Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Marika on 03/08/2018 09:16:14

Title: How fast would the earth spin if the moon was closer?
Post by: Marika on 03/08/2018 09:16:14
Donald wants to know:

If we could pull the moon to the same orbit as the ISS, how fast would the earth spin? How fast would the moon-earth rotation spin? And how high would the tides be?

What do you think?
Title: Re: How fast would the earth spin if the moon was closer?
Post by: Yusup Hizirov on 03/08/2018 11:42:30
If you reduce the distance from the Earth to the Moon (2000 km), the gravity of the Moon will reach Earth, resulting in:
1. It will be a static theory of tides, the lunar tidal current will move from east to west at a speed of 1600 km / h, skirting the Earth in 24 hours, wiping the ocean floor and flooding only the eastern coasts of the continents.
2. There is only one tidal hump, which will quickly reduce the Earth's rotation speed. (The force of gravity is added, not compensated).
3. The tides will occur only on the eastern shore of the continents, with a height of more than 1 km. The highest tides will be at the equator.
4. In the seas and lakes there will be high tides.
5. Ships and airplanes will move on a tidal wave at a speed of 1600 km an hour, from east to west.
6. Whirlpools and currents will disappear.
7. Every day, according to the schedule, there will be earthquakes.
8. The North Pole will become a continent. At the equator, the ocean will become deeper.
9. Under the moon, decrease the pressure of water and air.
10. The speed of water flow in rivers will change.
11. There will be no tides on the Moon, since the gravitational force will be compensated by the centrifugal force.
Title: Re: How fast would the earth spin if the moon was closer?
Post by: evan_au on 03/08/2018 12:14:06
Quote from: DOnald
If we could pull the moon to the same orbit as the ISS...
The radius of the Moon is 1700 km.
The altitude of the ISS ranges from 335-435km, depending on how recently they have had a boost to overcome friction with Earth's tenuous outer atmosphere.

If you attempted to put a 3400km-wide object into a 400km-high orbit, the Earth's surface would become a molten lava lake, just like it was after the formation of the Moon.
See: https://en.wikipedia.org/wiki/Origin_of_the_Moon
Title: Re: How fast would the earth spin if the moon was closer?
Post by: Kryptid on 03/08/2018 17:27:09
2,000 kilometers is well within the Earth-Moon Roche limit, so placing the Moon at such a distance would also cause it to break up. This would likely form a ring of debris around the Earth.
Title: Re: How fast would the earth spin if the moon was closer?
Post by: evan_au on 03/08/2018 23:20:09
Using the Moon to dig a 1,000km-deep trench around the Earth would also cause the Moon to break up...
Title: Re: How fast would the earth spin if the moon was closer?
Post by: Kryptid on 04/08/2018 02:31:06
Using the Moon to dig a 1,000km-deep trench around the Earth would also cause the Moon to break up...

I was thrown off by Yusup's post. I didn't know how far the ISS orbited, so I simply assumed that when he said 2,000 kilometers, that was the distance. I missed the correct distance as stated in your own post.
Title: Re: How fast would the earth spin if the moon was closer?
Post by: Janus on 04/08/2018 17:20:00
Assuming that you could compact the Moon to a size were it could comfortably orbit at ISS altitude while maintaining its mass, you could estimate how long it would take for the Earth to lock to it ( this would also alleviate the Roche limit problem as that is dependent on the relative densities of the bodies involved, and and small, extremely dense Moon would be able to survive at that altitude) .
 Also assuming that every other factor remains the same, then the time to full lock depends on the starting distance between the two bodies to the 6th power.  The Moon is presently 384,000 km from the center of the Earth, while the ISS varies between 6678 to 6778 km ( orbital radius).  If we split the difference to 6728, then the Moon's orbit is some 57 times larger.  To the power of 6 this 3.46e10. 
One rough estimate I found stated that, if left alone, the Earth would presently take ~50 billion years to tidally lock to the Moon.  1/34,600,000,000 of that is a bit under 1 1/2 years.  So you might assume that this is (very roughly) how long it would take for the Earth to lock to the new closer Moon.

Unfortunately, it isn't that easy.   The Moon slows the Earth rotation and moves away because its orbital period is longer than the time it takes for the Earth to rotate.   The ISS, in its orbit has a shorter period.  The resulting tidal effect in this situation would be to speed up the Earths rotation, while causing our new condensed Moon to spiral inward, eventually crashing into the Earth.  I would not expect this to take long.  Just before impact, the Earth would be rotating in just a few minutes less a day than it is now.   After impact, the total angular momentum of the "moon" would be transferred to the Earth.   At this point, the angular momentum of the "moon" would be ~50% that of the rotating Earth.
Title: Re: How fast would the earth spin if the moon was closer?
Post by: Petrochemicals on 10/08/2018 21:45:11
I do ot see why moving the moon closer would cause it to spin any faster, other than as a byproduct of the increaced orbital velocity around the mutual centre of gravity between the moon and earth . If the rotation of earth is merely a balanced motion that is dependant on the observer, ie measured from the sun. If you move the earth and moon closer however they would biorbit each other at an increased formulaic velocity. Could you explain why the spin would have to have a defacto increace?
Title: Re: How fast would the earth spin if the moon was closer?
Post by: Janus on 10/08/2018 23:21:47
I do ot see why moving the moon closer would cause it to spin any faster, other than as a byproduct of the increaced orbital velocity around the mutual centre of gravity between the moon and earth . If the rotation of earth is merely a balanced motion that is dependant on the observer, ie measured from the sun. If you move the earth and moon closer however they would biorbit each other at an increased formulaic velocity. Could you explain why the spin would have to have a defacto increace?
Initially, putting a Moon-massed object into a close orbit around the Earth would not cause an increase in the Earth's rotation rate.  But as it stays there, tidal interaction between the object and the Earth will transfer angular momentum from the object to the Earth. (This is the opposite effect from what is now happening with the Moon, where angular momentum is being transferred from Earth to Moon.  The difference in how the tidal interaction affects the Earth is due to whether the rotational period of the Earth is greater than or less than the orbital period of the object. If the object was placed at geosynchronous orbit distance, there would be no speed up or slow down.)
Title: Re: How fast would the earth spin if the moon was closer?
Post by: Professor Mega-Mind on 19/08/2018 19:52:40
Moon was 10 times closer after Theia bash .  Giant moon caused giant tides , changed 5 hr. day into 24 hr. one .  Moon lifted into present orbit by this .  Someday Earth & Moon both be tidelocked .  Bonus point-Sun has lifted Urth about 1 million miles so far .
O.K. , I rest obnoxiously heavy head now .  Owut ,   P.M.