luminosity - Stellar mass of galaxies

Given the magnitudes (in the i-band) of certain galaxies, I would like to calculate their stellar mass (in terms of solar masses). So far, I have calculated their absolute magnitudes and gotten to working out the mass-light ratio $M/L$ for each galaxy.

e.g. $M/L=0.563$

Values I have are the calculated $M/L$ for each galaxy, and the $i$-band apparent ($13.25$) and absolute ($-18.06$) magnitudes for the galaxy, as well as the distance ($18.44Mpc$).

From this I need to get the mass of the galaxy $M$ in terms of solar masses. Therefore I assume I first need to calculate the i-band luminosity for the galaxy in solar masses $L_i$. This is where I am stuck.

However, once I have $L_i$ next step would be ...
$$M_g = 0.563 * L_i$$

Ultimately, given these values, how would I go about estimating the stellar mass of a galaxy in terms of solar masses?

formation - The life course for a massive star from birth to death using the HR Diagram

I won't primarily explain the H-R diagrams, because I think focussing on some of the underlying physics is essential for understanding, especially stellar nucleosytheses.
For simplification let's assume the star initially consists of nothing else than ordinary hydrogen and traces of carbon and nitrogen.

Nuclear fusion of hydrogen forms helium; fusion of helium forms carbon; fusion of carbon leads to heavier elements like neon, also oxygen, sodium, magnesium; neon decays to oxygen; oxygen fuses to silicon and others; silicon fuses stepwise with helium to iron. Each of these phases of burning needs higher temperature, and it releases energy. The phases can be subdivided in first core burning, then shell burning.

Earlier phases last long enough to be be visible from outside, resulting in motion within the HR diagram. Heating from phase to phase generally results in an overall expansion of the star.
The last phases last only a short time, too short to propagate effects to outside.

Fusion of iron consumes energy. Therefore the star gets a problem after the core consists of iron. Outer pressure cannot be stopped by fusion and further heating: The core collapses to a neutron star or a black hole, while the outer part is blown off by a supernova.
Neutron stars usually rotate rapidly, and cool down over very long periods of time.

After this overall framework you may go deeper into details of the phases.

star gazing - What qualifies as a good place for stargazing, i.e. with least light pollution?

A good question, and in the early 2000s John Bortle published a categorization of a variety of conditions, with descriptions for each category. It is the commonly used scale to describe to others the sort of conditions at a location.

Probably one of the more significant factors provided by a dark sky site is: how faint do stars have to be for you not to see them anymore (overwhelmed by light pollution). There are specific stellar regions, each a triangle, and the idea is you could how many stars you can see in the triangle, and you look the number up in a table, and it will tell you the magnitude limit you are perceiving at that site.

Yes, high altitudes also help - less air between you and the stars means better seeing conditions/less atmospheric distortion.

Being able to see more stars IS better for star gazing. Living in a city, I am continually frustrated at the poor skies, and love being in dark sky locations like the International Dark Skies Reserve at Tekapo, New Zealand.

the sun - How are stellar elemental abundances quoted?

First of all, your first question.

This source clearly state that Values are given in the usual logarithmic (dex) scale, for the same formula that you quoted (similar job).
It is a bit tricky as the article "explains" the values, but you have to pay attention to the exact definition.

I think it is better to work out with an example. Let's take the He.

Good enough, you can better read the paper from here.

From the table, we have $A_{el}=10.93$. This is the abundance of He relative to H (in logarithmic scale).
From this you find out that $frac{N_{el}}{N_H}=0.08 = 8%$.
Indeed the work confirms this value (see the last page).

What you quote as about 25% He, is what they call abundances by mass of [...] Helium (Y), which means $Y = mass of Helium / mass of Hydrogen$, and this is indeed about $25%$.

astrophysics - Assuming a sufficient amount of mass above the density threshold, does the actual concentration of the mass matter in creating a black hole?

... does that mean that any sufficiently large volume of mass over that density is also a black hole? Or does the actual concentration of mass within the event horizon matter?

I'm not completion sure what distinction you're drawing between concentration and density, but I will assume that what you mean by the former is the details of the matter distribution, e.g., whether it's concentrated at the center, spread throughout, or whatnot.

