gravity - What it would look like to observe people with a different time flows?

Normal case:

The effect would not be very noticeable unless the large planet was extremely large / high gravity (e.g. it would look "almost" normal) looking at one another. If the planet was that large, it would probably not be able to support life, but to see what would happen, lets assume it can support life.

Relativistic case, from the large planet, observing the small planet:

If the large planet were extremely "heavy / massive" (think more like a neutron star), the people on the large planet would observe the people on the small planet moving much faster. It would be like watching a movie with "fast forward" on. However, light would also be blue shifted, which would produce other interesting visual effects (e.g. what was red might now be blue, and what was in invisible "infrared" might now be red depending on the amount of the shift.) The amount of blue shift (light wave compression) and "fast forwarding" would increase if the planet were made bigger. The rest of the universe would have similar effects when observed from the large planet.

Relativistic case, from the smaller planet, observing the large planet:

The people on the smaller planet would observe the people on the extremely large planet moving in "slow motion". It would be like watching a movie in slow motion. The people on the large planet would also be "red shifted". For example, something that was blue might appear red, and something in the ultraviolet range might now appear blue. The "slow motion" effect and red shift (light wave expansion) would increase if the extremely large planet were made bigger.

solar system - Planets and moons positions in cartesian coordinates?

Is there freely available and reliable source, where one can find positions of planets and moons of the Solar system at given time in cartesian coordinates? (I am writing a simple gravity simulator and it would save me a lot of work with conversion.)

general relativity - Travelling at light speed(inside water)

It is a said fact that 299792458 m/s is the speed limit,nothing can go faster than this speed, or it will take an infinite amount of energy for propulsion.What we perforce in vacuum is one thing.Can someone explain what will be observed(from the particle's frame and an observer frame at rest) if a particle of a non zero test mass moves at light speed inside a non vacuum medium(say water) as this velocity is definitely lesser than the limit.
THANKS IN ADVANCE

What is needed to break through the surface of Europa?

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

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

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

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

Evolution of Life - Astronomy

Lacking both observation of ET life and a good understanding of how life originated, this question remains a great mystery. One can never completely disprove the existence of extraterrestrial life.

There are two basic approaches to potentially answer this: one theoretical and one empirical.

• If a good theoretical understanding of the origin of life, abiogenesis, is achieved in laboratories, then the frequency of it happening given different observed exoplanetary conditions could be estimated.




• Empirically, of course we might be lucky enough to discover some statistics of actually observed living exoplanets.

But there's a third way too, the SETI way. The evolutionary steps to intelligence, to technology, to space travel all seem to benefit the proliferation of life and thus would tend to become more common over time, if they at all occur. Considering the small size of the Milky Way compared to its age and reasonable space traveling and settling speeds, one could put upper limits on how common life is.

If anyone anytime anywhere in the Milky Way developed space travel to its nearest stars, they (their offspring) should be everywhere today! They won't need to travel further than a few light years to "seed" the entire galaxy, because their Sun does the traveling through the galaxy for them. Our Sun makes a revolution every 0.25 billion years, 18 full revolutions since it was formed. We know that dinosaurs lived on the other side of the galactic center. Traveling to the nearest stars over time spreads a space traveling civilization to all over the place. If we don't find any signs of artificiality during the next few decades, given the rapid advancements in telescopy, we can say that space traveling civilizations never happened anywhere (or got too exotic for us to discover even if under our nose). And that might be extrapolated to how frequent biological evolution is overall. And most importantly, what unique event happened here to make us walk on the Moon.

On Earth, life has settled every habitable spot on Earth (everywhere where liquid water is found, life is also found). Maybe life tends to settle on interstellar scales too?

gravity - What are the arguments against the Feng and Gallo thin disk explanation of galactic rotation curves?

Feng & Gallo have published a series of extremely similar papers, all of which essentially claim that they have "discovered" a major flaw in the way (some) astrophysicists think about rotation curves. Instead of assuming spherical symmetry, they try to solve for the mass distribution, using a rotation curve, without assuming spherical symmetry, instead adopting a planar geometry with cylindrical symmetry.

