One model for a certain planet has a core of radius R and mass Msurrounded by an outer shell of inner radius R, outer radius 2R,and mass 4M. If M = 8.57 Ã 1024 kg and R = 8.60 Ã 106 m, what isthe gravitational acceleration of a particle at points (a) R and(b) 3R from the center of the planet?

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Deanna HettingerLv2

10 Mar 2019

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A satellite is orbiting around a planet in a circular orbit. The radius of the orbit, measured from the center of the planet is R=1.9 x 10⁷ m. The mass of the planet is M = 4.4 x 10²⁴ kg.

Part (a) Express the magnitude of the gravitational force F in terms of M, R, the gravitational constant G, and the mass m of the satellite.

Part (b) Express the magnitude of the centripetal acceleration a, of the satellite in terms of the speed of the satellite v, and R.

Part (c) Express the speed v in terms of G, M and R.

Part (d) Calculate the numerical value of v, in m/s.

ceruleanwolf844

1. The escape speed Vis the minimum speed needed to project a mass m upward from thesurface of another
mass M (such as a planet, asteroid, or star). It is given byusing:

M = 1.99 Ã 10³⁰ kg ,

G= gravitational constant 6.67 x10^-11 N*m2/kg2

R = 6.96 Ã 10⁸m. is the radius of thesurface from the center of M

v=â2GM ====>>>>>> v= 6.1758 x10⁵ m/s

R
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