Assuming an instantaneous force, it would be most efficient to do it at apogee. If we assume that the Moon remains intact, we could put it into an elliptical orbit where apogee is equal to the radius of the Moon, so that it just grazes the Earth (lots of assumptions made here, but should give us a good approximation).
To do this, you’d have to reduce the Moon’s speed from 0.950858 km/sec to 0.193016 km/sec. So you’d have to slow it down by 0.757842 km/sec, or reduce its speed by 79.7%
By contrast, an instantaneous prograde burst at perigee with a delta-v of just over 0.4 km/sec (increase of ~37%) could send the Moon entirely out of Earth’s orbit.
To a rough approximation, the moon has a mass of 7 x 10[sup]22[/sup] kg and a velocity of about 1000 m s[sup]-1[/sup]. By 1/2 mv[sup]2[/sup] that’s, oh, 3.5 x 10[sup]28[/sup] J of kinetic energy. Tsar Bomba pumped out about 2 x 10[sup]17[/sup] J so about 100,000,000,000 of those little toys would make an appreciable dent in the Moon’s orbit if we could arrange for most of their energy to be applied as braking thrust. Off you go. If Earth’s economy is up to making and delivering ten of them a year, we’ll be done before the Sun goes out.
I just had a silly thought - what if we could make a super strong rope (out of carbon nanotubes or something) and attach one end to the Moon and the other end to the Earth, so that it would wrap itself around the Earth as it rotated and gradually draw the Moon inwards. It seems as it it would work if the rope could be made strong enough, as per Wikipedia, the rotational energy of Earth is about 5.5 times higher than the Moon’s orbital energy (the day would end up being several hours shorter, not that it would matter after the Moon crashes).
Cool! Using the moon as a tether ball. We need to kick it up into a tilted orbit first so the people on the other side of the earth can’t reach up and stop it. It’s going to have a hell of an orbital velocity just before it hits us.
[music]
Well I’d like to blow up the moon,
From a rocket ship high in the air.
Yes, I’d like to blow up the moon,
'Cause I don’t think I’d like to live there.
There’s that factor of two I was talking about. The energy required to create the grazing orbit (or the escape orbit) would be even more than required to blow the moon up completely, unless I’ve dropped a decimal point.
Perhaps we could do something with dark matter. If (a) we can figure out what it is and (b)how to produce or capture it, we might pack it around the moon like styrofoam peanuts in a shipping crate, slowing it down as it orbits. Then things would get interesting.
And if that doesn’t work, we can try using dark energy to shove it away from the earth altogether.
To quote something Malacandra wrote earlier in the discussion, “Um, orbits don’t do that.” Or, more specifically, I’m not sure you grasp the orbital relationship between the Earth and its satellite, if you think altering the Earth’s orbit would move it relative to the moon. The little guy’s sort of along for the ride. Where we go, it goes.
(I’m sure if you altered the Earth’s orbit enough, eventually the moon’s orbit would destabilize… but long before that occurred, we’d have much bigger problems — mostly related to the fact that we were now all hurtling off on a trajectory which would quickly rob the planet of its ability to support life. There’s surprisingly less wiggle-room in that than you’d think!)
Even if you had a rope strong enough, the Moon isn’t strong enough. The super-rope would just rip loose from the Moon or slice through it, depending on how you attached it. On the scale of the forces we are talking about a moon or planet is about as solid as a drop of water.
Yeah, and I “like” the Sun. Go tell it to your “Friends” on the Facebook. And all that other feely-good hippy crap you kids are into these days. Makes me sick to my stomach.
Wake up, youngster, and just ask yourself for a moment: what have either of those two bastards ever done for us? They go twirling around the sky, shining on us and thinking they’re all that. But they’re not.
