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If there truly is some extraterrestrial Hitchhiker’s Guide to the Galaxy it would undoubtedly list a total solar eclipse as one of the sights to see while taking a break from probing Earth’s natives. Total solar eclipses, called totality for short, are pretty rare here on Earth; a casual observer might see only one or two during their lifetime.
Since the Earth is the only planet we have ever known, we can’t really appreciate how truly lucky we are. The odds of the size of a planet’s moon exactly matching the apparent size of its sun are pretty low. If the moon is too large, it blocks the majestic solar corona visible during totality. If it is too small, then all solar eclipses would be annular, allowing a ring of the sun’s light to pass . The “Goldilocks” combination of Moon and Sun sizes on Earth makes totality possible, and unique in our solar system.
But alas, this beautiful phenomenon is ephemeral, at least in the geologic sense. The lunar disc shrinks slightly every year as the Moon recedes from the Earth; the chance of a total solar eclipse decreases correspondingly. Somewhere near 1 billion years from now, the last total solar eclipse will grace whatever residents of Earth there may be.
Unless you’re planning on living forever, 1 billion years probably seems safely tucked away into the future. So much so, perhaps that it may be entirely irrelevant. But, as the Moon moves further away, the length of a day here on Earth increases by about half a second each year. So every few years, the official arbiters of time at the Greenwich Royal Observatory add a leap second to our day.
This effect, while small during a human lifespan, has dramatically increased the length of the day over geologic time. When the moon was first formed, an Earth day was approximately 6 hours. By the time dinosaurs roamed Pangea, a day had reached 21 hours. The ultimate fate of the length of a day is that it will match that of a month at about 47 days. At that point, the Moon will hang suspended over a single point on the Earth for all time. But again, don’t panic! This is predicted to occur sometime long after the Earth and Moon have been utterly destroyed by the red-giant phase of our sun.
Strangely enough, the Moon is the cause of its own diminution in our sky. The pull of the Moon’s gravity causes tides here on Earth; that much we all know. But, because the Earth rotates more rapidly than the Moon travels in its orbit, that tidal bulge pulls the Moon forward ever so slightly. This constant extra force accelerates the Moon, which forces it further away from the Earth.
So how fast is the Moon pulling way? About 3.8 cm/year right now. One of the great successes of Apollo lunar science was to place a series of corner-cubic laser reflectors on the surface of the Moon. Scientists back on Earth then fire laser beams at those reflectors through carefully aimed telescopes. The travel time between firing and receiving the return signal gives the distance of the Moon accurate to about 1 cm. Scientists are working on improving this accuracy to around 1 mm.
Historically, the Moon did not recede so quickly. We know this because certain species of coral have daily growth patterns and are buried by annual loads of sediment called rhythmites. So, by counting the growth rings of the coral buried in one year of sediment, geologists have calculated the length of the day as far back as 600 million years or so. Based on these findings, we know that the Moon has been receding at about 2 cm/year on average. It just so happens that the current orientation of the Earth’s continents is almost optimal for accelerating the Moon.
If you missed the opportunity to catch that last total eclipse, don’t worry, there will be plenty more for the next few hundred million years. And when you do witness an eclipse (hopefully not while staring directly at it) perhaps you can ponder the staggering odds which have brought us all this amazing, and temporary, event.
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Ah, yes… and the geographic poles are liable to flip if the sun doesn’t eat the earth when it goes supernova first. When the moon’s gravitational attraction is sufficiently small, it won’t be able to stabilize the earth’s rotation as it has for the last four billion years or so. See Gordon Emslie’s talk for more details.
I guess a over a distance of 250,000 miles, a +/- 1 cm error is not so bad, even if it is 25%’ish of a 3.5 cm measurment.
As for the next total eclipse in 1 billion years…let me mark my calendar before I forget!
Something isn’t quite right with your analysis… As the moon recedes from the Earth, it slows down, not speeds up. Stable orbits that are farther from the source are always at much slower speeds than those close by.
A quick derivation of that fact; Centripedal acceleration is a_c = v^2/r – and the acceleration due to gravity is a_g = Gm/r^2. If we equate the two (which is what happens when you’re in a circular orbit), then you find that the radius of the orbit is
r = GM/v^2
i.e. if you increase the speed, the radius decreses.
