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27 Sep 2019 13:40

Stellarator wrote:
Source of the post This was actually something I was quite interested in knowing. I cannot tell you how many times I've heard people cry out that the Moon will spin off into the void someday.

Lol yes, that's quite a common misconception.  Now you can explain for them that it never will, and instead they can be more concerned about the Earth's spin slowing down, and before that the Sun's luminosity increasing, and before that probably the climate changing or other things that are actually happening over human timescales. :)  
 
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27 Sep 2019 23:03

Watsisname wrote:
Source of the post and instead they can be more concerned about the Earth's spin slowing down, and before that the Sun's luminosity increasing, and before that probably the climate changing or other things that are actually happening over human timescales.

Mhmm, I'll talk to them of such things, and fill them with an appreciation of the now, and a loathing of the bleak future ;).
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28 Sep 2019 00:28

Thanks Wat!  I take it the future presented in The Time Machine and some other sci fi work will never happen?  That the moon will form a ring around the Earth, millions of years in the future?  Or maybe they thought that because they fear we will mine the moon until it crumbles into rocks......

Something I found fascinating is that we exist in a time period where the apparent angular size of the moon and the sun is almost the same, and that's why we can see the sun's corona during total solar eclipses!  The moon is 400 times closer to earth than the sun is and 400 times smaller!  During the time of the dinosaurs the sun's corona would not have been visible during total solar eclipses!
 
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28 Sep 2019 02:01

A-L-E-X wrote:
Source of the post  I take it the future presented in The Time Machine and some other sci fi work will never happen? That the moon will form a ring around the Earth, millions of years in the future?  Or maybe they thought that because they fear we will mine the moon until it crumbles into rocks

That would be pretty ridiculous. :)

A-L-E-X wrote:
Source of the post Something I found fascinating is that we exist in a time period where the apparent angular size of the moon and the sun is almost the same, and that's why we can see the sun's corona during total solar eclipses!  The moon is 400 times closer to earth than the sun is and 400 times smaller!


Yes, this is really interesting!  I recall Midtskogen brought it up too a while back.  To the best of my knowledge, we don't really have a good understanding yet for how much of it is coincidence or not.  Either way, it is fantastic for observing eclipses.  If Earth-like planets (whatever that means exactly) are rare, it seems pretty likely that ones with moons that neatly block out the Sun for total eclipses like ours must be exceptionally so.  

It helps of course that the Moon's orbit is fairly elliptical, so it actually spans a range of distances and angular sizes.  Sometimes (actually most of the time) it is too far from Earth in its orbit to block the Sun completely, and we get annular eclipses.  Annular eclipses right now are almost twice as common as total eclipses.  As the Moon continues to drift away, total eclipses will become rarer and briefer on average, while annular eclipses become longer and more common.


A-L-E-X wrote:
Source of the post During the time of the dinosaurs the sun's corona would not have been visible during total solar eclipses!


How sure are you? ;)

Put simply: there is no way the Moon was close enough during the time of the dinosaurs to block out the Sun's corona.  The visible part of the Sun's corona is big!  It typically spreads about 3 to 4 solar radii from the Sun.  Here's my best attempt to reproduce what it looks like by eye:

Image


For the Moon to block all of that, it would need to have been at least about 3 times closer to Earth than it is now.  How much closer was the Moon back then?  Well, the time of the dinosaurs was not that long ago (geologically speaking).  They spanned from about 250 to 65 million years ago.  250Mya is recent enough to approximate the Moon's orbital evolution as linear, in which case its current rate of 3.8cm/year times a quarter billion years is about 10,000km, which means the Moon was then only about 2 or 3 percent closer than it is today. 
 
So instead of blocking the corona, the change in angular size would have been... almost impossible to notice by eye!  Instead the most obvious difference is that the corona would have been visible for longer, since the totalities would have lasted longer on average.  Accounting for the elliptical orbit, some of the solar eclipses were probably basically the same as some that we have now.  There might even have still been annular eclipses then (though they would have been shorter and less common), depending on how elliptical the orbit was.

Besides all that, even if the Moon had been close enough to completely obscure the corona, it still wouldn't do so for the entire totality.  The start of the totality would block the corona on one side of the Sun, while the other side is still completely exposed, and then this would switch toward the end of totality.  The same thing happens with current eclipses for the covering and uncovering of the prominences:

 
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28 Sep 2019 07:15

Why is the moon 400 times smaller than the sun, and why does it line up perfectly with the Sun? Is there a natural explanation for these coincidences? 
 
