Question

# Calculate the amount of energy required to escape from the surface of the following bodies, relative...

Calculate the amount of energy required to escape from the surface of the following bodies, relative to that required to escape from the surface of Earth.

a. Uranus_____________x engery to escape earth = 3.65

b. Saturn____________x energy to escape earth....

I cannot find Saturns

From the Planetary fact sheet, mass of the Earth me = 5.97 x 1024 kg, mass of the Uranus mu = 86.8 x 1024 kg, mass of the Saturn ms = 568 x 1024 kg and the escape velocities are ve = 11.2 km/s, vu = 21.3 km/s and vs = 35.5 km/s.

The energy is required to escape from the planet must be equal to the kinetic energy due to planet's escape velocity, that means, kinetic energy K = mvesc2 / 2.

(a) For Unrnus relative to that required to escape from the earth,

Ku/Ke = (mvu2 / 2) / (mve2 / 2) = (vu/ve)2 = (21.3 km s-1/11.2 km.s-1)2 = 3.62.

(b) For Saturn,

Ks/Ke = (vs/ve)2 = (35.5 km.s-1/11.2 km.s-1)2 = 10.04.

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