For a spherically symmetric isolated body of mass $M$, it is completely irrelevant. The reason is Birkhoff's theorem: outside the gravitating body, spacetime geometry is necessarily Schwarzschild. This is the general-relativistic analogue of Newton's shell theorem. Therefore, it doesn't matter whether the (radial) distribution is uniform, concentrated at the center, or some kind of shell, or anything else: once it is compact enough that its outer surface gets to the Schwarzschild radius $2GM/c^2$ or below, it is fully enclosed by an event horizon, and is therefore a black hole.

So under those assumptions, the answers to your two questions are 'yes' and 'no', respectively, although you might want to be careful about how you define 'volume' when comparing overall densities.

What happens if we get rid of the assumption of spherical symmetry is a bit more complicated. If we're in an asymptotically flat universe, then we can think of a black hole as all the event from which an ideal light ray fails to escape to infinity, and the boundary would be the event horizon; more generally, we might have to be more careful about how we define 'inside' and 'outside'. Note that this makes the event horizon depend on the future, i.e. it depends on what light rays escape or don't escape even if you wait an arbitrarily long time for them. Hence, in a dynamic situation (such as a collapse to a black hole), where the location of the event horizon depends on not only on the past and present, but also on what will fall into the black hole in the future.

This makes general statements about density quite difficult in situations that don't have some simplifying assumptions. Density is too simplistic; the general notions of a black hole and event horizon are highly non-local.

Nevertheless, there is a general result that is morally similar to the above that is very relevant to your second question: the no-hair theorem. In general relativity, any isolated black hole is fully characterized by conserved quantities at infinity (mass, angular momentum, electric charge...). That means that the details of the matter distribution inside the event horizon do not matter at all. Of course, the singularity theorems guarantee that at least under some general assumptions about the behavior of the matter, it will collapse to a singularity, but that's a separate issue.

Star formation analogy - Astronomy

To begin with, star-formation occurs when relatively stable and huge clouds of gases and dust are disturbed by external disturbances such as shock waves from a supernova explosion. This brings some material closer when gravity kicks in, bringing together more of the gases, which accumulate and grow dense to pull in more material.

This process continues till an enormous amount of material has been accumulated, making it dense at the core i.e. the "center" of the gigantic gas cloud, as well as raising the temperatures and pressures there. This is when the star "ignites", meaning that a fusion reaction kicks in, releases the outward-energy required to balance the inner-crushing gravity of the star.

Since the magnitude of the pressures, temperatures, size of the gas clouds etc. involved here are huge, it's impossible to find such phenomena on the earth.

You can view the episode "Extreme Stars" from the series How the Universe Works (Season 1 Episode 4) that were aired on The Discovery Channel for a detailed visual understanding of the Star formation process.

Have we ever observed a large meteor hit the Moon?

Yes, we have, and the impacts occur very frequently according to "Bright explosion on the moon" (NASA):

For the past 8 years, NASA astronomers have been monitoring the Moon for signs of explosions caused by meteoroids hitting the lunar surface. "Lunar meteor showers" have turned out to be more common than anyone expected, with hundreds of detectable impacts occurring every year.

On March 17, 2013 a significant impact occurred that could have been observed from the Earth.

Updated information about lunar impacts is found at the Marshall Space Flight Centre's Lunar Impacts page. Below is a map of the impacts that occurred on the lunar surface between 2005-2008, all of which, according to the article "Amateur Astronomers see Perseids hit the Moon, could have been seen from the Earth (with a telescope):

There have been instances throughout our history when, so is believed, people on the ground have witnessed lunar impacts. One of the more famous ones was in 1178 AD, when monks witnessed fire coming from the moon; However, according to the article "Historic lunar impact questioned", the accuracy of this historical account is questionable.

radio astronomy - How LOFAR pass through the ionosphere?

LOFAR does not go 'through the ionosphere' as it's ground based. Rather, it is able to receive signals from outside the ionosphere due to the very low frequencies involved. These frequencies (naturally) have very long wavelengths, which means that LOFAR must be very large to obtain a decent level of resolution. The number of antennae will affect sensitivity and reliability.