What actually happens in this case is that there is friction due to the tides; these cause the moon to lose energy (give or take) and this causes it to slow down, and recede from the earth.
Hmm, perhaps I was being a little loose with the wording, let me be more careful here.
If you pull the moon forward and accelerate it a little bit, it can no longer remain in its current orbit because it is moving too quickly. At that point, the Earth’s gravity is not high enough to hold the Moon as close as it once was, so the Moon receeds. But, the Moon then loses some of its kinetic energy to gravitational potential energy as it pulls away from the Earth. So, the net effect is that the Moon loses some velocity even though it has indeed accelerated (and has more total energy).
So, you’re right in that if the Moon’s orbital velocity increased that must mean it is closer to the Earth. I should have been more careful and said “This constant extra force accelerates the Moon, which forces it further away from the Earth.” Because on the whole, the Moon does actually slow down as you correctly pointed out.
Anyway, thanks for bringing a bit of physics and a few equations into the comments section!
In the end, we are all screwed :) does it really matter -how- we are gonna get screwed?
Yes, there is friction but it causes the earth’s rotation to slow down, not the moon’t orbit. Really it’s just a transfer of energy from the rotational momentum of the earth to the orbital momentum of the moon. But it’s not 100% efficient- the friction also causes the earth to heat up. Like the article says, eventually only half of the planet will ever see the moon, because once the earth’s rotation and the moon’s orbit are in lockstep (the moon is in a geosynchronous orbit) then there won’t be any more accelleration. This has already happened to the moon- it rotates in the same amount of time that it orbits, which is why we only ever see the one side.
Even more mind-boggling is that the sun causes tides on the earth too. So in a long, long, long time only one side of the earth will ever see the sun, and a day will be the same length as a year.
Actually, if it doesn’t escape then the moon would probably crash into the earth eventually, because once the earth and moon have locked step the sun’s tides would slow down the earth’s rotation, which would (through the same mechanism menitioned in the article) decellerate the moon and bring it closer and closer in. Only after the moon is gone could the earth completely be locked with the sun.
Not that we -or in that case the sun, earth and moon- will be around that long.
So when is the next total eclipse? I’m to impatient to wait out my 56k and look it up…
There’s a list at Wikipedia: http://en.wikipedia.org/wiki/List_of_solar_eclipses
The next total eclipse will be on August 1, 2008, and will be visible in “North America (Canada), Europe, Asia”.
vernondalhart said: “Something isn’t quite right with your analysis… As the moon recedes from the Earth, it slows down, not speeds up. Stable orbits that are farther from the source are always at much slower speeds than those close by.
A quick derivation of that fact; Centripedal acceleration is a_c = v^2/r – and the acceleration due to gravity is a_g = Gm/r^2. If we equate the two (which is what happens when you’re in a circular orbit), then you find that the radius of the orbit is
r = GM/v^2
i.e. if you increase the speed, the radius decreses.
What actually happens in this case is that there is friction due to the tides; these cause the moon to lose energy (give or take) and this causes it to slow down, and recede from the earth.”
huh?
ke4roh said: “Ah, yes… and the geographic poles are liable to flip if the sun doesn’t eat the earth when it goes supernova first. When the moon’s gravitational attraction is sufficiently small, it won’t be able to stabilize the earth’s rotation as it has for the last four billion years or so. See Gordon Emslie’s talk for more details.”
Well since were picking nits, and throwing real math around here(btw, I read this in the morning with my coffee, and the math hurts us, my precious) ;-), our Sun is too small to go supernova.
Thanks for the link Crispy. I’ll have to remember to take my welding goggles to work that day….hopefully it won’t be overcast.
Marius said: “Well since were picking nits, and throwing real math around here(btw, I read this in the morning with my coffee, and the math hurts us, my precious) ;-), our Sun is too small to go supernova.”
I don’t think anyone mentioned supernova. Says in the article the “red-giant phase of our sun” which is not supernova, just means it’ll swell up and encompass the inner planets, which it is massive enough to do. Not that I want to nit-pick.