Of course they do have a point; statements that the flat rotation curve can be compared with a Keplerian prediction (that assume spherical symmetry, or that all the mass is concentrated at the centre) are overly simplistic. So far so good, but they then go on to claim that their analysis is compatible with the total stellar mass of galaxies and that dark matter is not required.

So, in their planar model (and obviously this is open to criticism too) they invert rotation curves to obtain a radially dependent surface density distribution that drops pseudo-exponentially.

Problem 1: They concede (e.g. in Feng & Gallo 2011) that "the surface mass density decreases toward the galactic periphery at a slower rate than that of the luminosity density. In other words, the mass-to-light ratio in a disk galaxy is not a constant". This is an understatement! They find exponential scale lengths for the mass that are around twice (or more for some galaxies) the luminosity scalelengths, so this implies a huge, unexplained increase in the average mass to light ratio of the stellar population with radius. For the Milky way they give a luminosity scalelength of 2.5 kpc and a mass scale length of 4.5 kpc, so the $M/L$ ratio goes as $exp[0.18r]$, with radius in kpc (e.g. increases by a factor 4 between 2 kpc and 10 kpc). They argue this may be due to the neglect in their model of the galactic bulge, but completely fail to explain how this could affect the mass-to-light ratio in such an extreme way.

Problem 2: In their model they derive a surface mass density of the disk in the solar vicinity as between 150-200 $M_{odot}/pc^2$. Most ($sim 90$%) of the stars in the solar neighbourhood are "thin disk" stars, with an exponential scale height of between $z_0= 100-200$pc. If we assume the density distribution is exponential with height above the plane and that the Sun is near the plane (it is actually about 20pc above the plane, but this makes little difference), a total surface mass density of $sigma = 200M_{odot}/pc^2$ implies a local volume mass density of $rho simeq sigma/2z_0$, which is of order $0.5-1 M_{odot}/pc^3$ for the considered range of possible scale heights. The total mass density in the Galactic disk near the Sun, derived from the dynamics of stars observed by Hipparcos, is $0.076 pm 0.015 M_{odot}/pc^3$ (Creze et al. 1998), which falls short by an order of magnitude. (This does not bother the cold, baryonic dark matter model because the additional (dark) mass is not concentrated in the plane of the Galaxy).

Problem 3: For the most truncated discs that they consider with an edge at $r=15$ kpc, the total Galaxy mass is $1.1times10^{11} M_{odot}$ (again from Feng & Gallo 2011 ). The claim is then that this "is in very good agreement with the Milky Way star counts of 100 billion (Sparke & Gallagher 2007)". I would not agree. Assuming "stars" covers the full stellar mass range, then I wouldn't dissent from the 100 billion number; but the average stellar mass is about $0.2 M_{odot}$ (e.g. Chabrier 2003), so this implies $sim 5$ times as much mass as there is in stars (i.e. essentially the same objection as problem 2, but now integrated over the Galaxy). Gas might close this gap a little, white dwarfs/brown dwarfs make minor/negligible contributions, but we still end up requiring some "dark" component that dominates the mass, even if not as extreme as the pseudo-spherical dark matter halo models. Even if a factor of 5 additional baryonic dark matter (gas, molecular material, lost golf balls) were found this still leaves the problem of points 1 and 2 - why does this dark matter not follow the luminous matter and why does it not betray its existence in the kinematics of objects perpendicular to the disc.