The furthest horizon in the Solar system

The distance depends on the diameter of the planet and of your height above the surface (such as on a mountain). The greater the diameter, the farther away the horizon will be.

You can see this in the figure below. $d_3 > d_1 > d_2$. On a large planet your horizon (at distance $d_1$) will be farther away than on a smaller planet with horizon distance $d_2$. But if you stand on a mountain on the same planet then the distance will be even larger ($d_3$).

You can calculate the height from Pythagoras' rule because we have a triangle with one unknown edge. The distance from the planet's centre to the point where you see the horizon is the radius of the planet and the distance of the eye of the observer is the radius of the planet plus the height of the observer above the surface.
$$(r+h)^2 = r^2+d^2$$
where $r$ is the radius of the planet, $h$ the height above the surface, and $d$ is the horizon distance. If we rewrite this equation we get:
$$d^2 = (r+h)^2 - r^2 $$
$$d^2 = r^2+h^2+2rh-r^2$$
$$d^2 = h^2 + 2rh$$

For Venus we have $r=6052textrm{km}$ and $h=11textrm{km}$ (Maxwell Montes), we therefore get a horizon distance of 365km. This is still smaller than the horizon distance from Olympus Mons. Olympus Mons is the highest mountain and all other rocky planets are smaller, the horizon distance from Olympus Mons is, therefore, the greatest horizon distance.

Whether the horizon distance in the Rheasilvia crater is greater depends on whether you would be able to see the crater edge from the middle of the crater. Vesta's radius is 262km. If you stand on the crater edge, which is 13km above the crater surface, you would only have a horizon distance of 83km. This means that from the centre of the crater you would not be able to see the crater's edge.

EDIT Above I assume that the 13km is the height of the crater edge above the centre of the crater as measured from the geodesic. If the height is the height above a flat (not spherical flat) surface than the horizon is indeed 505km (see comments below).

cosmology - Dark Matter Particle Candidates

Dark matter appears to dominate the matter component of the universe as compared to luminous, or baryonic, matter. Though it does not interact electromagnetically (it doesn't absorb, scatter, or emit photons), there is an ever-increasing mountain of evidence for its existence through it's gravitational interactions with stars, galaxies, and clusters, as well as it's influence on objects behind it through what's known as gravitational lensing.

My question is, what are the most promising particle candidates of dark matter, and which experiments currently exist (or will exist) to attempt to answer this question?

planetary science - Is there another explanation than an asteroid/volcano for the extinction event on Earth millions of years ago?

Look at Earth's orbit around the Sun. The orbit is an ellipse, but Earth never gets close enough for the Sun to cause any mass extinction. The Earth orbits the Sun every year, and because the orbit is stable, on average we are about 8 light minutes from the Sun.

One way the Earth's orbit might change is if the Sun has a sister companion, that is, a binary star; thus far no evidence suggests the existence of another star in our solar system, but a binary star could alter the orbit of a planet. You could become an Astronomer and try to prove your hypothesis and it would not be a wasted journey.

---

I see you edited your question. Now you have included some aspects about gravity which contradict current knowledge of gravity. I highly recommend reading about gravity. To start you off I will share with you a known fact about gravity. The Earth exerts the same gravitational force on the Sun that the Sun exerts on the Earth. $$F_1=F_2 = G *m_1*m_2/r^2$$

That is, both these objects attract each other with the same amount of force. Moreover, gravity is related to an objects mass, so unless the Sun or the Earth lost mass there would be no change.

light - Time dilation on an object circling earth

At 99% the speed of light the behaviour would be almost completely determined by special relativity. The scenario is well-investigated for synchrotrons. In principle a synchrotron or a storage ring, e.g. around the equator of Earth, could be built.

