If a person was standing on the moon, how would they be affected - would they be disintegrated? Knocked flat? Would the sudden change in orbit be so swift that they would die from the force? Would they have time to contemplate the magnitude of the problem, or would they be killed very shortly after seeing what had happened?
There’s nothing to transmit the shockwave. He could get hit by large pieces of Earth, though.
Neat! So all that would make it to the person would be light? What about the sudden change in orbit? Would have have any effect on the person?
Depending on what you mean by ‘exploded’. If you mean ‘every part of the Earth is sent off in a different direction so that it doesn’t just recollapse into a ball’ then the explosion would be large enough to overcome the planet’s gravitational binding energy, which would need about a week’s worth of the Sun’s total output concentrated into a single bang.
You wouldn’t want to be standing out in the open on the Moon if that went off.
All that mass has to go somewhere; it can’t just disappear. If the Earth exploded outwards uniformly in all directions, then it wouldn’t affect the orbit until the expanding cloud of matter hit the Moon; all that matters in such a case is the total mass of the Earth, and that doesn’t change.
Also: Any Earth-shattering kaboom worthy of the name would have to launch fragments of the Earth outwards from the surface at a speed at least as high as escape velocity. These fragments would slow down as the gravity of the rest of the Earth pulled them back, but they would reach the moon in [quick differential equation] a little under 3 days. A more energetic explosion would reduce this time, of course; but your hypothetical astronaut might have quite a while to contemplate his fate.
Beautiful =] thanks a bunch
You didn’t need to do the calculation, as the experiment has already been done. On the occasions we did send fragments of the Earth to the Moon at the slowest possible speed, it did indeed take about 3 days.
In my defense, I did in fact realize that, but only after I had solved the differential equation. 
“Need answer quick?”
The awesome “how to destroy the earth” website includes the detail that to do this you need 25,000,000,000,000 tonnes of antimatter… anything smaller and the earth will just re-coalesce again.
Username/post combo!
If the Earth “just exploded”, wouldn’t the Moon start flying off in a mostly straight line as Earth’s gravity faded away? By the time chunks of Earth reached the Moon’s orbit, I suspect the Moon would be much farther away. [del]At least, that’s the way we’ve figured it.[/del]
And as for needing 25 Teratonnes of anti-matter? According to the data from our small scale tests you can easily do the job by just…
Oh.
Nevermind.
Yeah. 25TT of anti-matter. Yep, that’s what the job would take. If you can’t come up with that, just call in the dogs, piss on the fire, and head back home. It’s not going to happen. Nuh-uh. No way.
Earth’s gravity would not do anything that could be described as “fading away” until the debris reached the Moon. Remember, all that mass is still there.
That’s an interesting sidebar…if, hypothetically, Skald the Rhymer managed to perfect his Dimensional Shunt and slide the whole planet into the dimension next door, how long would it take for the sudden lack of planetary mass to cause a tangible loss of (ETA: “the Earth’s former”) gravitational pull on the Moon?
The loss of gravitational pull would happen immediately.
Speed of gravity:
maybe… it’s not quite that simple:
http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html
Assuming the earth started dispersing evenly in all directions, then the center of the earth’s mass wouldn’t change location. And the law of gravitational attraction applies any time the two masses (the moon and earth) are completely external to each other. So the moon wouldn’t feel earth’s gravity begin to fade away until some of the mass of the earth started to move beyond the moon’s orbital path.
I pointed out in a another thread recently that the mathematical equations that we use to describe gravity actually require that matter and energy are not created or destroyed. If you try to describe a situation where the Earth just pops out of existence, you get inconsistent equations, requiring things like 1 = 0 somewhere. I suppose that you could think about opening up a wormhole large enough to swallow the Earth, but in such a case I would guess that said wormhole would have its own gravity large enough to significantly perturb the Moon’s orbit well before the Earth was sent upon its merry way.
And even after the Earth’s mass had moved past the orbit of the Moon, the Moon would still not fly off in a straight line. Instead, it would be in orbit around the Sun and more-or-less follow the Earth’s former orbit.