Question

Consider a spherical, homogeneous planet with a radius of rp=3985 km and a mass of mp=8.97×1024 kg. A spherical object with a radius of r0=9.21 m and mass m0=868 kg approaches the planet.

Part 1) When the object is 5.33×109 km away from the planet, what is the magnitude of the force the planet exerts on the object? F= N

Part 2) When the object is 8.10 m above the surface of the planet, what is the magnitude of the gravitational force of the planet on the object? F= N

Part 3) What is the acceleration due to gravity on objects close to the surface of this planet? g= m s?2

Answer 1

Given  

mass of planet is mp = 8.97*10^24 kg

radius of planet is rp = 3985000 m

mass of object mo = 868 kg, radius is ro = 9.21 m

Part 1

the distance from object to the planet is r = 5.33*10^12 m

From F = G*m1*m2/r^2

F = 6.674*10^-11*8.97*10^24*868/(5.33*10^12)^2N

F = 1.829127387544*10^-8 N

Part2

if r = 8.10+3985000 +9.21 m

F = 6.674*10^-11*8.97*10^24*868/(8.10+3985000 +9.21)^2 N

F = 32721.8573 N

Part3

F = mg

g = F/m

g = 32721.8573/868 m/s2

g = 37.7 m/s2