At 99% the speed of light the frequency $f_s$ of the circling object should occur red-shifted by a factor of a little more than 7 to an observer in the center of the circle due to the transverse relativistic Doppler effect:
$$f_o = f_s/gamma=f_scdotsqrt{1-v^2/c^2}=f_scdotsqrt{1-0.99^2}=f_scdotsqrt{0.0199}=0.141067 f_s.$$
For an observer immediately near the ring, the frequency $f_o$ is the same as for the observer at the center for the signal emitted, when the particle was diametral on the other side of the ring. When approaching the observer along the lign of sight, the signal of the particle is blue-shifted to
$$f_o=f_scdotsqrt{(1+v/c)/(1-v/c)}=f_scdotsqrt{1.99/0.01}=f_scdotsqrt{199}=14.1067cdot f_s.$$
When leaving the observer along the lign of sight, the signal of the particle is red-shifted to
$$f_o=f_scdotsqrt{(1+v/c)/(1-v/c)}=f_scdotsqrt{0.01/1.99}=0.070888cdot f_s.$$

By this we now have calculated the observed frequencies for three positions of the circling particle/radio to give some idea about the oscillation of the observed frequency.

More details about the relativistic transverse Doppler shift, see e.g. Ives-Stilwell experiment. Close to the experiment with the observer in the center of the circling particles are Mössbauer rotor experiments. In this cases ions or atomic nuclei emitting or absorbing at known wavelengths are used as "radios".

This paper describes a slower version of the transverse Doppler shift, as observed by using the GPS satellites moving with just 4 km/s. In this slow case the gravitational frequency shift, as predicted by general relativity to be induced by the gravitational field of Earth, plays a relevant role, relative to the (in this case) small transverse Doppler shift. Here the GPS satellites are the moving radios.

cosmology - If we "turned universe upside-down" and changed all matter to anti-matter instantly

...what would be the immediate consequences?

Or putting it better, if (from big-bang or whathever), the universe were always made of what we call Anti-matter what would it be?

The scientists of this universe would call 'Matter' 'Anti-Matter'.

Will the universe looks like exactly the same? By "looks", I mean the laws of Physics, the constitution of the universe with its superclusters of galaxies containing clusters containing galaxies and so on...

How did the Hulse-Taylor Pulsar Provide Confirming Evidence of General Relativity?

One of the predictions of General Relativity is that certain objects can give off energy in the form of gravitational radiation. This means that over time, the orbit of the two neutron stars should "decay", and they should come closer to each other. Using General Relativity, it is possible to predict the changes in the orbits and the energy of the emitted gravitational waves; analysis of the system showed that General Relativity's predictions were correct. More information (certainly more in-depth) can be found here and here.

N.B. Studying gravitational waves requires linear approximations of the theory of Relativity, involving mathematics that I can't quite explain properly but, fortunately, aren't too important to this topic.

Edit

I haven't been able to find out if other theories (such as Brans-Dicke theory) make similar predictions that agree with observations.

Edit

Referring to the past edit: See this paper for details on the differences in predictions. Long story short, Brans-Dicke theory and general relativity may make identical predictions of gravitational waves, but there is no definite answer.

climate - What is the current accepted theory for Neptune's immense wind speed?

Disclaimer: Most of what is written here is based highly on theory and speculation. Voyager 2 is the one and only trip we have taken to Neptune and most of these theories are built upon the data it has sent back. Leave large room for error

Is Neptune windy?

Before we start answering why Neptune is windy we should first specify if Neptune is even windy in the first place. What proof do we have?

1. The Great Dark Spot

One observation was of a large abhorrence on the surface of Neptune aptly titled "The Great Dark Spot". Repeated viewings placed the movement of the GDS to be about 700mph.

Sourced from: http://nineplanets.org/neptune.html

1. Keck Telescope

A lot of observations and images of Neptune have come from the Keck II Telescope, which is able to observe other markings moving at similar to faster speeds on Neptune.

Sourced From: http://www.keckobservatory.org/recent/entry/keck_images_of_neptune_best_ever_captured1

What causes the winds on Neptune?

It's theorised that there are two potential causes to Neptune's winds. Shallow processes in the outer atmosphere or much deeper atmospheric changes that extend into the interior.

http://www.space.com/21157-uranus-neptune-winds-revealed.html (paraphrased for simplicity) Claims that

The researchers found the windy layers of Neptune occupy the outermost 0.2 percent of It's mass, suggesting that shallow processes drive those winds, such as swirling caused by moisture condensing and evaporating in the atmosphere.

