# To find the mass and radii of hill sphere of a planet after passing through a region of planetary nebula

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!

(In the hill sphere formula you can consider a and M to be constants)

Thank you!

• I have just finished my 12th grade and no scientist 😅. But I'm very much interested to be an astrophysicist. Since I lack the knowledge in this field I request for ur help. I'm writing a research paper on the fate of Jupiter after the death of our sun as a hobby and need help over here, I really tried my level best with my knowledge but with no success I have come here. Thank you for ur help! – Tushar Sharma Jun 7 '20 at 14:30