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As the sun expands and the Moon grows farther away, total solar eclipses will become shorter and shorter. Someday, a mixed total-annular eclipse in the tropics will occur near lunar perigee and solar aphelion. Then afterwards all eclipses will be annular.
When will this final total solar eclipse occur?
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About one billion years in the future.
http://www.astronomycafe.net/qadir/q74.html
Order of Kilopi
Only it won't be the final total solar eclipse. The Moon will one day start to approach the Earth again. It will continue to do so until it comes within its Roche limit (18,500 km), at which point it will disintegrate and form a ring around the Earth.
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How so? When the Earth becomes tidally locked to the sun?Originally Posted by Eroica
Order of Kilopi
My understanding is that
a) Sun will expand into red giant and then collapse into white dwarf long before Moon even reaches its farthest (tidally locked) orbit. Hence by the time Moon begins approaching Earth, there will be no eclipses because Sun will be black and tiny.
b) Assuming Earth and Moon survive (a), once they are tidally locked the system will lose energy and grow closer (while remaining tidally locked) only due to gravitational radiation. It will take on the order of 10^18 years for Moon to crash into Earth* at that rate - and a similar amount of time for all planets to crash into absolute-zero black dwarf that Sun will be by then.
* Yes, I know it is "disintegrate inside Roche Limit" rather than "crash into" -- but the resulting ring will end up on Earth's surface within negligible time, compared to 10^18 years.
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Estimated age of the sun is 5 billion years. Estimated time before it goes red giant is another 5 billion years so there is plenty of time for the last eclipse.
Order of Kilopi
I saw your post here on the subject, but am unable to find anything about the work or the author. Where's this from? I'd love to have a clearer understanding of the processes involved.
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It is very unlikely the moon will have a chance to spiral into the earth. Once the earth and moon are locked synchronously there will be no tidal effects to radiate gravitational energy. When the sun goes red giant it will either incinerate the earth and moon or friction with the sun's atmosphere will cause the earth and moon to spiral into the sun.
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Interesting, but will there be any creatures left on the Earth to view it?
It would certainly make for a good sci-fi short story.
- Maha "goodbye moon?" Vailo
Order of Kilopi
Doh! Found the paper I was asking about in my earlier post, courtesy of this thread.
Now, off to see if I'm able to understand it... 8-[
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Trivial question, likely, but when was the first total solar eclipse as we know it? I don't mean just the Moon blotting out the Sun entirely, that's easy, 4point something billion BP, whenever the Moon coalesced out of impact debris.
But I mean the current situation, where the apparent diameters are so similar at around 30', that we can discern prominences and features of the inner corona with the naked eye during totality. Yeah - it's a bit notional, but I suppose we could take prominences as a touchstone, because they don't stray far from the solar disc (maybe 2' of arc at most?).
Order of Kilopi
This is bizarre that I noticed this thread now. I just sent in an article to Night Sky about this today! I couldn't go into details there due to lack of room. Oh well.
Assuming an average recession rate of roughly 2 centimeters per year, the last solar eclipse will be in roughly one billion years. The first one was also roughly one billion years ago (before then, the Moon was always so big it completely blotted out the Sun). We're in the middle of an eclipse season!
There are several complications:
1) The recession rate over geologic time is very hard to pin down. Right now we're at a high point, 4 cm/yr or so. It was less in the past, because the timing of the Moon's orbit has a resonance with the sloshing of the oceans. If it weren't for that, the recession rate would be less now. When will this current high rate end? Beats me.
2) Sure, the Moon will recede until one day = one month. But there will still be tides: the Sun's tides on the Earth are currently 1/2 those of the Moon, and will grow in proportion as the Moon's tides shrink due to recession. So that affects the system as well.
3) After a billion years, the Earth may migrate out from the Sun somewhat. By the time the Sun goes red giant, it may be far enough out to not be engulfed by the expanding Sun. The timing of this is not well known, AFAIK. So the whole system's evolution is fairly uncertain. But it's interesting to think about!
Order of Kilopi
The Once and Future Sun
Order of Kilopi
The Sun will still create tides, won't it?
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Eroica,
Nice link there. A lot of guesswork of course but interesting. Yes, the sun will create tides. However, once the earth-moon system is synchronous there is no tidal interaction between the earth and moon to drain angular momentum from the earth. There is still an incredibly minute relativistic effect operating but at the relative orbital velocity of the moon around earth it would take a very, very long time to make a difference. Of course, if the earth-moon system does survive the demise of the sun then there is nothing but time. The only other possible wild card is an encounter with a passing body (star?) that disrupts our system.
Order of Kilopi
The point Sawicki is making, though, is that when the Earth and Moon are in synchronous rotation, the tidal effects of the Sun will cause the Earth's rotation to slow even more, so that the day will last longer than the month. Then the tidal bulge - which currently leads the Moon, tugging on it and "pulling" it into a higher orbit - would lag behind the Moon, "pulling" it into a lower orbit.
Order of Kilopi
Ordinarily I wouldn't find much delight in speculation, however in this particular examination of the Earth-Moon system I have to confess it's been quite fun to ponder the fate of the Moon -- particularly the above components (despite that the variables are so numerous that it's made my head spin at times).
If I'm correct in understanding that a supercontinent on Earth would equate to a slower rate of lunar recession, it's certainly interesting to imagine what the distant future holds if a situation like this comes to pass, let alone anything beyond a mere 250m years.
Thanks to Eroica for introducing me to the works by Sawicki and Pogge, thought-provoking stuff. 8)
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Eroica,
I wonder how that would work out? At the point that the earth and moon are synchronous the rotation of the earth will then be about 30 times slower than it is now. How long will it take to get to that point? 10 billion years? Longer? By then the sun will have shed a lot of it's mass and will no longer have nearly as great a tidal effect on such a slowly rotating earth which is then considerably farther out. If it takes ten billion years to get to that point it might take hundreds of billions just to get back to where it is now (the moon).
I suspect the chance of another body perturbing the solar system in that period of time is pretty good.
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