Problem 4: Feng & Gallo do not include any discussion or consideration of the more extended populations of the Milky Way. In particular they do not consider the motions of distant globular clusters, halo stars or satellite galaxies of the Milky Way, which can be at 100-200 kpc from the Galactic centre (e.g. Bhattachargee et al. 2014). At these distances, any mass associated with the luminous matter in the disk at $r leq 15$ kpc can be well approximated using the Keplerian assumption. Proper consideration of these seems to suggest a much larger minimum mass for the Milky way independently of any assumptions about its distribution, though perhaps not in the inner (luminous) regions where dark matter appears not to be dominant and which is where F&G's analysis takes place. i.e the factor of 5-10 "missing" mass referred to above may be quite consistent with what others say about the total disk mass and the required dark matter within 15kpc of the Galactic centre (e.g. Kafle et al. 2014). To put it another way, the dynamics of these very distant objects require a large amount of mass in a spherical Milky Way halo, way more than the luminous matter and way more even than derived by Feng & Gallo. For instance, Kafle et al. model the mass (properly, using the Jeans equation) as a spheroidal bulge, a disk and a spherical (dark) halo using the velocity dispersions of halo stars out to 150 kpc. They find the total Galaxy mass is $sim 10^{12} M_{odot}$ and about 80-90% is in the spherical dark halo. Yet this dark halo makes almost no contribution to the mass density in the disk near the Sun.

Problem 5: (And to be fair I do think this is beyond the scope of what Feng & Gallo are doing) Feng & Gallo treat this problem in isolation without considering how their rival ideas might impact on all the other observations that non-baryonic dark matter was brought in to solve. Namely, the dynamics of galaxies in clusters, lensing by clusters, the CMB ripples, structure formation and primordial nucleosynthesis abundances to state the obvious ones. A new paradigm needs to do at least as well as the old one in order to be considered competitive.

asteroids - Detecting Deep Impact

Something to consider might be a large very dark (low albedo) asteroid. I would say it is quite possible a large dark asteroid (e.g. P-type) "could" be headed for us, and we would not know it until it hit us (e.g. distance 0). I think you are asking for the closest distance. It appears the main method of detecting asteriods is with telescopes, but we are starting to scan the skies in infrared too. Hopefully infrared will reveal these darker asteriods better. Sources for further research include:

http://en.wikipedia.org/wiki/P-type_asteroid

http://www.space.com/3126-asteroids-data-sheet.html

http://www.nbcnews.com/science/space/how-we-scan-solar-system-find-dangerous-asteroids-f8C11480423

For the furthest distance, that question is trickier. It would largely depend on what is considered an asteroid, for example, if we consider Pluto to be an asteroid, we can at least detect very large asteroids out to the distance of Pluto, and we could track its path and see if it were on a collision course with earth.

On average, it is said that we have already detected most of the globally threatening asteroids and it does not appear we are in immediate danger. Still, I'd say we need to stay on the lookout, and especially look out in infrared to detect any dark asteroids we may have missed :-).

Summary:

• Closest distance before large threatening asteriod detection: 0 (e.g. upon impact)


• Furthest distance before large threatening asteroid detection: Beyond the orbit of Pluto (and most asteroids tracked are in the asteroid belt between Mars and Jupiter)

astrophysics - What causes the dimensions of a star increase when its hydrogen fuel is exhausted?

The Sun will never run out of Hydrogen. This is a common misconception.

At this moment the Sun is fusing Hydrogen into Helium. This fused Helium remains at the core until it will reach a critical mass. At this point the core will begin to collapse. This collapse increases the temperature and pressure around the core where Hydrogen is being fused causing the increase the Hydrogen fusion which also causes an increase of the radiation pressure making the outer layers to expand and cool.

Once the core reaches a temperature of about 100 million Kelvin Helium fusion starts dramatically (Helium Flash) with high radiation pressure in the core. Here is where the Sun will reach 250 times it's current radius.

When the Helium fusion stabilizes the radiation pressure at the cores decreases making the Sun's radius to shrink.

The temperature will only drop at the surface because as it's expands it's further from the core.

meteorite - Are micrometeorites cosmic dust?

Micrometeorites are just tinier versions of regular meteorites. As such, they can have the same composition as any other meteor class. There's nothing that we know of that says they have a chemistry more like one kind of dust source, although this is controlled entirely by observational bias. Certain types of particles are more likely to make it to our planetary neighborhood.

