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View Full Version : Earth's centrifugal non-sphericality, compared to its lunar tidal bulge



Delvo
2018-Nov-22, 02:56 AM
I just watched this National Geographic show (https://www.youtube.com/watch?v=m7ys1zrY7nc) on what it would be like if the Earth slowly stopped spinning over 5 years.

The main driver of the catastrophes it describes is that the Earth's equator has a larger diameter than the distance between the poles, so, with centrifugal force diminishing, the oceans and atmosphere shift toward the poles, drowning the most northern & southern continental lands, thinning out the air on land near the equator, and eventually exposing dry land at the equator where the ocean floor was. By the end of the 5 years, the planet can mostly be described as having two polar oceans and a single equatorial ring-shaped megacontinent between them.

But the explanation I've always seen before for how the Earth is actually slowing down much slower than that, and the moon is gradually drifting away, is related to a bulge that would tend to "point" toward the moon (although it gets pushed a bit ahead of that by the planet's rotation too). With the Earth rotating so different points on the surface are closest to the moon at different times each day, this bulge of the Earth's shape must be able to travel around the planet as a wave roughly once per day.

So the former story depends on the Earth not reshaping itself yet within 5 years (the span of the story on humans dealing with the change), and the latter depends on the Earth constantly reshaping itself hour after hour. I presume that the way to reconcile them is that the latter is a much smaller bulge, but... how much smaller? And how long would it take before a non-spinning Earth settled to a spherical shape (neglecting hills & valleys)? Or would it never get there at all because that amount of change is too much for the planet's amount of stiffness/solidity?

WaxRubiks
2018-Nov-22, 08:22 AM
I presume that the way to reconcile them is that the latter is a much smaller bulge, but... how much smaller?.



Earth tide (also known as solid Earth tide, crustal tide, body tide, bodily tide or land tide) is the displacement of the solid earth's surface caused by the gravity of the Moon and Sun. Its main component has meter-level amplitude at periods of about 12 hours and longer.
https://en.wikipedia.org/wiki/Earth_tide

profloater
2018-Nov-22, 12:58 PM
If the water drifts to the poles as the rotation slows, then the oblateness also reduces towards spherical and the water would redistribute back to something like it is now, wouldn't it? the Earth has only a thin skin of solid rock so its oblateness is a balance between the centrifugal force and local gravity which is trying to hold to a sphere with a uniform water covering. If there is still the moon its force would change to its orbital period instead of the earth rotation rate. That would be very different because of ocean resonances.

Hornblower
2018-Nov-22, 03:08 PM
Some technical points:

1. The tidal elongation is a pipsqueak compared to the depth of the oceans, not to mention the oblateness.

2. Suppose we magically stopped the rotation in five years without tearing up the planet. I would expect it to start settling toward hydrostatic roundness and in the process cause a lot of ongoing earthquakes in the crust. I do not know what the time constant of that settling would be. It is my understanding that the hot underlying mantle is plastic over long time scales.

3. If the rotation is stopped, the Moon will overrun it and start spiraling in, and the tidal drag would gradually spin up the planet.

I looked at a few seconds of the video and was put off by the sensationalist manner of it, not at all what I have expected from National Geographic over the decades. I had no further desire to watch. Did they address the issue of gravitational settling of the main body of the planet?

Delvo
2018-Nov-23, 12:32 AM
Did they address the issue of gravitational settling of the main body of the planet?They did include earthquakes in places where earthquakes hadn't happened before because of stress on the plates, but nothing about how long it might take for that stress to work itself out.

dtilque
2018-Nov-24, 08:41 AM
not at all what I have expected from National Geographic over the decades.

National Geo TV is not the same as the magazine anymore. The network is more than half owned by Fox and it shows. It's not really much better than the History Channel.

Hornblower
2018-Nov-24, 11:27 PM
National Geo TV is not the same as the magazine anymore. The network is more than half owned by Fox and it shows. It's not really much better than the History Channel.

I might have known! When I first got cable TV 35 years ago, Discovery Channel and its siblings were worth the cost of the service. Since then they have become in large part schlock, and Fox appears to be more of the same.

wd40
2018-Nov-25, 08:57 AM
Venus is almost the same size and mass as the Earth. The difference is that the Earth is spinning at 1000mph, whilst Venus is only spinning at 3mph. Is there a significant difference in the rotation-induced non-sphericality between the two?

Hornblower
2018-Nov-25, 02:15 PM
See these tables, which include oblateness of the planets.
http://www.astronomynotes.com/tables/tablesb.htm
If they are accurate, the answer is yes. Mercury and Venus, with their extremely slow rotation, show no measurable flattening or bulging.