# Density of Asteroids, Escape Velcoity and Jumping

1. Feb 7, 2008

### TFM

[SOLVED] Density of Asteroids, Escape Velcoity and Jumping

1. The problem statement, all variables and given/known data

The question wants to know the maximum radius of an asteroid that you can escape from by simply jumpibng off.

The Variables given:
densities = 2500 kg/m cubed
height of jump = 1m

2. Relevant equations

v(Escape) = sqrt(GM/r)
m = d/r cubed
V squared = U squared + 2as (for initial jump speed)

3. The attempt at a solution
using a = 9.8 and s = 1, I calculated the initial jump speed is 4.43
rearranging the equation for EScape Velocity:
v(escape) = sqrt[(G(d/r cubed))/r]
v sqyared = (G(d/r cubed))/r
v squared = GD/r squared
r squared = Gd/v sqyared
r = sqrt [GD/v squared]

but this isn't giving me the right answer?

2. Feb 7, 2008

### kamerling

This isn't right. mass is density * volume. and the volume of a sphere is?

Last edited: Feb 7, 2008
3. Feb 7, 2008

### Shooting Star

HI TFM,

It's given that you can jump 1 m on earth. Using that, find the speed you can generate at the start of the jump. Then apply that speed for v_escape to find r. All other data are given.

4. Feb 7, 2008

### TFM

The question assumes the asteroids are speherically symmetrical - which is why I should use the volume of a sphere, 4/3 Pi r cubed.

i.e:

(escape) = sqrt[(G(d/(4/3) pi r cubed))/r]

TFM

5. Feb 7, 2008

### Shooting Star

Yes, spherically symmetrical and of uniform density. However, the following formula you've written is not correct.

>
2. Relevant equations

v(Escape) = sqrt(GM/r)

>

6. Feb 7, 2008

### TFM

I've just checked -its sqrt[(2GM)/r]

this all gives:

R squared = (3*V escape squared)/(8*G*density*pi)

TFM

Last edited: Feb 7, 2008
7. Feb 8, 2008

### TFM

I have now got the (right) answer of 3.7km (using a 10^-3 conversion factor)

Thanks all,

TFM