Effects of spontaneous gravity reduction

[happytadpole]

Can anybody direct me to a discussion on the effects of a sudden reduction of the Earth's gravity - say by 50%? Purely speculative, of course. I'm assuming its orbit around the sun would be essentially unchanged, but that the moon would recede or maybe head off on its own merry way. Any other musings on air pressure, human survival, sea level, etc also welcomed.

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

 

[tony873004]

I don't know where else you might find a discussion on this. But you're right, the Moon would go on its merry way, orbiting the Sun in its very own Earth-crossing orbit. In a short time scale by astronomical standards a collision between the Earth and the newly escaped moon is almost inevitable. Prior to that, I think a reduced air pressure would kill most life.

 

[pervect]

Meanwhile, you can look to plenty of excitement on earth, as the change in pressure will cause global earthquakes of an uprecedneted magnitude as the Earth re-adjusts to the different pressure. I'd imagine that most dormant volcanos would become active, as well, spewing up magma. The atmosphere would also thin out - if the event happened instantaebnously, the "thinining out" process would gererate very large winds as well.

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.

 

[BobG]

Can anybody direct me to a discussion on the effects of a sudden reduction of the Earth's gravity - say by 50%? Purely speculative, of course. I'm assuming its orbit around the sun would be essentially unchanged, but that the moon would recede or maybe head off on its own merry way. Any other musings on air pressure, human survival, sea level, etc also welcomed.

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:
$$v=\sqrt{\frac{\mu}{r}}$$

Minimum escape velocity is:
$$v=\sqrt{\frac{2 \mu}{r}}$$
($$\mu$$ is the Earth's mass times the gravitational constant

Instant 0: Moon is traveling 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 exactly the escape velocity. The Earth and Moon should still be in resonance. I think the Moon would wind up in one of the LaGrange points (which would have also instantly changed) or in an orbit similar to Cruithne, the asteroid that's sharing the Earth's orbit (sometimes called Earth's second Moon), at least for several thousand years.

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.