Escape velocity from asteroid

Homework Statement

We assume an asteroid with density similar to earth. An astronaut performs a spot jump of 1 meter. Which is the maximum radius of the asteroid in order to escape the astronaut from the asteroid?

Homework Equations

Vesc=√2GM/R=R√8ΠGρ/3

The Attempt at a Solution

Vesc,earth/Vesc,ast=Rearth/Rast→ Rast=Rearth Vesc,ast/Vesc,earth
So the values of Rearth and Vesc,earth are known i need one more equation in order to calculate Vesc,ast which will be the minimum velocity that is necessary to reach 1 meter above the ground. So i am stuck!!!

The Attempt at a Solution

Andrew Mason
Homework Helper
I am having difficulty understanding how a person doing a jump of only 1 m. from the asteroid can possibly escape. Can you give us the exact wording of the question?

AM

Also for me is difficult. But as i can understand speaking for an imaginary asteroid we try to find the necessary radius for which the escape velocity is equal with the begging velocity that we need for a jump of 1 meter (according to the energy conservation: v0=√2gh).

Redbelly98
Staff Emeritus
Homework Helper
I suspect the wording of the question is different than what is posted here. Are you translating from a language other than English?

A velocity that results in a jump of 1 meter height can never be equal to the escape velocity, which produces a jump of infinite height. This is a simple logical fact. Perhaps you mean the velocity that would produce a 1 m jump height under different conditions -- but we need to know what those conditions are.

p.s. Welcome to Physics Forums.

Andrew Mason