I wonder what density the material would have to be to be something that could keep you planted.
It's not too hard to get an approximate idea.
We know astronauts in lunar 1/6th g can hop around. Let's just assume you could shuffle along at 1/20th of a G.
So our theoretical asteroid would need it's acceleration due to gravity to be about ~
Ga = 1/20 x 9.8m/s^2
Ga~ 0.5m/s^2
Force on a 300lbs astronaut + gear =
F = mass of astronaut and suit x Ga
F ~ 70N
Newtons laws of Gravitation gives the force between two masses as
F= G(m1xma)/r^2
r = 2000ft ( distance from the center of mass of our asteroid to the center of our astronaut - we'll ignore the extra 3 ft to his center)
m1 = 300lbs
ma = mass of the asteroid
G = the
gravitational constant (6.674×10−11 N
· (m/kg)2)
F= 70N
ma = 2.86x10^15 kg
Now we divide by the volume of the asteroid. We'll assume a sphere with a 2000ft radius.
Va = 4/3 Pi r^2
Va ~.95km^3
Density of our asteroid = ma/va
Density = 3.0x10^6 kg/m^3
Osmium is the densest element at 22,600 (2.26x10^4) kg/m^3
So our asteroid would need to be 100x denser than that.
Wolfram Alpha puts it at
- 20x denser than the a solar core
- 3% as dense as white dwarf.