What is the main source of energy for these winds?

So now you are probably wondering where Neptune get's this energy from as it is so much further from the Sun than we are.

http://nineplanets.org/neptune.html Claims that this is due to Neptune's own internal heat source radiating twice as much energy as it receives from the Sun.

Why does Neptune have stronger winds than Earth then?

So theoretically, if it was down to energy, it would make sense that Earth, being so much closer to the Sun, would have much more energy required to reach these speeds.

Yes and No.

The Sun is the main provider for our energy but it also creates turbulence in the atmosphere. It's cooling and heating of the layers keeps air constantly rising and falling, disturbing natural air flows and stemming the size of our storms.

On top of this http://www.space.com/18922-neptune-atmosphere.html claims that 80% of Neptune's atmosphere is molecular Hydrogen.

Hydrogen being the smallest and lightest element requires less energy to reach high speeds than our larger, nitrogen based atmosphere. This may not be a main factor to consider but it is certainly contributing in no small amount.

angular resolution - Inability of Hubble to clearly resolve nearby celestial objects

This has to do with the angular resolution of the Hubble telescope and the ratio between the distance of an object in space and its size in space. The galaxies that the Hubble telescope can see are bigger in size than they are far in light years away compared to pluto from earth.

Take the galaxy NGC 5584 for example:
It spans 50,000 light-years and it's 72 million light-years away which gives us a ratio of 0.00069

Then for pluto:
Pluto spans 2400 km in size and 4675 million km away which gives the ratio of 0.00000051

Take for example a clear view at a mountain with trees on it. You would see the mountain fairly clearly: you can see it has trees on it, perhaps snow, and other aspects. But if you look at any given tree on that mountain you can't make anything other than it's observable color and that it's most likely a tree. The relationship of distance in size is what gives you a good view of the mountain but not a tree on the mountain; the trees size to distance ratio is much smaller than the mountain's size per distance ratio.

the sun - What is the largest recorded solar flare?

A spike in Carbon-14 content was recorded from tree rings in Japan, possibly due to a solar flare 20 times more energetic than the 1859 Carrington Event (the largest definitively recorded solar storm). This event has been dated to 774 AD. I think this could be the most energetic (tentatively) recorded solar flare.

Such a solar storm would be far more devastating today than it was back then, in the sense that we rely so much on technology that the EM interference would cost trillions of dollars in damage to power grids and communications.

A flare would need to be disastrously large, I think, to give us on Earth radiation poisoning. Certainly, animals that use Earth's magnetic field for navigation and would get rather confused. But our atmosphere and magnetic field are adequate protection when we're on Earth.

Here is a good write-up of the situation, with a couple of Nature papers if you have access.

_{If you're going to delve into considering the effects of solar storms on human health (i.e. the effects of magnetic field perturbations), put your tinfoil hat on first. There's a lot of pseudoscience and little substantive research.}

big bang theory - Why aren't the farthest objects close to each other?

I'm going to try to expand a little on my comment regarding inflation. Let me know if it is in any way useful.

Just after the Big Bang, the universe was quite small. Tiny. Smaller than the head of a pin. Then the universe reached the grand old age of $1 times 10^{-36}$ seconds old, and it had a little bit of a growth spurt. Between $1 times 10^{-36}$ seconds and $1 times 10 ^{-33}$ seconds, it expanded at an incredible rate, reaching a size closer to its present-day size.

Before inflation, the universe was - well, we don't really know. Prior to $1 times 10^{-43}$ seconds, all four fundamental forces were unified. But after inflation, they slowly (relative to the time scales we're talking about) became the distinct forces we know today.

Another curious thing happened after the inflationary epoch: baryogenesis. Prior to this, the universe had been made out of an exotic quark-gluon plasma. Now, some of the matter (now spread out throughout space) formed quarks which grouped together to form baryons - some of which are the protons and neutrons we know today. Later on (but still within the first second), electrons formed, and, gradually, the particles we know today came into being.