We know that interstellar dust grains are found in meteorites, as are all kinds of other grains. Most (or many) meteorites we have contain grains from all over our cosmic neighborhood, including those formed long before our Earth, and they're conglomerated together in the meteorite matrix. Micrometeorites are smaller and will have less types of grains and likely more weathering due to their higher surface area to volume ratio.

To answer your question: are micrometeorites cosmic dust?

Some probably contain microscopic bits of cosmic dust, but some won't, and those that do aren't necessarily entirely made of cosmic dust.

classification - What physical features determine if a planet is a major, minor or dwarf planet?

Planets

For a body to be classified as a planet it must have a few physical characteristics:

Mass

It must have enough mass to have a strong enough gravity to overcome electrostatic forces to bring it to a state of hydrostatic equilibrium.

Hydrostatic equilibrium is important because early in a planets life it is nearly entirely fluid, crust and all

Internal Differentiation

The life cycle of a planet essentially leads to denser heavier metals being at the centre of a planet, surrounded by a mantle which must at some point have been fluid (it can still be solid and called a planet as long as it used to be fluid.)

Atmosphere

This is usually driven by its mass but a planet should have an atmosphere. This means it should be massive enough to have a strong enough gravity to hold some gasses to its surface.

More massive planets are capable of keeping lighter gasses, such as hydrogen, bound to them too. I.e Jupiter.

Magnetosphere

A magnetosphere suggests that the body is still geologically active. This means they have flows of elements that conduct electricity in their interiors.

As specified by the IAU:

A celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.

Minor Planets

Minor planets are things such as asteroids, they are usually small mass, rocky bodies. This is different from small mass bodies that might be predominantly ice or water.

Dwarf Planets

Size and Mass

The IAU have not specified an upper or lower limit for mass to be considered a Dwarf Planet, therefore it is predominantly determined by one other feature called:

Orbital Dominance

Orbital dominance is achieved when a body has cleared it's orbit of all other bodies.

For example planets are able to remove small bodies out of their area through impact, capture, or gravitational disturbance.

Any body that is incapable of doing so is therefore classified as a dwarf planet. So if Jupiter was incapable of clearing its neighbourhood of bodies then it too would be a Dwarf planet.

Do we expect life to develop only in certain regions of the galaxy?

There's a short answer here and a long answer.

Short Answer: It isn't special.

Long Answer: Yes and No.

The Local Bubble really isn't so special with regards to where it's placed in the galaxy. Location-wise, it's perched on the inner edge of the Orion Arm, one of the Milky Way's spiral arms. The Orion Arm, too, isn't incredibly special. It's relatively small - it's often referred to as the "Orion Spur" - and near 1/4 of the way out from the galactic center. Not too far away, but not too near. The donut-shaped area 4,000-10,000 parsecs out from the galactic center is, however, sometimes called the Galactic Habitable Zone. In theory. life as we know it could exist quite nicely any where in this area (I should note that the scientific community is divided on whether the Zone is important, with some saying that it is arbitrary).

But let's dive in deeper. Actually, we're in a decent spot in the "Arm." We're on the edge of it - not too near large groups of stars that could effect our system via gravity, or near any supernova candidates. And the "Arm" itself isn't really a spiral arm. It is, as I said earlier, more of a spur, or bulge. There aren't as many stars to watch out for. Also, we're near the corotation circle - i.e., we orbit the galaxy at such a distance that we move at a similar speed to the arms, reducing further the likelihood of crossing them. Is this necessary for life? Nope. But does it help? Oh, yes.

There are, of course, other factors that make this area a nice spot: No black holes nearby, gamma-ray bursts, etc. But could life survive elsewhere? Yep. These same characteristics can be found in many other places in the galaxy - and life can probably survive in even more dangerous spots.

By the way, I'd avoid using the term "nebula". Technically, we're not in one, or anywhere near one. The term can refer to a multitude of objects - planet-forming areas, "clouds" surrounding white dwarfs, and other rather photogenic places - none of which we inhabit.

