What is the gravitational force acting on a 10 kg object on the surface of a pla

Question

What is the gravitational force acting on a 10 kg object on the surface of a planet that has eight times the Earth's mass and twice the Earth's radius? What is "g" for the surface of this planet? 3. a. Mars has a mass of 6.42 times 1023 kg and has a moon Phobos with an orbital radius of 9380 km. What is the period of Phobos as it orbits Mars? b. Phobos has a mass of 1.07 tims 1016 kg. If an astronaut were to land on Phobos, what gravitational field strength would they experience? (Phobos is irregularly shaped but has an approximate radius of 1.11timesl04m.)

Explanation / Answer

2 -

Mass M = 10 kg

Mp is the mass of the planet

Me is the mass of Earth

Mp = 8 Me

Rp is the radius of the planet

Re is the radius of earth

Rp= 2 Re

Force on 10 kg mass on the planet

F = m*gp

F = m (GMp/Rp2)

F = m G (8 Me)/(2 Re)2

F = (2m)GMe/Re2

F = 2x10 (9.8)

F = 196 N

(b)

gp = GMp/Rp2

gp = G(8Me)/(2Rp)2

gp = 2G(Me)/(Re)2

gp = 2(9.8)

gp = 19.6 m/s2

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