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happytadpole

Oh, and it goes without saying that I am lazy, stupid and posting in the wrong forum.

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- Thread starter happytadpole
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- #1

happytadpole

Oh, and it goes without saying that I am lazy, stupid and posting in the wrong forum.

- #2

tony873004

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One way of looking at this is to look at the magnitude of the energies involved. The Earth's total binding energy is EXTREMELY large. It's not only than the total energy in any historical asteroid impact, including the one that killed off the dionsaurs, it's a LOT larger. It's so large that it is difficult to find any plausible mechanism that could disrupt the Earth. Here we are talking about 3/4 of this energy disappearing suddenly.

(see the formula at http://en.wikipedia.org/wiki/Gravitational_binding_energy for more detail).

Since I loooked up the formula I might as well work out the numbers - the total binding energy of the earth is 2.2*10^32 joules, 3/4 of that is 1.7*10^32 joules

That's the equivalent to the energy in 40 zeta-tons (zeta = 10^21) of high explosive.

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BobG

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happytadpole said:

Oh, and it goes without saying that I am lazy, stupid and posting in the wrong forum.

If the 50% reduction were because of a loss of 50% of the mass, the Moon's current average velocity is the escape the velocity.

Speed in the orbit is equal to:

[tex]v=\sqrt{\frac{\mu}{r}}[/tex]

Minimum escape velocity is:

[tex]v=\sqrt{\frac{2 \mu}{r}}[/tex]

([tex]\mu[/tex] is the Earth's mass times the gravitational constant

Instant 0: Moon is travelling at the speed defined by the first equation.

Instant 1: Instantaneously cutting the mass by 50% is essentially eliminating the 2 out of the second equation.

Before the Earth lost half of its mass, both objects were essentially orbiting the Sun with the Earth seriously perturbing the orbit of the Moon, enough that the Moon's path around the Sun appeared as an orbit.

After the Earth loses half of its mass, the Earth is still perturbing the Moon's orbit, just not enough for the Moon to pass the Earth one way or the other. I'm not sure that would make for a collision at

If the force of gravity suddenly decreased 50%, you'd have a more chaotic situation. Every planet and every moon in the solar system would wander off through the universe its own trajectory.

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