To make things convenient, lets express things in terms of the average density of the material in the asteroid, call it 'Rho'. Now, density times volume equals mass, and if we approximate the asteroid as a sphere with a radius R, then:
4 3
M = --- pi x R x Rho
3
The escape velocity from a body of mass, M, and radius, R, is just,
1/2
V(escape) = (2 G M/R)
or
1/2
V(escape) = ( 8 pi G Rho / 3 ) x R
so that for an asteroid like Ceres with the constant of gravity equal to G =
6.6 x 10^-8 dynes cm^2/gm^2 ;
R = 380 kilometers, and Rho = 3 gm/cc, you get an escape velocity
of about 490 meters/sec. Now, you can probably jump 3 feet in one second
which is 100 centimeters/sec; so on Ceres you would not go into orbit.
On the asteroid Eros, R = 7 kilometers and V(escape) = 9 meters/sec which
is a little bit better; finally asteroid Apollo has a radius of
0.5 kilometers, so its escape velocity is about 0.6 meters/sec. I would say
that any asteroid with a size less than 1 kilometer would be a good candidate
for jumping into orbit. Of course, you would have to jump in just the right
direction!
Copyright 1997 Dr. Sten Odenwald Return to Ask the Astronomer.