I hope this helps.

earth - Why do some artificial satellites decrease and increase in brightness multiple times?

I do not know for sure, but you are viewing the satellites by the reflection of sunlight. As the satellite moves across the sky, the Sun-satellite-you angle changes, therefore there is no reason to expect that the brightness should stay the same.

As for why it should fade and brighten again - if you imagine the satellite to consist of a number of surfaces, these surfaces may essentially cast a beam of light onto the Earth, which move across the Earth's surface. The satellite will brighten as one of these beams crosses you. I suppose this could happen several times for the same satellite.

The extreme examples of this are the Iridium satellite that "flare up" to magnitude -8, before fading in a matter of seconds.

gravity - Is the moon moving further away from Earth and closer to the Sun? Why?

Yes, the moon is moving away from Earth at around 1.48" per year. According to the BBC:

The Moon is kept in orbit by the gravitational force that the Earth exerts on it, but the Moon also exerts a gravitational force on our planet and this causes the movement of the Earth's oceans to form a tidal bulge.

Due to the rotation of the Earth, this tidal bulge actually sits slightly ahead of the Moon. Some of the energy of the spinning Earth gets transferred to the tidal bulge via friction.

This drives the bulge forward, keeping it ahead of the Moon. The tidal bulge feeds a small amount of energy into the Moon, pushing it into a higher orbit like the faster, outside lanes of a test track.

So, tidal forces are ultimately what causes this to happen.

Also, there is a Wikipedia article on tidal forces:

Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon), and the primary planet that it orbits (e.g. the Earth). The acceleration causes a gradual recession of a satellite in a prograde orbit away from the primary, and a corresponding slowdown of the primary's rotation. The process eventually leads to tidal locking of first the smaller, and later the larger body. The Earth–Moon system is the best studied case.

cosmological inflation - Is there matter forming in the inflationary space?

A note: don't talk about inflation for the current expansion. Inflation is the brief period immediately after the BB when the universe expanded at an outlandish rate.

Matter was formed when the universe was so compact that its temperature was billions and even trillions of Kelvin hot. The energy of the vacuum in any given volume was so high that matter-antimatter pairs were created, which usually quickly annihilated. Sometimes, however those short-lived particles collided, releasing large amounts of energy. For instance, to create an electron you need an energy of 0.5 MeV. The graph below shows that at a temperature of $10^{16}$ K collision energy could be as high as 1 TeV.

Because of its expansion the universe has cooled so much that its temperature is less than 3 K, which isn't nearly enough to create any new particles.

The graph shows how temperature and energy drop as the universe expands in the first seconds after the BB. Note that at 1000 seconds (about 20 minutes) the energy is too low to create electrons (0.5 MeV), let alone heavier elements.

What is created in the expansion, though, is dark energy. Its density is constant, so when the universe expands to double its size the amount of dark energy will also be doubled. (That's the reason why the expansion goes ever faster and faster, with nothing to stop it.)

light - Do contracting objects show redshift?

shouldn't contracting objects show a redshift?

Yes, they should. But do they, actually? That's the better question.

To have any appreciable redshift, the speed of the object needs to be huge. That will be a very short implosion. Also, there aren't many mechanisms that can accelerate implosions that much.

What I'm saying is - it's theoretically possible, but in practice you won't see it that often, if ever.

And if so it should be less towards the edges than towards the centre,
right?

Sure. If the object is transparent to its own radiation, then you'd see blueshift from the other side, too. Again, this is very theoretical.

constellations - When is the belt of Orion slanted from right to left, going up? (Egypt)

EDIT: entirely new answer based on comments

You may actually be on to something here.

The most obvious (and thus least interesting) answer is that they were
depicting Orion shortly after sunset, not shortly before sunrise (all
times UTC):

Here is the helical rising of Orion today, and it does indeed go right
to left:

If we go back 1000 years, it's much closer to being a straight line:

And if we go back to 1473 BCE (which is -1472), the rising is clearly
left to right:

Interestingly, if we go far enough south, the rising is right to left
even in -1472:

Note that position in which Orion rises doesn't change much from day
to day. In other words, the position of Orion's stars at helical
rising are the same as the position of Orion's stars at rising any
other day of the year. Because of precession, the position does
change over long periods of time, but not day to day.

