So some flat earth arguments are actually correct if general relativity is correct, namely that gravity is an illusion and that the real reason we are stuck to the earth is that the earth is accelerating toward us at 9.8 m/s^2
So we're curving in towards the center of the mass of the Earth, but the reason we don't end up in the core of the Earth is because the surface stops us. The Earth is "pushing" us away from the center, and that's the acceleration. It's accelerating you off your straight line path, and this is the deviation from the geodesic.
What's confusing me here is the notion that when two objects collide, they accelerate into each other. Why and how is force constantly applied after the collision? My intuition is falling down here, and none of the resources I've looked at so far have explained why the acceleration happens.
I don't really understand why, that was just the explanation Derek gave.
The acceleration an observer sees you undergoing is the same as the inherent "proper" acceleration you're undergoing, minus the acceleration of their coordinate frame with respect to yours. For me to stay still with respect to you, if you're in a frame that is accelerating away from me, I need some proper acceleration to catch up and counteract the fact that our frames are diverging. But if spacetime is curved, your frame probably is accelerating relative to mine - c.f. the example on the Earth's surface, where our frames inexorably accelerate towards each other as we move parallel to each other. So for me to stay still with respect to you, I need to have some proper acceleration to balance out the coordinate acceleration derived from the fact that our frames are moving in a curved space.
If the object's velocity isn't enough to traverse the curved space-time, it will move toward the center of the mass generating the distortion and fall out of the sky.
If the object is traveling quickly enough, it can continue traversing the distorted space-time and orbit that mass.
If the object is traveling even more quickly, it will traverse the distorted space-time and continue on without orbiting the mass.
In all three cases, from the perspective of the object traversing the distorted space-time, it continues to travel in a straight line, as it's the space-time that's distorted.
A (flawed) analogy would be riding a bicycle between the peaks of two identically sized hills. Starting at the top of the first hill, you coast down increasing your velocity.
Once you reach the bottom of the first hill and head up the second, your velocity decreases.
If your velocity at the bottom of the first hill is too small, you'll go up the second hill and as your velocity reaches zero, you roll back toward the bottom of the hill.
You will pick up velocity and then roll back up the first hill, then down again, then back up the second, etc. until you end up stopped at the bottom of the hill. This is akin to falling to the center of the distorting mass.
If your velocity is high enough to carry you back up to the top of the second hill and then stop, you'll roll back down and get to the bottom with the same velocity you had coming down the first hill. You'll then oscillate between the tops of both hills. This is akin to orbiting the mass.
If your velocity at the bottom of the first hill is enough to carry you past the top of the second hill, you'll just keep going after reaching the top of the second hill. That's akin to flying by the mass.
It's a flawed analogy, because in a curved space-time the directional portion of the motion vector doesn't change.
As John Wheeler[0] simplified it: "Mass tells space-time how to curve, and space-time tells mass how to move."
