Consider a planet with initial mass m* kg and radii of hill sphere as r*.
The planet it traveling (assume) perpendicular to the nebula at a speed of 13km/s and the nebula is approaching the planet at 15 km/s.
The nebula has a density of D kg/km^3.
The planet travels through this region for 1.4yrs in which it covers 570.5 million km.
Is is possible to calculate the mass and volume of hill sphere of the planet at the end of 1.4 yrs? If so how? The problem I face is that with gain in mass the planets radii of hill sphere increases, hence more mass falls in which in turn again causes the hills spheres radii to increase, this process goes on and on till the end . I'm struggling to imply integration!