Jupiter has a mass of 1.9 × 1027 kg, and its moon Europa has a mass of 4.8 × 1022 kg. Their centers are separated by a distance of 670,900 km.

Question

a. What is the force of gravity acting on Europa?

b. What is the acceleration of Jupiter due to the force of gravity between it and Europa?

c. Europa has a radius of 1569 km. What is the acceleration of gravity on the surface of Europa?

d. You drop a rock from a height of 20 m on Europa. How long does it take the rock to reach the surface?

Answer 1

a)

Where G = 6.674 x 10^-11 Nm²/kg², M = 1.9 x 10²⁷ kg, m = 4.8 x 10²² kg, and r = 670,900 x 10³ meters = 6.709 x 10⁸ m so:

F = (6.674 x 10^-11)(1.9 x 10²⁷)(4.8 x 10²²)/(6.709 x 10⁸)²

F= 1.4 x 10²² N

b) Since F = ma, a = F/m = (1.4 x 10²²)/1.9 x 10²⁷) = 7.1 x 10^-6 m/s²

c)

F = ma

F = mg

GMm/r² = mg

GMm/mr² = g

GM/r² = g = (6.674x10^-11)(4.8 x 10²²)/(1569000)² = 1,3 m/s²

d)

x = 1/2gt²

t = √(2x/g) = √(2•20/1.3) = 5.5 seconds