object revolved around the Earth, including the moon, and that the moon was thus the closest satellite of the Earth. A few ancient Greek philosphers supported the Heliocentric theory, that the Earth and the planets revolved around the sun. Some of them could have believed that the moon also revolved around the sun, but as far as I know all heliocentric believers also had the moon revolve around the Earth.

By the last few centuries BC there were many educated persons who believed that the Earth, the moon, and the sun were giant balls of rock (and thus somewhat similar objects), that the sun was a giant burning rock, and that the stars and planets might also be giant burning rocks far, far away from the Earth and appearing as dots as seen from Earth. Since everybody already since prehistoric times believed that the moon revolved around the Earth, by the last few centuries BC educated people in Western civilization believed that the moon was what we now call a natural satellite of the Earth, though some of them believed and some did not that the sun and planets were also natural satellites of the Earth.

average number of exoplanets in a system

Best answer is that we don't know. The techniques that are used for finding exoplanets are incomplete - that is they are capable of finding planets around stars in some circumstances but not in others.

For example, finding stars using the transit detection technique is more sensitive to planets that are (i) big, (ii) close to their parent star and (iii) orbiting their star with an edge-on orientation from our point of view. The doppler techniques are sensitive to (i) massive exoplanets, (ii) those that are close-in to their parent star, (iii) favour detection when the line of sight lies close to the orbital plane.

Each detection method (and each observing strategy and telescope/satellite) has their own particular selection bias, but overall the picture is that the census of exoplanets is more complete for close-in massive planets, and very incomplete for planets that are either small or orbiting with periods much longer than 10 years. Then at very large separations and very long orbital periods (think 100s of years), direct imaging surveys are again capable of spotting massive exoplanets. Microlensing observations are also capable of detecting even small planets at large distances from their star.

The result of all this is that any figure for the observed fraction of stars with exoplanets or the number of exoplanets per star is a lower limit.
The exception is where researchers try to account for the various selection effects and give a figure for the fraction of stars with certain types of planet in certain types of orbit around certain types of star.

At the moment it looks like the modal number of exoplanets per star is at least 1. In other words it seems increasingly likely that most stars have exoplanets of one sort or another.

Some facts and figures. From Kepler transit data, Petigura et al. (2013) say that 22% of Sun-like stars have "Earth-sized" planets orbiting in their habitable zone (my italics), but their plots show that the overall results for planets with orbital periods in the range 5-100 days (where Kepler is most sensitive), are that nearly 60% of stars have planets from Earth- to Jupiter- sized in this range. Cassan et al. (2012) use microlensing survey data to claim that 17% of stars have "Jupiters" at 0.5-10 au from their parent star, and that Neptune-sized or "super-Earth" sized objects orbit a further (approximately) 50% and 60% respectively. The combination of these figures also suggests multiple planets are not rare and indeed the title of their paper is "One or more bound planets per Milky Way star from microlensing observations".

The frequency of multiple planet systems is also hard to assess. All the techniques are capable of detecting certain types of multiple system, but equally all are capable of missing multiple planets even when they are there.
Kepler did detect many multiple transiting systems, so they are not rare. A study by Tremain & Dong (2012) estimated a minimum fraction of 20-30% of stars that have one transiting planet will also have others. This is on top of the 15% of Kepler planetary systems where multiple planets can be directly observed (i.e where the orbital planes are very close together).

gravity - Does rotation affect gravitational lines of force

An spherical electric charge has the same electric field lines whether spinning or not. The difference between those two cases is entirely in the magnetic field. Thus, one should expect as similar thing to happen for gravity.

The parametrized post-Newtonian formalism, weak-field GTR has the metric
$$mathrm{d}s^2 = -(1+2Phi),mathrm{d}t^2 + 2mathcal{A}_j,mathrm{d}t,mathrm{d}x^j + (1-2Phi)delta_{ij},mathrm{d}x^i,mathrm{d}x^j$$
where $Phiequiv -U$ is essentially the Newtonian gravitational potential, while $mathcal{A}_jequiv-tfrac{7}{4}V_j - tfrac{1}{4}W_j$ in terms of the other PPN potentials. For the four-velocity $U^alphaequiv{mathrm{d}x^alpha}/{mathrm{d}tau} = (U^0,vec{U})$, the geodesic equation for time-independent $Phi$ and $mathcal{A}$ becomes, to linear order in $Phi$,
$$frac{mathrm{d}vec{U}}{mathrm{d}tau} = U^0(vec{G} + vec{U}timesvec{H})text{,}$$
where the gravitoelectric field is $vec{G} = -nablaPhi$ and the gravitomagnetic field is $vec{H} = nablatimesvec{mathcal{A}}$, here $nabla$ being used in the ordinary sense of $nabla_i = partial_i$, i.e. with respect to the Euclidean metric $delta_{ij}$. If $Phi$ and $mathcal{A}$ are not time-independent, then $vec{G} = -nablaPhi - partial_tvec{mathcal{A}}$, paralleling electromagnetism, but there will be an extra term in the analogue of Lorentz force that has no electromagnetic counterpart.

