Question

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

Answer 1

Answer:

From the Planetary fact sheet, mass of the Earth m_e = 5.97 x 10²⁴ kg, mass of the Uranus m_u = 86.8 x 10²⁴ kg, mass of the Saturn m_s = 568 x 10²⁴ kg and the escape velocities are v_e = 11.2 km/s, v_u = 21.3 km/s and v_s = 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 = mv_esc² / 2.

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

    K_u/K_e = (mv_u² / 2) / (mv_e² / 2) = (v_u/v_e)² = (21.3 km s^-1/11.2 km.s^-1)² = 3.62.

(b) For Saturn,

   K_s/K_e = (v_s/v_e)² = (35.5 km.s^-1/11.2 km.s^-1)² = 10.04.

answered by: anonymous