# Escape velocity problem

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1. May 6, 2015

### 15ongm

1. Problem
A rocket has landed on Planet X, which has half the radius of Earth. An astronaut onboard the rocket weighs twice as much on Planet X as on Earth. If the escape velocity for the rocket taking off from Earth is v , then its escape velocity on Planet X is

a) 2 v
b) (√2)v
c) v
d) v/2
e) v/4

I reasoned out this problem mathematically, but what is the conceptual reasoning behind this?

2. May 6, 2015

### PeroK

I would say this is a mathematical question. To see it more clearly, you could try to derive a formula for escape velocity in terms of the radius $R$ and the surface gravity $g$ of a planet.

3. May 7, 2015

### BvU

Conceptually you are supposed to quickly approach this from the other end: ${\tfrac 1 2}mv_{esc}^2$ is the kinetic energy needed to overcome the gravitational potential energy. I expect you know how to write the latter as $GM_{planet}\over R_{planet}$. To see how this ratio relates to idem earth you need Mplanet/Mearth. That follows from the factor 2 in g and the expression for g PeroK is asking for