The objects you're talking about formed 420 million years after the Big Bang - way after inflation! They were never close together; however, their constituent particles were. The reason they are so far away now is mostly because of inflation, but also partly because of the current expansion of space, which comes courtesy of dark energy. The reason we can see these objects in all directions is because inflation made space expand in every direction, so matter is, therefore, in every direction.

I hope this helps.

general relativity - Hulse-Taylor binary pulsar - what is the rate of mass/energy loss from the source?

For reference, the relevant bit from the paper is:

The observable pulsar is a weak radio source with a flux density of about $1,mathrm{mJy}$ at $1400,mathrm{MHz}$. ... Our most recent data have been gathered with the Wideband Arecibo Pulsar Processors (“WAPPs”), which for
PSR B1913+16 achieve $13,mathrm{mu s}$ time-of-arrival measurements in each of four $100,mathrm{MHz}$ bands, using $5$-minute integrations.

Those are millijanskys, aka milli flux units, so that the flux density is about
$$1,mathrm{mJy} = 10^{-29},frac{mathrm{W}}{mathrm{m}^2cdotmathrm{Hz}}text{,}$$
and hence the detected irradiance is on the order of $10^{-27},mathrm{W}/mathrm{m}^2$. Since we're about to make rather uncertain assumptions anyway, I won't bother worrying about doing more than an order-of-magnitude calculation.

Assuming that this flux is uniform across a conical beam with cross-sectional radius 5 arc degrees and assuming that the source is 21,000 light years from Earth ... - How much energy is emitted (per second) from the source in the beam?

A spherical cap has surface area of $A = 2pi Rh$, and here $R = 21,mathrm{kly}$. Now, I'm unclear what cross-sectional radius means if measured as an angle, but I take it to mean that the opening half-angle of the cone is $frac{vartheta}{2} = 5^circ$, in which case
$$A = 2pi R^2left(1-cosfrac{vartheta}{2}right) sim 10^{39},mathrm{m}^2text{.}$$
Thus, the power would be $Psim 10^{12},mathrm{W}$, but note that in addition to the assumptions you've just listed, we're only talking about a particular radio band.

star - Pulsation Modes of Cepheids

Cepheid pulsations

The basic description of the mechanism behind Cepheid pulsations is given here:

The accepted explanation for the pulsation of Cepheids is called the Eddington valve,[38] or κ-mechanism, where the Greek letter κ (kappa) denotes gas opacity. Helium is the gas thought to be most active in the process. Doubly ionized helium (helium whose atoms are missing two electrons) is more opaque than singly ionized helium. The more helium is heated, the more ionized it becomes. At the dimmest part of a Cepheid's cycle, the ionized gas in the outer layers of the star is opaque, and so is heated by the star's radiation, and due to the increased temperature, begins to expand. As it expands, it cools, and so becomes less ionized and therefore more transparent, allowing the radiation to escape. Then the expansion stops, and reverses due to the star's gravitational attraction. The process then repeats.

I can't really describe it much better than this, but let me know if it needs to be made more clear.

Note that this mechanism isn't restricted to helium II/III. Other classes of variable star operate in the same way. e.g. RR Lyraes and $beta$ Cepheids.

The equilibrium state of stars

In all phases, stars are presumed to be in hydrostatic equilibrium: the outward force of pressure in the star (from the gas, radiation and sometimes electron or neutron degeneracy) is precisely balanced by the inward force of gravity. In many phases, we can additional regard the star as being in local thermodynamic equilibrium. What we really mean here is that the star is not generating (or absorbing) energy through expansion and contraction. This isn't true for, say, pre-main-sequence stars, which are only generating energy by their contraction toward the main sequence.

Cepheid pulsations are oscillations about the equilibrium state. They aren't linearly stable but the non-linear components mean that the oscillations aren't big enough to tear the star apart. The calculation of the frequencies is either a tricky sixth-order eigenvalue problem or a simulation of the oscillation from which the frequencies can be determined by analysing the output.

