Let's imagine a moon orbiting a planet at 75000km distance (assume circular orbit). Now let's say that the Hill Sphere of this planet only extends to 78,000km (small planet in the habitable zone of a small star).
As with the moon/Earth situation, this moon is slowly drifting farther away from the planet. (ie Deimos and Mars).
What factors effect the time frame of this moon being lost so that it would be in orbit of the star and not the planet.
Does anybody know of a computer simulation showing this happen? Wondering what the trajectory and duration of the transition period would look like.