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28 Sep 2019 12:45

Cantra wrote:
Source of the post Is there a natural explanation for these coincidences?


Just coincidence most likely. The size of the moon is probably arbitrary, but the importance of having a decently sized one may not be for life.

There are some models which argue the moon had to be this way for Earth to have a stable rotation, allow for things like tides and seasons, potentially affecting plate tectonics, which in turn made us possible.
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28 Sep 2019 14:41

Cantra wrote:
Source of the post Why is the moon 400 times smaller than the sun, and why does it line up perfectly with the Sun?  Is there a natural explanation for these coincidences? 

In addition to most likely being coincidences, they aren't as strong of coincidences as they might seem. 

The Moon is 400 times smaller than the Sun, but because of its elliptical orbit, its distance ranges between 369 and 412 times closer than the Sun.  So sometimes it is closer and appears larger than the Sun, and sometimes it is farther and appears smaller than the Sun.  This is why some solar eclipses are total while others are annular.

The Moon also doesn't line up perfectly with the Sun.  The Moon's orbit is tilted with respect to the ecliptic (the plane that the Earth orbits around the Sun in) by about 5 degrees.  So sometimes instead of passing in front of the Sun, it misses and passes a little above it, or a little below.  This is why we do not get a solar eclipse every month.  Instead it's about once every 18 months on average.

If the Moon's orbit was tilted more, then solar eclipses would still happen -- just more rarely.
 
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29 Sep 2019 03:07

Watsisname wrote:
Source of the post The Moon is 400 times smaller than the Sun, but because of its elliptical orbit, its distance ranges between 369 and 412 times closer than the Sun.

That's an often ignored point indeed. Just to show it visually the red circles correspond to the maximum and minimum angular diameters of the Sun as seen from Earth (it changes because Earth's orbit is elliptical also). The black circles show the same for the Moon.
Image
There is plenty of room for good matches in those more or less wide ranges.
I would also point that total eclipses were not possible in the past and would be imposible also in the future because of the aforementioned evolution of Lunar orbit. This means "the coincidence" would have happened sooner or later as the Moon progressed towards the outskirts of Earth's sphere of influence.
 
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01 Oct 2019 17:27

FastFourierTransform wrote:
Source of the post I would also point that total eclipses were not possible in the past and would be imposible also in the future because of the aforementioned evolution of Lunar orbit.

Total eclipses were definitely possible in the past. :)  They started happening basically as soon as the Moon formed!  The Moon was closer and had a larger apparent size on the sky, so it completely covered the Sun more easily.  Total eclipses also lasted longer on average, since even though the Moon orbited the Earth faster, its increased angular size more than made up for it, as well as the faster rotation of the Earth which would keep an observer in the shadow longer.

So we are not in a special moment in time where total eclipses are possible.  Instead, we are in a special moment where both total and annular eclipses are possible.  (As well as 'hybrids', which change from one to the other during the path.  A hybrid eclipse could be said to be a more perfect match of apparent size of Sun and Moon than a regular total eclipse.)  As the Moon drifts farther away from Earth in the future, total eclipses will be less common and shorter on average, while annular eclipses will be more common and last longer.  Eventually (in some few hundred million years), there will only be annular eclipses.
 
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03 Oct 2019 23:24

Watsisname wrote:
A-L-E-X wrote:
Source of the post  I take it the future presented in The Time Machine and some other sci fi work will never happen? That the moon will form a ring around the Earth, millions of years in the future?  Or maybe they thought that because they fear we will mine the moon until it crumbles into rocks

That would be pretty ridiculous. :)

A-L-E-X wrote:
Source of the post Something I found fascinating is that we exist in a time period where the apparent angular size of the moon and the sun is almost the same, and that's why we can see the sun's corona during total solar eclipses!  The moon is 400 times closer to earth than the sun is and 400 times smaller!


Yes, this is really interesting!  I recall Midtskogen brought it up too a while back.  To the best of my knowledge, we don't really have a good understanding yet for how much of it is coincidence or not.  Either way, it is fantastic for observing eclipses.  If Earth-like planets (whatever that means exactly) are rare, it seems pretty likely that ones with moons that neatly block out the Sun for total eclipses like ours must be exceptionally so.  