The only problem with the "most obvious" answer above is that we know
the Egyptians were very interested in helical risings, so it would be
odd to see a depiction of a "helical setting".

orbit - Average amount of annual daylight at any place on earth

Wikipedia strikes again:

The naive expectation is that, for every place on Earth, the Sun will
appear to be above the horizon for exactly half the time. Thus, for a
standard year consisting of 8760 hours, apparent maximal daytime
duration would be 4380 hours. However, there are physical and
astronomical effects which change that picture. Namely, atmospheric
refraction allows the Sun to be still visible even when it physically
sets below the horizon line. For that reason, average daytime
(disregarding cloud effects) is longest in polar areas, where the
apparent Sun spends the most time around the horizon. Places on the
Arctic Circle have the longest total annual daytime of 4647 hours,
while the North Pole receives 4575. Because of elliptic nature of the
Earth's orbit, the Southern Hemisphere is not symmetrical: Antarctic
Circle at 4530 hours receives 5 days less of sunshine than its
antipodes. The Equator has the total daytime of 4422 hours per
year.

Further details here on astronomical causes of average daytime variation, and here on Insolation, the solar radiation received at the top of the atmosphere and its effects on the energy received at ground level.

stellar evolution - Burning Out Stars

The easiest way to think of it is terms of the cube square law coming into play.

The speed at which a star can radiate heat is mostly dependent on its surface area. but it's ability to generate heat is dependent on its volume. Surface area increases with the square of the increase in radius but volume increases with cube of the radius. As a star grows in a diameter it's inside grows faster than its outside.

Even if all other factors stayed the same, the star would grow hotter because it has less surface area to radiate from.

Since gravity is dependent on volume, the gravitational compression (simplistically) scales with the cube as well. So, a larger star compresses its interior more per unit of mass than does a smaller star.

As Joan.bdm pointed out, stars have an interior volume, the burning zone down towards the core in which the pressures are high enough for fusion to take place. Probably should call it the burning volume

The burning volume is the volume in which fusion can occur. Fusion occurs once a specific threshold of heat and pressure have been reached. Below that threshold, fuel consumption is zero.

The cube square law means that the relative size of the burning volume to total volume increases faster than the diameter. E.g If a small star has ten percent of its mass inside the burning zone, a star with twice the diameter will have 20% of its total volume inside the burning zone. (actual ratios invented for demonstration purposes.)

A higher percentage of the larger star's total mass is inside the burning zone compared to a smaller star so a higher percentage of the star's mass is subject to fusion at any given time, so a higher percentage of the star's total "fuel" is being "burned" at any one time than in a smaller star.

The addition of more fusible isotopes also does not scale linearly. Fusing heavier elements does not release as much energy per unit of mass as lighter ones and they require higher temperatures to start i.e. heavier elements are a poorer fuel. The heavier elements are also produced by fusing lighter ones so the star has to burn fuel to make fuel. Since heavier elements require higher temperatures to fuse, the burning volume for them is smaller than that for lighter elements. Stars usually can't burn more than small percentage of the elements isotopes they produce so the notional increase in fuel supply doesn't compensate for the higher burn rate of lighter elements.

It's like the bard said, "The candle that burns twice as bright, burns half as long."

Why are planets spherical? - Astronomy

When a planetary system is born, most material to build bodies is in fine dust(gas state/plasma) because it has termo-dynamic high , thus is easy that gravity force create regular spherical forms width very weight materials as iron (earth center) after that system planetary is yougest (lower termo-dynamic),it has planets and smal bodies with regular forms but with trajectory collision, after has collisions occurred , it has regular and irregular bodies, when it reach state like as solar system, it has regular forms(spherical) semi-regular(with flat surface but irregular form as phobos) and irregular (asteroids),

Other razons:

because the main axis force from Centripetal force of solar system, has a direction to west-east axis (earth)

Some bodies(planets and satellites) has liquid state matter and this dragg solid matter in her surface

Tectonic plate changes create deformation in surface bodies( Monts etc.)

exoplanet - What does the term alien planet actually refer to?

