Question

Planet Z is 7000 km in diameter. The free-fall acceleration on Planet Z is 7.0 m/s2.

What is the mass of Planet Z?

What is the free-fall acceleration 1.0×104 km above Planet Z's north pole?

Answer 1

here,

diameter , D = 7000 km

radius , r = D/2 = 3500 km = 3.5 * 10^6 m

let the mass of planet be M

The free-fall acceleration , g = G * M /r^2

7 = 6.67 * 10^-11 * M /( 3.5* 10^6)^2

solving for M

M = 1.3 * 10^24 kg

the mass of planet is 1.3 * 10^24 kg

the free-fall acceleration 1.0 * 10^4 km above Planet Z's north pole , g' = G * M /( r + 1 * 10^7)^2

g' = 6.67 * 10^-11 * 1.3 * 10^24 /( 3.5 * 10^6 + 1 * 10^7)^2 m/s^2

g' = 0.47 m/s^2

the free-fall acceleration 1.0 * 10^4 km above Planet Z's north pole is 0.47 m/s^2