Map d Sapling Learning macmillan learning The Roche limit for a planet-natural s

Question

Map d Sapling Learning macmillan learning The Roche 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 = 8.25 × 1024 kg, the radius of the planet R = 6250 km, the natural satellite mass m 2.65 × 1018 kg and the radius of the satellite r= 2530 km, find the Roche limit of this system. Number 9.27x 10 5 km There is additional feedback available! View this feedback by clicking on the bottom divider bar. Click on the divider Incorrect. bar again to hide the additional feedback. Close

Explanation / Answer

d ( Roche limit) = 1.44 ( Rm) (density of planet/ density of satellite)^1/3

d = 1.44( 6250 x 10^3) ( 8.25 x 10^24 x 2530^3 x 10^9)^1/3 / (2.65 x 10^8 x 6250^3 x 10^9) ^1/3

d= 9 x 10^6 ( 2.02 x 10^ 8 x 2530 x 10^3) / (0.642 x 10^3 x 6250 x 10^3)

d= 9 x 10^6 ( 5110.6 x 10^ 11) / ( 4012.5 x 10^ 9)

d = 11.46 x 10^8 = 1146302.8 km apprx

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