It helps of course that the Moon's orbit is fairly elliptical, so it actually spans a range of distances and angular sizes.  Sometimes (actually most of the time) it is too far from Earth in its orbit to block the Sun completely, and we get annular eclipses.  Annular eclipses right now are almost twice as common as total eclipses.  As the Moon continues to drift away, total eclipses will become rarer and briefer on average, while annular eclipses become longer and more common.


A-L-E-X wrote:
Source of the post During the time of the dinosaurs the sun's corona would not have been visible during total solar eclipses!


How sure are you? ;)

Put simply: there is no way the Moon was close enough during the time of the dinosaurs to block out the Sun's corona.  The visible part of the Sun's corona is big!  It typically spreads about 3 to 4 solar radii from the Sun.  Here's my best attempt to reproduce what it looks like by eye (something that's surprisingly hard to do, even with HDR techniques):

Image


For the Moon to block all of that, it would need to have been at least about 3 times closer to Earth than it is now.  How much closer was the Moon back then?  Well, the time of the dinosaurs was not that long ago (geologically speaking).  They spanned from about 250 to 65 million years ago.  250Mya is recent enough to approximate the Moon's orbital evolution as linear, in which case its current rate of 3.8cm/year times a quarter billion years is about 10,000km, which means the Moon was then only about 2 or 3 percent closer than it is today. 
 
So instead of blocking the corona, the change in angular size would have been... almost impossible to notice by eye!  Instead the most obvious difference is that the corona would have been visible for longer, since the totalities would have lasted longer on average.  Accounting for the elliptical orbit, some of the solar eclipses were probably basically the same as some that we have now.  There might even have still been annular eclipses then (though they would have been shorter and less common), depending on how elliptical the orbit was.

Besides all that, even if the Moon had been close enough to completely obscure the corona, it still wouldn't do so for the entire totality.  The start of the totality would block the corona on one side of the Sun, while the other side is still completely exposed, and then this would switch toward the end of totality.  The same thing happens with current eclipses for the covering and uncovering of the prominences:


Wow, I wonder what the max duration of totality was back then?  Currently, it's around seven and a half minutes.  Do you think there was a time in the extremely distant past when the moon appeared so large it actually blocked out the corona?  And how long do you think a total eclipse can be without the moon blocking out the corona?
 
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04 Oct 2019 01:17

Maybe it's something we can view on SE modifying the moon's orbit.
It would be amazing and sky would be very dark.
The universe is not required to be in perfect harmony with human ambition.

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04 Oct 2019 12:33

A-L-E-X wrote:
Source of the post Wow, I wonder what the max duration of totality was back then?  Currently, it's around seven and a half minutes.

As it so happens, I had just been working on a program to compute the evolution of the Moon's orbit, and from which get the duration of totalities. :)  Here's what I find:

Image


Totalities lasted much longer in the past, and in the future there will only be annular eclipses (which can be thought of as a totality with negative duration, as the smaller disk of the Moon crosses in front of the Sun.)


How did I calculate this?  For the sake of sanity, I made a large number of simplifying assumptions (like treating the Earth and the Moon's orbits as circular and coplanar, and ignoring contribution of solar tides, obliquity changes, and so forth.)  Also, computing how the Moon's orbit changed over time is somewhat complicated, so I instead find it as a function of a conserved quantity: the angular momentum.  I transfer some angular momentum between the Earth's spin and the Moon's orbit to see how both change, and from there can find relevant quantities as a function of the Moon's orbital distance.  With some geometry it is then fairly simple to get the duration of totality for solar eclipses.  To maximize the duration of any eclipse, I treat the viewer as being on the equator and with the Sun at zenith, so that they are closest to the Moon and also rotating fastest along with the shadow.


A subtle flaw in the above plot for length of total eclipses:

If you look closely, it might seem like the maximum duration of totalities now (when the Moon is at perigee) is too small.  In fact, this predicts they should last just over 5 minutes, instead of 7.5.  Why?  Because I pretended the Earth's orbit is circular with a 1AU orbital distance.  The longer totalities of up to 7.5 minutes require the Earth to be near aphelion, so that the Sun's apparent size is a little smaller (as FastFourierTransform showed just above).  At aphelion, the Earth is at about 1.02AU, and if I plug that in for the Earth-Sun distance then it confirms the 7.5 minute max length of totality.

