Question

What is the largest moon (or asteroid) that we can jump off?

Express the escape speed in terms of a density instead of a mass. Then use your estimates above to estimate the largest radius (in km) we could jump off of.

(All numbers must be entered as, say, 5000 or 5e3 or 5.0e3 and not with commas as in "5,000"

All numbers must be entered as, say, 5000 or 5e3 or 5.0e3 and not with commas as in "5,000" and not as fractions as in "3/4".)

Answer 1

let the density of the asteroid be rho, and radius be R
and mass of person is M
then
mass of asteroid is m = 4*rho*pi*R^3/3

now, let escape velcity = V
then from conservation of energy

0.5MV^2 = GMm/R
V = sqrt(2Gm/R) = 2R*sqrt(2*rho*G*pi/3)

now, density, lets take it to be 3000 kg/m^3
then
V = 0.00129474*R

now, just by jumping, on earth humans can reach an average height 20 cm
hence
0.5MV^2 = Mg*0.2
V = sqrt(0.4g) = 1.980908882 m/s
hence, R = 1529.96654 m

largest averavge density asteroid from which an average human can jump off has a radius of 1.529 km