Much the same thing can be done in any stationary spacetime, including the rotating Kerr black hole. See also Costa and Natário (2014) for a much more general treatment of several gravito-electromagnetic analogies.

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References:

1. Costa, L. F. O, Natário, J. "Gravito-electromagnetic analogies". Gen. Rel. Grav. 46, 1792 (2014)[arXiv:1207.0465]

distances - What would be the apparent magnitude of Betelgeuse if it were as close to Earth as Sirius?

The distance to betelgeuse is poorly known, so we don't actually know how bright it is with much accuracy measurements of its parallax by satellite give a distance of 197 parsecs +/- 45 parsecs (1 parsec is 3.26 light years). The absolute magnitude (the brightness if it were 10 parsecs distant) is estimated to be -5.85. This is based on both the distance and models of how bright red supergiants "should" be.

To convert from absolute (M) to apparent (m) magnitudes at distance D one can use the formula:
$$m-M = 5 ((log_{10}{D}) - 1)$$
And at a distance of Sirius (2.54 parsecs) that gives a brightness of -8.7, bright enough to cast shadows, as bright as a crescent moon

A supernova would be a lot brighter. A typical supernova has an absolute magnitude of between -15 and -20, with the low end more likely. Assuming an absolute magnitude of about -16, gives an apparent magnitude of about -19. This would be a bright as interior lighting.

After the supernova, there might be a neutron star which, if it was like the crab pulsar, might have an absolute magnitude of about 4, and at the distance of sirius appear to have a magnitude of about 1, just a little less bright than Betelgeuse is now.

How bright can white dwarf stars glow as they accrue matter?

I realize this is kind of general as it would depend on the size of the white dwarf and the rate of accrual. The general idea I got thinking about is what would happen if a white dwarf star - lets say 0.8 solar mass, well below Chandrasekhar was to accrue a bunch of hydrogen rather quickly. I thought it might be get very hot and bright, perhaps similar to a red giant for a relatively brief period of time.

Mostly White dwarfs add mass by siphoning from the outer layer from a near by co-orbiting star, but I imagine, that mostly happens quite slowly, not fast enough to make the white dwarf shine like a main sequence star.

Are there studies on how quickly mass can be added in this way and how bright it makes the white dwarf? Does Hydrogen quickly fuse on the surface of a white dwarf or does it need to build up to a certain thickness first, perhaps creating a mini flash? or does the fusion happen rather quickly.

A very rough calculation, the escape velocity of a white dwarf, which would be similar to the terminal velocity of matter (mostly hydrogen) falling into it is about 5,500,000 meters/second for a 1 solar mass white dwarf. Source.

The velocity needed for hydrogen fusion is about 20,000,000 meters per second. Source (under the what makes fusion hard section). So, white dwarf's aren't massive enough to create fusion upon impact, but the high density and high heat of impact seems like it could create fusion relatively quickly as matter builds up around them, perhaps creating something that perhaps glows like a star and expands rather rapidly - assuming there's a sustained burn and not a kind of very quick explosion of sorts. I think it could glow very hot and perhaps expand rather large, but I'm just kind of guessing.

If a white dwarf was to crash into, say, a brown dwarf or very low mass star, hydrogen rich, say about .1 solar mass? Such a brown dwarf would be much larger than the white dwarf but also quite a bit lighter, probably light enough to get penetrated completely though the impact would also likely create fusion and it's difficult for me to imagine what would happen with so violent a crash. It seems to me that the density of the white dwarf, if it could retain most of the matter from the brown dwarf would be sufficient that you'd be left with a fast burning light weight fusion star, with a very dense core. This might be an impossible question, but how quickly would a .8 solar mass white dwarf consume the hydrogen from a .1 solar mass brown dwarf, should this rare kind of collision happen. Would it actually form a star-like object for a period of time, say a million years or so, or would the enormous energy of impact basically blow it apart no new star? Perhaps a near miss and an inside the Roche limit approach would be better than a direct impact for new star formation.

Thanks.

Double Planet Orbiting Wide Binary Star?

