Question

The escape velocity of a bullet from the surface of planet Y is 1599.0 m/s. Calculate the escape velocity from the surface of the planet X if the mass of planet X is 1.33 times that of Y, and its radius is 0.887 times the radius of Y.

Answer 1

For a spherically symmetric, massive body such as planet, the escape velocity for that body, at a given distance, is calculated by the formula.

      where    G is the universal gravitational constant (G ≈ 6.67×10⁻¹¹ m³·kg⁻¹·s⁻²).

M the mass of the body to be escaped.

r the distance from the center of mass of the body to the object.

For plant Y escape velocity is 1599.0 m/s that is

      ------------------------------------------------------(1)

let V_x is escape velocity for planet X, given by

   --------------------------------------(2)

As given mass of planet X is 1.33 times that of Y, and its radius is 0.887 times the radius of Y. Now divide equation (2) by (1) we get

V_X/1599 =

V_X = 1599*1.2245 = 1958 m/s

escape velocity from the surface of the planet X is 1958 m/s