Please don\'t use the Wikipedia Roche formula cos it didn\'t work, I have tried.
ID: 1262327 • Letter: P
Question
Please don't use the Wikipedia Roche formula cos it didn't work, I have tried. Please help me out this problem and thanks a lot.
The Ruche limit for a planet-natural satellite system is the smallest distance between their centers at which the gravitational attraction between the celestial bodies could break apart the satellite. Knowing the mass of the planet M = 4.45 x 10^24 kg, the radius of the planet R = 6090 km, the natural satellite mass m = 3.25 x 10^18 kg and the radius of the satellite r = 2850 km, find the Roche limit of this system. Consider the natural satellite as being made of two equal-mass spheres in contact, with a distance between their centers equal to the radius of the satellite. One half is closer to the governing planet than the other half by the satellite's radius. Each half of the satellite is subject to the attractive pull from the planet and is held together by the gravitational attraction between the two spheres. At the Roche limit, the difference in the attractive gravitational forces between the planet at the two halves is equal to the gravitational force between the two halves themselves. Use Newton's formula of gravitational attraction.Explanation / Answer
The Roche limit can be found from d = 1.26 R_m (M_M / M_m)^1/3. In our case, d = 3.987 10^5 km. Here M_m and R_m are the mass and the radius of the satellite, and M_M is the mass of the largest body.