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

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