Semi-competent physicist here...

I primarily deal with radiation physics (similar concepts as nuclear physics but different focus) so I'm no cosmologist, but I'll give this a shot.

Gravity has a "speed" yes, but that's really how fast gravity waves or particles (hypothesized "gravitons") propagate through space. I know almost nothing about gravitons. However,

https://www.forbes.com/sites/startswith ... 3f4fee604b looks like a great resource for understanding gravity waves!

MrEen and Isemmens are pretty close when talking about "g" (aka "small g"). Gravitational acceleration

on Earth's surface is around 9.81 m/s^2, although it varies with elevation and distance from the equator, among other things.

More universally, Newton's Law of Universal Gravitation gives us the force of gravitation attraction between any two objects 1 and 2:

F = (G* M * m)/r^2 where r is the distance between the two objects, M and m are their respective masses, and G (aka "big G") is the "gravitational constant".

If you also use Newton's Second Law: F = m*a where m is any mass and a is its acceleration, you can call this particular acceleration "g" and then set the two forces equal to each other.

F = F

(G * M * m)/r^2 = mg

(G * M)/r^2 = g

For Earth, use our mass (~5.97x10^24 kg) and radius (~6.378x10^6 m) and you get g = 9.8 m/s^2 at Earth's surface. For any other body -- the Sun, another planet, the Moon, any star, and so on -- your "g" will be different because they have different masses and different radii.

Why am I mentioning this? Because you're both right.

Gravity does propagate at a particular speed, but that doesn't affect how quickly things "fall". That's determined by Newton's Law of Universal Gravitation. As orbiting bodies are really in constant free-fall towards their sun, this also affects their behavior if gravity is switched off.

lsemmens wrote: ⤴Wed Mar 06, 2019 8:35 pm

If gravity were turned off the planets would keep traveling in a straight line at a tangent to the the original arc of momentum at the point gravity ceased.

That's pretty much it.If gravity were to suddenly quit affecting them, they'd fly off in exactly a straight line from how their velocity vector was pointing at that exact instance at the exact same velocity magnitude.

otacon14112 wrote: ⤴Wed Mar 06, 2019 8:52 pm

For example, even though at 0.0000000001 seconds after the string breaking, the acceleration is is negligible enough to say that it hasn't even moved, even though it has moved a very small distance

Not exactly. Acceleration isn't negligible even for a super-short time period "dt"; it's always constant. In this case, on Earth, a = 9.81 m/s^2. Now the

*displacement* would be negligible enough for sure! (Displacement would be the double integral of acceleration with respect to time; equivalently, acceleration is the second derivative of displacement with respect to time).

otacon14112 wrote: ⤴Wed Mar 06, 2019 8:52 pm

I'm asking if the point in time that the attraction ceases to exist between the two (ignoring the very slight attraction of distant objects elsewhere in space) would be the same point in time that gravity is "shut off"? Or would this point in time be later?

This is where things get freaky.

Yes, no, maybe so, depending on your frame of reference. First off, the time interval between gravity going MIA and you seeing the planet flying off depends on light speed alone. You can't see any result before light has had time to reach you. No matter the real speed at which gravity propagates, you're limited by how quickly you can observe its effects.

As I understand it, though, the big issue with this thought experiment is that gravity is just the curvature of space-time. If gravity ceases to exist, then space-time as we know it would be fundamentally altered. Maybe our concept of elapsed time would be very different in that scenario.

I hope that's right??

Cheers!

Fred