If everyone jumps up and down throughout the daytime perhaps we can push the Earth safely away from the dealy grasp of the evil sun. sUN = ERTH/J*mp^2
Stuart said: “I don’t think anyone mentioned supernova. Says in the article the “red-giant phase of our sun” which is not supernova, just means it’ll swell up and encompass the inner planets, which it is massive enough to do. Not that I want to nit-pick.”
ke4roh mentioned supernova, and I was trying to be a smarta$$. Sorry.
Quote BigT383 – “Even more mind-boggling is that the sun causes tides on the earth too. So in a long, long, long time only one side of the earth will ever see the sun, and a day will be the same length as a year.”
If only one side of the earth is ever exposed to the sun, how can a day be the length of a year…?
Surely a day would last forever since the same part of the earth is always exposed to the sun…
Aatwo,
It just depends on your point of view. If you were sitting above the solar system looking down with the telescope, you would notice that the Earth rotates a full turn relative to its position for each orbit around the sun (if it were tidally locked as BigT383 mentioned). Also, on Earth you would notice that the pattern of stars would continue to change each night. But, you’re right, the Sun would no longer rise in the East each morning!
Marius said: “ke4roh mentioned supernova, and I was trying to be a smarta$$. Sorry.”
Ooh missed that comment. Hoisted by my own petard. For shame. Apologies.
Wait, Wait Wait!
The moon causes the tides, which causes it to move closer which in turn causes it to move farther away?
Physics is dumb.
Scientists have shown that the moon is moving away at a tiny yet measurable distance from the earth every year. If you do the math, you can calculate that 85 million years ago the moon was orbiting the earth at a distance of about 35 feet.
This would explain the death of the dinosaurs.
Well, the tall ones, anyway.
Just a thought, the article talks about the amount of time in a day…what about how long a year is/has been. Have years gotten longer and if so, could this account for the biblical account of people living for hundreds of years? I mean since a year is in fact how long it takes the earth to revolve around the sun, could this not explain it?
jchristman said: “Just a thought, the article talks about the amount of time in a day…what about how long a year is/has been. Have years gotten longer and if so, could this account for the biblical account of people living for hundreds of years? I mean since a year is in fact how long it takes the earth to revolve around the sun, could this not explain it?”
1) the rotation of slows by about 1 second every 500 days. 500 rotations of the earth at this moment take 500 days. The next 500 will take 500 days and 1 second. so it would take a tremendously long time for any effect to be noticeable. 50-60 thousand years ago the day was only ~1 second longer than it is today. If you are a bible literalist, that wouldn’t work for you, as the generally accepted number for literalists is 5-15 thousand years since creation. ;)
2) Slowing the day down doesn’t change the length of the year. It would still be the same length. A year is a year regardless of whether a day is 2 hours or 24. It would just have more or less days in it.
thats damned interesting. having cured cancer and aids, our scientists are able to have fun researching this stuff.
This is Damn interesting but I think I’ll have to stop reading these because I’m starting to feel stupid.
well…seeing as i got 1 billion years time to kill…i think i gonna go get sum pie…
i remember seeing an eclipse…but i cant remember if it was a lunar or solar… ancient history
Huh? A month is 47 days now?
A day at that time will equal 47 of our days. Since the moon would be in a geostationary orbit, a month (which is roughly equal to the lunar cycle) would be the same period of time. So a month isn’t 47 days NOW, but it will be THEN.
Please correct me if I’m wrong… I’ve been guilty of being an idiot before.
“Scientists have shown that the moon is moving away at a tiny yet measurable distance from the earth every year. If you do the math, you can calculate that 85 million years ago the moon was orbiting the earth at a distance of about 35 feet.
This would explain the death of the dinosaurs.
Well, the tall ones, anyway.”
:D
Anyone care to explain that one to me?
thekenemy, It is doubtfull you are still checking for an explanation, but by extrapolating back to when the moon was essentially in the same position of the earth, it appears that the moon actually came from the earth. It is theorized to be caused by a massive collision between some very large object with the earth. This flung lots of matter into a relatively low orbit which eventually formed into the spherical moon gradually receding from the earth. I think the mention of “the tall dinosaurs” was a joke. I was thinking this collision happened long before the dinasaurs romed though.