Question

A certain planet has an escape speed V. If another planet has twice size and twice the mass of the first planet, its escape speed will be

Answer 1

Answer:

Explanation:

Given:

M₂ = 2 × M₁

R₂ = 2 × R₁

Escape velocity, V = √2GM/R

Let V₁ and V₂ be the escape velocity of the first and second planet respectively.

V₁ = √2GM₁/R₁

V₂ = √2GM₂/R₂

Equating V₁ and V₂, we have:

(V₁)^2 × R₁ /(2 × M₁) = (V₂)^2 × M₂/(2 × R₂)

(V₁)^2 × R₁ /(2 × M₁) = (V₂)^2 × 2 × R₁ /(2 × 2 × M₁)

(V₁)^2 = (V₂)^2 × (2 × M₁)/R₁ × 2 × R₁/(4 × M₁)

(V₁)^2 = (V₂)^2

V₁ = V₂

Answer 2

Answer:

The escape speed on the other planet is V

Explanation:

Escape velocity V = √2GM/R where M = mass of planet and R = radius of planet. G = gravitational constant

Let  V₁ and V₂ be the escape speeds on planet one and two respectively.

if V₁ = √2GM₁/R₁ and V₂ = √2GM₂/R₂ and M₂ = 2M₁ and R₂ = 2R₁ (since it is twice the size of the first planet)

V₂ = √2GM₂/R₂ = V₂ = √(2G × 2M₁/2R₁) = √2GM₁/R₁ = V₁ = V

So the escape speed on the other planet is V