Accounting for the Earth's orbital eccentricity here would be a horrendous task, since it changes over time in a very complicated way (a part of the Milankovitch cycles.)  Instead, I think it makes a lot more sense to show it in these "average" terms for the Earth at 1AU.


Going back to the tidal evolution, here's what I find for the evolution of the Earth's spin and Moon's orbit (in terms of their angular velocities), as a function of the angular momentum transferred from the Earth to the Moon (compared to the present day):

Image


0 on the x-axis, marked with a vertical line, represents today.  To the right, positive angular momentum transfer raises the Moon's orbit and slow's the Earth's spin, so the angular velocities of both are decreased, until eventually they would end up being equal to each other in a mutual tidal lock of about 1.39 microradians per second, or a spin and orbit period of about 52 days.  (Note the plot is on a semi-log scale, which distorts the shape of the curves.  The change in Earth's spin rate vs. angular momentum transfer is actually linear, since rotational angular momentum of a sphere is proportional to the angular velocity.  The Moon's orbital angular velocity vs. angular momentum is inverse cubic, and these two curves intersect twice.)

To the left, negative momentum transfer (i.e. from the Moon to the Earth, or backwards in time) brings the Moon closer, and both it and the Earth revolve faster.  Extended all the way, we might predict they would have been in a tidal lock in the past, with the Moon much closer to Earth and the Earth spinning much faster.  But such extrapolation can't work that far out.  If they had started out mutually locked, then they would have stayed that way. The Moon didn't really form quite that close, and the Earth was never spinning quite that fast.

Here's the same figure as above again, except recast more intuitively in terms of the Moon's orbital distance (instead of angular momentum), and in terms of spin/orbit periods in hours (instead of angular velocities.)  Again I have chosen a log vertical scale.

Image


Here we can see more easily the changing length of the Earth's day and the lunar month as the Moon's distance changes.  We can also clearly see why the Moon never escapes the Earth.  The tidal interaction leads to them being tidally locked with the Moon a little less than 600,000km away.  But that won't even happen in the next 5 billion years before the Sun dies.  By then the Moon will only recede to roughly 475,000km or so.


Explanation of how the duration of totality changes with Moon distance:

Intuitively, the Moon being closer to Earth would make it larger on the sky, so it should cover the Sun longer.  But closer orbits are also faster.  The increased angular size matters more, so the duration of totality increases with decreasing distance to the Moon.  

But there are more effects to consider.  One of the most important is that the Earth's rotation rate is changing!  During an eclipse, the shadow of the Moon sweeps over the Earth (from west to east -- the same direction the Moon is orbiting), but the Earth's rotation also sweeps the viewer from west to east.  The Moon's orbital velocity is faster than the Earth's rotational velocity (even at the equator), so the shadow still sweeps over from west to east, but not as quickly.  In the past, the Earth rotated faster, which more than compensated the Moon's faster orbital velocity when it was closer.  This helped further increase the duration of totalities in the past.

If we extrapolate the Moon's distance as close as it could have been (at the Roche limit), at left side of the figure, then the duration of totalities explodes to over an hour!  This is again due to the combination of the Moon's angular size being much larger as it gets closer (1/r dependence), along with the Moon orbital angular velocity starting to closely match the Earth's rotational angular velocity.  That would mean the Moon would not only have looked huge, but also move very slowly across the sky, and thus cover the Sun for a much longer time.


Another insight to the question of the "coincidence", that the Moon and Sun appear similar in size on the sky.

This cosmic coincidence is perhaps most striking when we look at the first plot for the totality duration.  Again, the Moon's orbit is elliptical, so the range of distances it covers helps make the match more likely.  This range is shown with the perigee/apogee lines in yellow and blue.  Still, this range seems to be fairly narrow compared to the full range of distances that the Moon's orbit could cover, and the point where the Moon and Sun's apparent sizes are equal runs right through the middle of it.  So maybe it still looks like a really strong coincidence.