Very interesting article!. The term alien planet is not a scientific one, so I think you already answered your own question by saying that it was used in the article to generate more buzz.

In the English language the word is used to describe something that's not familiar, so you could argue that this is in fact an alien planet, but because of the subject in question being an exoplanet I would bet they did this as a technique to get more attention.

Where is a Hollow Object's Center of Gravity?

If by "a hollow object" you mean a spherical shell -- a theoretically perfect sphere Moon, with a perfect sphere of material removed from the center: The center of mass, and therefore the center of gravity remains at the geometric center. Ref Newton's Law; Bodies with spatial extent.

The body of the moon is plastic; Meaning the gravitational forces are strong enough to reshape the material... it basically flows into a sphere. So if you magically removed a small amount of the center, it would collapse into a smaller sphere. If you removed most of the center, then the "thin" shell may or may not be strong enough to support it's shape.

Inside a hollow spherical shell, there is no net gravitational force. So you would be in a zero-G environment everywhere within the shell. From outside the shell, the gravity is the same as if all the remaining mass was located at a point at the geometric center.

solar system - Determining North-South Line Via Watch Method: Theory & Reason

When the Sun is on the meridian and is due South (local noon in Northern Hemisphere) your hour hand will point to (or close to 12) - assuming your local noon and civil noon are similar! (Daylight saving means 1pm fills this role).

The Sun crosses the sky in 24 hours, the hour hand travels round the watch in 12 hours. Hence the watch hour hand is twice as fast, so when the hour hand has reached 2pm, the Sun has only gone half as far (ie "to 1pm"), so if you point the hour hand towards the Sun in this case, the meridian is an hour further behind rather than 2 hours.

By the time we get to 4pm the Sun will have travelled "two watch hours" away from the meridian and so on.

nebula - Do heavier elements breakdown during supernova?

The answer is that in a pre-supernova star, most of its mass is still in the form of hydrogen and helium. It is only the central core where the primordial H and He has fused to heavier elements.

This picture of onion layers is typically what you see in elementary text books. It is completely misleading in a quantitative sense. It schematically represents what's at the centre of the pre-supernova star, but in terms of the mass that is in each shell (it is obviously a 3d object) you get completely the wrong idea, because this diagram is only about 1 Earth diameter across, compared with the actual stellar radius of something like the distance between the Earth and the Sun!

Here is a more sophisticated plot taken from a paper by Fuller et al. (2015). It shows time until the supernova along the x-axis and the y-axis represents a radial assay of the chemical composition from the centre of the star to the outside. The initial total stellar mass is $12M_{odot}$. As you move leftwards towards the supernova explosion, notice how what is at the core changes - from being H dominated, to He dominated, to C/O dominated then Si and finally Fe (actually iron-peak elements). Note how much mass is contained within these core region for each stage of nuclear burning. The edge of the "helium core" encloses the central $4M_{odot}$ of the star. The subsequent heavier element cores inside the onion ring structure enclose significantly less mass, until the iron core is around $1.3M_{odot}$ just prior to the explosion. Blue shading indicates regions that are thoroughly mixed and homogenised by convection.

After the explosion, the neutron star that is produced will also have a mass of around $1.3-1.4M_{odot}$. In other words most of the rest of the star (about $10M_{odot}$ just prior to the explosion) gets blown out in the supernova. But of the $8.6M_{odot}$ that makes into the interstellar medium, well over half is still in the form of hydrogen and helium; the minority will be carbon, oxygen, neon, silicon, iron etc., and only a very small fraction of that will have been transformed (by the r-process) into elements heavier than iron and nickel.