Which modes are excited is a similarly complicated problem. There are many things we haven't actually solved! But you can think of the system as a driven, damped oscillator. The driving is given by the opacity mechanism described above, and the damping is related to the equilibrium structure of the star. So, the excited modes are usually around where these match best, which may happen to be the fundamental mode (where the entire star expands or contracts as a whole) or the overtones (where different layers are expanding or contracting).

star - Why does iron consume more energy in the fusion process than it produces?

It would be good if you referenced your sources, because you may be misunderstanding them. We'd be able to see what they actually say, and help you understand them.

Nucleosynthesis of iron does not use more energy than it produces.

It is, however often referred to as the heaviest element created in fusion that results in more energy produced than consumed.

However, that isn't quite true. Heavier elements can be produced by fusion that produce more energy than is used, except these fusion reactions don't occur in stars. (Eg 40Ca + 40Ca)

Also, it is possible for heavier nuclei to be fused in stars that result in more energy being produced than is used, but these are unstable isotopes and they decay quickly.

So, more accurately, iron is the heaviest element produced in stellar nucleosynthesis in any significant quantity that produces more energy in fusion than the fusion consumes.

This is called the alpha process ladder. Keep adding alpha particles to the newly generated nuclei, until you stop getting more energy out than you put in.

The last step in the alpha process that does produce energy is 52Fe + 4He => 56Ni(excuse the rubbish notation; if this answer is considered helpful at all I will try to tidy up the notation)

56Ni + 4He => 60Zn uses more energy than it produces.

56Ni has a very short half-life of just 6 days, decaying to 56Co which has a half life of 77 days, which decays to 56Fe, which is stable. So when a star is on the limit of collapsing, it will be producing a lot of iron in it's final stages - some of it from decaying heavier radioactive isotopes.

Why does the alpha process stop producing energy at this point? It is because that is where the peak binding energy is. More.

What is the current theory for the formation of the Earth's Moon?

The current accepted theory is known as the Giant Impact Hypothesis, where according to this NASA webpage "Origin of the Earth and Moon" (Taylor) a Mars sized object collided into the early Earth.

This theory allows explanations of (from the link above):

The chemical makeup:

The giant impact hypothesis is consistent with our ideas for how planets were assembled and explains some important features of the Earth-Moon system, such as why the Moon has only a tiny metallic core.

and in terms of orbits:

To account for the amount of angular momentum in the Earth-Moon system, Cameron estimated that the object would need to be about 10% the mass of Earth, about the size of Mars. (Angular momentum is the measure of motion of objects in curved paths, including both rotation and orbital motion. For the Earth and Moon this means the spin of each planet plus the orbital motion of the Moon around the Earth.)

Image source

However, recently, there has been some revisions to this theory.

According to NASA's page "NASA Lunar Scientists Develop New Theory on Earth and Moon Formation", based on concerns that the Mars-sized would likely to have had a different composition to the Earth (inconsistent with the current similarities in geochemistry).

The new hypothesis is (from the link above):

After colliding, the two similar-sized bodies then re-collided, forming an early Earth surrounded by a disk of material that combined to form the moon. The re-collision and subsequent merger left the two bodies with the similar chemical compositions seen today.

This is also discussed in "Huge Moon-Forming Collision Theory Gets New Spin" (Wall, 2012), basing the revised hypothesis on the rotation rate, which is theorised to have been very fast, from the article:

Earth's day had been just two to three hours long at the time of the impact, Cuk and Stewart calculate, the planet could well have thrown off enough material to form the moon (which is 1.2 percent as massive as Earth).

Further discussion, based on the geochemical makeup is discussed in "Geochemical Constraints on the
Origin of the Earth and Moon" (Jones and Palme) conclude that:

Although none of these observations actually disproves
the giant impact hypothesis, we find it disquieting that the
obvious consequences expected of a giant impact are not
observed to be fulfilled.

So, there is still some question as to precisely how the Moon was formed.

fundamental astronomy - Calculation of Horizontal Coordinates

Given a fixed coordinate location on Earth (i.e. a latitude and longitude), and a fixed equatorial coordinate location of a particular astronomical object in the sky (i.e. right ascension and declination), how can I calculate the horizontal coordinates as a function of date and time on Earth?

date time - Why do we need to add a second to 30 June and risk upsetting Internet?

