Would you gain momentum falling towards a large asteroid if the large asteroid was moving away?

Were the boosters already active before you jumped out, or did the asteroid only start moving when you jumped?
Does this atmosphere have an atmosphere that would push you downwards?

If there’s no atmosphere and the asteroid wasn’t already moving, if you drop out of the window and then suddenly the asteroid starts moving away from you, I think you’d fall slower.
It also depends on how strong the gravity is and how much the thing accelerates. If the difference is large enough you might even escape the asteroid’s gravity altogether.

Interesting question. :)

Side note: you speed up when you fall anyway, until you reach terminal velocity; I assume the question is whether you accelerate faster.

What you’re describing is a special case of the three body problem. The solutions to three body problems, if they’re soluble at all, tend to be extremely complex and depend on whether you’re using Newtonian or quantum rules. Suffice to say it requires a shitload of Greek symbols and more skullsweat than either of us probably want to squander on it.

I have a better understanding of my question yesterday by seeing a satellite as similar to a helicopter rising and falling but on two dimensions.

While a helicopter tries to escape earth by going up the satellite trys by going sideways as the earth curves.

If the asteroid was accelerating at the same rate as you were, then you would be in permanent freefall, and would never reach the surface of the asteroid.

To an observer from a 3rd point in space, you would both seem to be accelerating at the same rate.

If the asteroid is moving away from you as you fall toward it, then you would fall faster but in an exponentially slower acceleration, thus never overtaking the departing object. It’s gravitational pull on you would be falling by the inverse square of its distance from you, which would be constantly increasing.

Let’s turn this into a 2-body problem. There’s just you and the asteriod moving away from you. The rest of the universe is empty. The answer is: yes, you would still gain momentum i.e. the product of mass and velocity is increasing in absolute terms. The acceleration i.e. increase in velocity is getting smaller and smaller over time.