Generally speaking, there's 2 types of planet systems in a binary - see pretty picture. Source. The writer is a sci-fi writer so the entire article might be of interest to you.

Due to binary star tidal forces, there are some setups that are unlikely but in your example with a 100 AU distance between the stars, an orbit around the larger star is reasonable.

A double planet system is less likely. It's unlikely to form on it's own during planet formation as that requires too much planetary angular momentum during formation.

It's possible, but also unlikely to form by giant impact, as that's more likely to leave 1 planet and 1 moon. I've read (but can't find an article right now) that there's a giant impact size ratio and it's in the planet-moon range, not planet planet. Much less than 1 to 1. Pluto-Charon is 9-1 and Earth-Moon 81-1. A giant impact is also unlikely to create an Iron rich core for both objects. It's not a good way to create planet-planet.

That leaves a 3rd possibility, also unlikely, but perhaps the most likely of the bunch is planet capture. Planets can form in Trojan points in the same orbit (Theia). The difficulty with orbital capture is that the velocity needs to be just right and capture's are likely to be significantly elongated orbits, which, maybe, over time, perhaps with a 3rd asteroid, could even out to slightly more circular. This is very improbable, but it might be the most likely way to form a double planet.

My 2 cents, as a layman.

Frequency of gravitational wave detection

As you may have guessed, this question is of great interest to the LIGO team. Simultaneously with the publication of the paper you mentioned announcing the discovery, the LIGO team submitted a number of companion papers with further details about the discovery, and predictions. One of these addresses your question:

The Rate of Binary Black Hole Mergers Inferred from Advanced LIGO Observations Surrounding GW150914

Their event rate estimation method considers both GW150914, and another significantly weaker (and less statistically significant) event. They consider a number of models for how the event rate might depend on system properties, and ask what the observations of GW150914 and the other candidate event imply for the overall rate. The results vary from model to model, but they chose models they felt could roughly bracket astrophysically plausible behavior. As summarized in their abstract:

Considering only GW150914, assuming that all BBHs in the universe have the same masses and spins as this event, imposing a false alarm threshold of 1 per 100 years, and assuming that the BBH merger rate is constant in the comoving frame, we infer a 90% credible range of $2-53 , mathrm{Gpc}^{-3} ,
mathrm{yr}^{-1}$ (comoving frame). Incorporating all triggers that pass the search threshold while accounting for the uncertainty in the astrophysical origin of each trigger, we estimate a higher rate, ranging from $6-400 ,
mathrm{Gpc}^{-3} , mathrm{yr}^{-1}$ depending on assumptions about the BBH mass distribution. All together, our various rate estimates fall in the conservative range $2-400 , mathrm{Gpc}^{-3} , mathrm{yr}^{-1}$.

Note that the paper is submitted, not published, i.e., still under peer review. Speaking as someone with expertise in such calculations, some aspects of the method look fishy to me, so I think it's worth checking back on the article in a few weeks for revisions. It doesn't take fancy methodology to see that the order of magnitude here (a few to ~100 per cubic gigaparsec per year) is in the right ballpark. But the paper presents a methodology that could make more detailed and more precise estimates and predictions as data accumulate, so it's important to make sure the methodology is sound.

special relativity - Observing a point 13.82b ly away, 1b years ago

Time is kind of funny when you look at such distances. Let's imagine that you are running away from a person throwing a ball at you. The ball will travel further to hit you, based on your speed, than the distance that was present when you started to run.

The universe is expanding. The early Universe expanded very quickly, giving large deviations from the expected position today than what we see through a telescope. Something that we see that is 12 billion years old is actually quite a bit further away today, although we can't know exactly where it is. As I understand, this hypothetical object would be around 40 billion light years away today (See this question), given current theories.

But yes, if you looked at a galaxy that appears in today's distance to be 13 billion light years away, then the universe was 800 million year old, roughly speaking. Galaxies took about a billion years to form, however, so you probably wouldn't see such a galaxy.

How to calculate a planet's apparent size when the planet is viewed from a moon in orbit around it?

By a straightforward bit of trigonometry, if the distance from the observer to the (centre of) the planet is x km, then the radius, r km, of the planet subtends $arcsin(r/x)$, and so the angular size of the planet is twice this: $2arcsin(r/x)$

For Io x = 420,000 km, and the radius of Jupiter is r = 70,000 km, so the angular size is
$2arcsin(1/6)=19^circ$. For comparison, the moon from the Earth has an angular size of about half a degree.

Stellarium can be set up to view from other worlds of the solar system