Thus although the material injected back into the interstellar medium is enriched with heavier elements, there is still plenty of hydrogen to start a new generation of stars. It is also the case that star formation is an inefficient process, so the material from which the supernova progenitor formed will still mostly be around in the interstellar medium. The picture you should have is of a gradual enrichment with heavy elements, especially as the interstellar medium gets churned up and mixed through a variety of processes (including supernova explosions!).

EDIT: Here is an even more awesome picture. The lower plot shows the relative mass fraction of each element as a function of enclosed mass as you work your way out from a 15 solar mass star (it has shed 2 solar masses during its evolution). The really awesome thing is that it is animated, so it shows you the first few moments after the core-collapse and how things start to change. Note that the outer $5M_{odot}$ of the envelope is about half H and half He by mass prior to the core collapse. Lots of He and then O in the layers below that. The upper plot show how the density temperature and outward velocity are behaving. The image is from the website of Woosley and Heger (2007), a canonical work on the subject.

Hmm. I can't upload the animated gif. Here it is; well worth a look.

Is it possible for a person to not see the new moon at different places on earth?

+taupunkt basically answered this: the thin lunar crescent after New Moon is only visible for a short while after sunset. While the sun is up, the moon is invisible and it becomes visible when, after sunset, the sky turns dark enough. However, the moon will set typically 1-2 hours after sunset, and will become invisible some time before that due to atmospheric extinction. Whether or not, and if so for how long, you can actually see the moon's crescent depends on the local cirumstances: the distance between the sun and moon (which correlates with the lunar phase and depends on your geographical longitude), the angle between the ecliptic and the horizon (depends on your latitude), whether you're in a mountainous area (and if so, whether you're on a mountain top or in a valley), atmospheric humidity, the weather (a few clouds at the western horizon is all it takes), whether you use your naked eye, binoculars or a telescope, your eyesight and experience, etc.

Because of this, it is difficult to predict when you can see the first/last moon crescent. I use this paper to do that for the Netherlands (Google translation, should be ok since it's a table) and for the naked eye. One thing that strikes me is that of the 25 cases of a first/last crescent sighting this year, the lunar phase ranges from 1.2-9.2%, with a mean of 4.0%, so 0.8% seems to be rather optimistic. You may allow the use a telescope though.

The table doesn't list how long the moon is visible for (the prediction of whether the moon is visible or not is sufficiently uncertain by itself), but it will definitely not be more than the time difference between the rise/set times of the sun and moon (~1-2h). If we use half of the average of those numbers, we get 45 minutes, which may well be optimistic but is not too unrealistic either (for a ~4% crescent). The other ingredient is how long the lunar phase is at 0.8%. Assuming that this means between 0.75% (below which it would be rounded down to 0.7%) and 0.85% (above which it would be 0.9%) this was the case for ~97 minutes for the last time this happened (July 27). Together with the 45-minute observation window, this gives a ~142-minute window of opportunity, or about 10% of a day, indicating that the crescent would be visible from ~10% of the earth.

Remember that we assumed a 4% crescent here, not 0.8%, so this 10% is an overestimation. My guess is that it is a huge overestimation, since in most places you will not be able to see the moon with the unaided eye at all. Even if the moon were somehow visible for an instant everywhere, the fraction of the earth the 0.8% crescent is visible from would drop to ~6.7%. If you want a more precise definition of 0.8%, e.g. 0.80%, or between 0.795% and 0.805%, the moon spends about 10 minutes at the desired phase and this would be visible from 0.7% of the earth.

Then again, you may allow the use of a telecope, so that you can see the moon even during day time. If you also don't worry about the weather, the window of observation would be 12 hours (since the moon is up for observers at about 50% of the earth's surface) and with the 97-minute time window for which the crescent is between 0.75% and 0.85%, the 0.8% crescent would be visible from about 57% of our planet's surface. For 0.795%-0.805%, this would be 51% of the earth.

The conclusion is that a 0.8% crescent of the moon is visible from beteen 0% and 60% of the surface of the earth, depending on your exact definitions and your choice of accuracy and optical aid.