There's quite a few things here that need comments.

First off, the "linking" you describe was actually the first definition of the second (day, hour, and all the way down to second). Remember, since the dawn of civilization we've used celestial bodies to keep time for us.

The phenomena of the Sun and the Moon had good enough precision for all practical purposes until very recently. It was then that the definition of the time unit was rebased to a different phenomenon. BTW, the second of time is not a physical constant. It is a unit of measure currently defined as a multiple of the frequency coming out of the transitions of a certain atom between two different states.

Of course, the motion of the Earth follows its own clock, different from atomic phenomena, so it ought to drift off after a while. Do we "need" to make adjustments then? That's debatable. We still prefer to keep the Earth's clock and our clock in sync, and therefore we make adjustments when necessary. But is it needed in an absolute sense? No, not really. It's just convenient.

As to the risk of "upsetting the Internet", this is an alarmist rumor the likes of the "Y2K bug". I actually happen to work in a related field - I've done infrastructure at a variety of tech companies in the Silicon Valley; the NTP infrastructure (Network Time Protocol - what keeps Internet services in time sync) is something I'm very familiar with. A jump of 1 second should be and will be tolerated by essentially everything that's out there now.

Will there be stragglers here and there that will hiccup when the time takes a tiny leap? Yes. And that's a bug, the engineers need to look at the software and fix it. Remember, a lot of existing services (like Google Search, or Instagram) have servers and instances right now that are off by more than 1 second (just the way there are cars coming out of the assembly line with missing bolts once in a while), and usually nothing bad happens as long as the drift is not too big); fix NTP, the time base jumps on that instance, and again nothing bad happens in the vast majority of cases.

Relax, nothing important will be "upset". In fact, I doubt that the vast majority of people will be affected in any perceivable way.

core - What is the current accepted theory as to why Mercury, despite its size, has a similar density to Earth?

The most-widely accepted hypothesis at the moment is that Mercury was struck by a large impactor that removed a significant fraction of its mantle (I believe this theory was originally proposed by Cameron & Benz in 1987, and the qualitative theory hasn't changed very much). For planets that are close to their parent stars (such as Mercury), the collision with the secondary body likely occurs at high velocity due to the rapid orbit speeds there (> 40 km/s). As this is much larger than a typical rocky planet's escape velocity (~10 km/s), material is lost from the planet in these collisions. This collision is also more likely to be "grazing," as "direct hits" are rare, and thus the outer parts of the planet are preferentially removed.

Because the mantles of rocky planets are primarily composed of silicates, which have a lower density than iron that resides in their cores, the collision results in a surviving planet with a higher average density.

regarding curvature of earth - Astronomy

Earth's rotation doesn't help airplanes much: the air is almost stationary with respect to the earth and airplanes move relative to the air. Suppose a hot air balloon. Air is dragged along with the rotation of earth, so the balloon will almost be stationary. (Ok, it moves, but only slowly.) So whether the plane travels east or west for 1000 km, it has to travel 1000 km against air which is 900 km/h slower.

There is a meteorological effect that planes can use, though. The jet stream is a channel of very high speed winds at high altitude.

Planes traveling east, for instance from the US west coast to the east coast, or from America to Europe, take advantage of this jet stream to save fuel. Note that the jet stream isn't anywhere as fast as the earth's rotation. At 50 degrees north the earth's rotation is about 1000 km/h, while the jet stream is about 200 km/h.

observation - How can an amateur astronomer verify the position of near Earth objects?

Sometimes, hobby-astronomers use rather professional means to observe the big voids of space. Every now and then (think in months, not days) even I can locate an NEO (near Earth object).

Now, I'm assuming governments and institutions worldwide track such NEOs, have the best options to observe them, and most probably accumulated more data than we could wish for.

For hobby-astronomers who spot an NEO, it could be of interest to verify the location of the spotted NEO, and maybe even learn more about a specific NEO from additional data like name, type, path, direction, speed, first observed, etc.

Is there any publicly available, NEO-related database out there? Or is there a specific institution a hobby-astronomer can/should turn to to be able to learn more about individual NEOs?