Question

At what point between Earth and the Moon will a 5.00 × 10⁴ kg space probe experience no net gravitational force?

Answer 1

let m = 5.00*10^4 kg

M_earth = 5.97*10^24 kg

M_moon = 7.35*10^22 kg

distance between the moon and the earth, r = 3.844*10^8 m

let at x distance from Earth the space probe experience no force.

use, Force eaxrted by earth on space probe = force exerted by the moon space probe.

G*M_earth*m/x^2 = G*M_moon*m/(r - x)^2

M_earth/x^2 = M_moon/(r - x)^2

(r - x)^2/x^2 = M_moon/M_earth

(r - x)/x = sqrt(M_moon/M_earth )

= sqrt(7.35*10^22/(5.97*10^24))

r - x = x*0.11096

r = 1.11096*x

==> x = r/1.11096

= 3.84*10^8/(1.11096)

= 3.456*10^8 m from the Earth <<<<<<<<<<-----------------Answer