Earth's momentum and the moon

[EmilyHopkins]

What would happen to the Earth's momentum theoretically speaking if the moon was destroyed by some outside body such as a asteroid ?

 

[Simon Bridge]

depends on the details ... basically the asteroids momentum would get added to the system.

 

[EmilyHopkins]

depends on the details ... basically the asteroids momentum would get added to the system.

Interesting what about if the moon was destroyed by weapons from earth. The gravitational biding energy of the moon is 1.245×10^29. The largest nuclear bomb detonated was Tsar bomb, which only had around 10^17 joules. So You would need roughly 1,000,000,000,000 of them.

Say if we had the means to launch these bombs into space to reach the moon, and they were successful in destabilizing the gravitational attractive force holding the moon together. Then using conservation of momentum and applying it to the Earth-moon system would the momentum of the Earth gradually increase,remain the same, or continue to decrease but at a slower rate ? How would this affect our orbit as well, would we become more elliptical and be closer to the sun ?

 

[mfb]

Why do you think the momentum of Earth decreases currently?
Do you mean the rotation? This is slowing down, and if you remove the moon the slowdown would be smaller (tides from the sun are still there). At the same time, the orbit would slowly move outwards due to those tides.

Depending on the moon destruction mechanism, there might be an additional effect: Earth is constantly moving around the common center of mass of (earth+moon). If you suddenly "remove" the moon , we keep this velocity, and it can change the orbit a tiny bit.

 

[Simon Bridge]

Lets say we totally vaporize the moon. The mass is still there - maybe still gravitationally bound to the Earth. Depends on how we do it.

Strap a rocket to the moon and accelerate it out of orbit (actually, this is happening - albeit slowly) ... maybe we use materials found on the moon so we don't have to worry about the effect of launching a billion nukes from Earth.

You can probably work that out - put two masses in orbit about their common center of mass, give one of them an extra radial velocity. See what happens. That would be a good exercize for you ... builds character ;)

Then the nuke option - this would be treating the Moon as a cue ball and smacking it out of orbit. The Moon vaporizes ... but maybe all the bits acquire escape velocity in the right direction to leave.

That would be like the slow version, only very quickly.

Magic the Moon out of existence but insist that angular momentum is conserved?
Then the Earth would have to gain angular momentum to compensate ... also by magic. The kicker with these things is to consider the process.

I am hoping this is idle curiosity?

 

[Andre]

To carry it further, the Earth spin axis is now wobbling around in a precession cycle of about 26,000 years, this precession is caused by the gravity difference of the equatorial bulge in relation to the sun and moon, causing a torque. If the moon was gone the precession rate would be much slower, how many years?

There is also an obliquity cycle of about 41,000 years. It is hypothized that when frequency of both precession and obliquity are approaching each other, resonance will bring the planet to extreme obliquities, known as the chaotic zone, where is our moon when this start to happen?

 

[Martinaston]

Would detonating a nuke on the Moon be as effective as on Earth, due to the lack of atmosphere.
Would the blast just radiate into space and have no effect on the Moons orbit ?

As for the Earth and Moons centre of mass (below the Earth's crust), Would landing on the Moon and leaving the lander behind (Mass) have an affect on this ?

 

[mfb]

A nuke under the surface would be similar to one on earth. A nuke above the surface would vaporize some rock, melt some more rock and make some rock radioactive, but apart from that nothing serious would happen.

Would landing on the Moon and leaving the lander behind (Mass) have an affect on this ?

Not in a significant amount for reasonable masses in spaceflight.

 

[Simon Bridge]

@Martinaston: welcome to PF;

1. depends what you mean by "effective" - what effect were you thinking of? Certainly the atmosphere means there are extra effects.

2. the kind of blast that would have a noticable effect on the Moon's orbit would also do serious damage to the Moon.

Phil Platt did the math for a much bigger explosion, but it tells you what sort of calculations you have to do.

3. By going to the Moon and leaving stuff behind, you are effectively moving mass from the Earth to the Moon (though Apollo missions also brought mass back from the Moon).

You can get an idea of the scale of the effect by working out how much mass you'd have to move to get the center of mass between the Earth and the Moon to sit on the surface of the Earth. It's not a hard calculation. Then, looking up how much mass got transferred in each Apollo mission, you can work out how many missions this would have taken.

 

[Martinaston]

@mfb

Describe "not a significant amount" after 43 years + however much more junk is up there from all the other probes/landers, please.

I'm kind of more interested in the shift of tidal forces withing the Earths mantle.

@Simon Bridge
Thanks and helo.

1 i was thinking along the lines of the dam busters, when they used the surrounding water pressure to concentrate the blast into the dam.

Would it reduce the effect of the blast wave, not having the atmosphere to help contain it against the Moons surface ?

3, as per my reply to mfb

 

[mfb]

@mfb

Describe "not a significant amount" after 43 years + however much more junk is up there from all the other probes/landers, please.

According to wikipedia, the total mass of all man-made objects on the moon is about 180 tons.
Moon has a mass of 7.3*10^19 tons = 73 000 000 000 000 000 000 tons.

We had some 4000 rocket launches in history - most of them to Earth orbits, only a small fraction went to the moon. Even if all rockets would have been designed to deliver mass to moon, this would not exceed ~40,000 tons.