The expansion of the Moon's orbit over time means this match was almost bound to happen sooner or later, but that still doesn't explain why we exist during the time that it does.  The key (or at least another part of it) is that evolution does not occur at a constant rate!  When the Moon was closer, the tidal interaction was stronger, so angular momentum was transferred more quickly and the Moon's orbit was expanding faster.  So the Moon did not spend as much time very close to Earth as it will spend at larger distances.  There is an inherent bias for an observer at a random moment in time to find the Moon farther away where the evolution is slower.  Hence this "coincidence" is actually a lot more likely than it seems. :)


A-L-E-X wrote:
Source of the post Do you think there was a time in the extremely distant past when the moon appeared so large it actually blocked out the corona?

Shortly after it formed (a few hundred million years, maybe even a billion), it might have been close enough to do this during the mid-point of totality.  A competing effect however is that as Salvo says, when the Moon was closer and larger on the sky, its shadow on the Earth was larger, so the sky during totality would be darker.  This would make the Sun's corona appear even larger, since the fainter extended parts would be more visible.  For an idea, you can compare images of the Sun's corona taken during eclipses to those taken from space using coronagraphs:

Image
 
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08 Oct 2019 02:03

Wow, Wat this is absolutely fascinating!  Great research!  I wonder if we can simulate the long times of these prehistoric eclipses in modern times during flight (that is, artificially extending the duration of a total eclipse on an airplane by following the path of the moon's shadow.)

Also, it makes me wonder how much the moon's influence on the tides back then caused life to emerge from the seas and onto land.  It may have played a vital role in evolution on our planet!
 
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10 Oct 2019 14:34

What if there was an atom with electrons in the center, and the protons and neutrons surrounding the electron nucleus, in a shell or a housing.
 
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10 Oct 2019 20:27

Cantra wrote:
Source of the post What if there was an atom with electrons in the center, and the protons and neutrons surrounding the electron nucleus, in a shell or a housing.

Fascinating question.

First off, the reason that the protons and neutrons are in the central nucleus surrounded by electrons, and not vice versa, is because the protons and neutrons are much heavier, so the center of mass is essentially fixed inside the nucleus.  Electrons feel an electric attraction to the protons in the nucleus, and vice versa, but the massive nucleus mostly stays still and the much lighter electrons "orbit" around it.  (I emphasize the quotes around "orbit", since the electrons really don't orbit at all like planets orbiting a star.  What they really do is deeply quantum mechanical.)

If we instead place the electrons in the center of a spherical shell containing an equal number of protons (and maybe we throw in some neutrons as well because why not?), then what happens?  Well, the neutrons might actually prove to be irrelevant, since they are electrically neutral.  In a nucleus they serve to help bind the protons together, preventing them from flying apart.  But spread that same number of protons and neutrons across a spherical shell around the electrons, and most of the time they will never be in contact with each other.    If the protons are free to move throughout the shell, then they will quickly spread out as far as they possibly can from one another. 

Also, neutrons that are not confined within an atomic nucleus are unstable.  They decay with a half-life of about 10 minutes.  In a few hours, all of the neutrons in this housing would decay into more protons, electrons, and neutrinos.  Maybe in this hypothetical scenario we get around this problem by constructing the housing in such a way that the neutrons inside are kept stable -- although I have no idea how that would be possible.  

So, it sounds like we have a spherical shell will some protons that quickly become evenly spread around it, with an equal number of electrons stuck inside.  How would this "inverted atom" behave?

It would be surprisingly boring.  

If the atomic number for this atom is large (a large number of protons), then the shell of them more closely approximates a uniform spherical shell of positive charge.  But the electric field inside a hollow sphere of charge is zero, everywhere.  So the electrons inside it will feel basically no net electric force from the protons at all.  But they will feel electric repulsion from the other electrons.  So they will fly outward away from each other and distribute themselves evenly along inner surface of the shell of protons.  Our inverted atom would just be a thin shell of electrons stuck against the inside wall of a shell of protons.

Everywhere inside this shell, the electric field is zero.  And if the number of protons equals the number of electrons, then the electric field is zero everywhere outside as well.  Our inverted atom is tiny, electrically neutral, and doesn't form chemical bonds to anything.  It would act a lot like a noble gas like neon or xenon -- single atoms that don't do anything interesting chemically.1  

So, basically, we've built a weird, inside out version of a noble gas atom. :)

1. Actually this is not entirely true -- noble gases can bond with other elements under certain conditions.  For example, very short-lived bonds between xenon and oxygen can occur when the gas is electrically excited, which adds an eerie green glow to some plasma globes.  In fact there are a fairly large number of noble gas compounds that have been synthesized.

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