Question

What is the distance from the center of the Moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is 5.97 × 1024 kg, the mass of the Moon is 7.35 × 1022 kg, the center-to-center distance between Earth and the Moon is 3.84 × 108 m, and G = 6.67 × 10-11 N ∙ m2/kg2.

Answer 1

Answer:

$r = 3.84 \times 10^7 m$

Explanation:

Let say the distance at which gravitational force due to both Earth and moon is zero is given by force force balance

so it is given as

$F_{moon} = F_{Earth}$

$\frac{GM_{moon}}{r^2} = \frac{GM_{earth}}{(d - r)^2}$

so we have

$\frac{M_{moon}}{r^2} = \frac{M_{earth}}{(d - r)^2}$

$\frac{7.35 \times 10^{22}}{r^2} = \frac{5.97 \times 10^{24}}{(3.84 \times 10^8 - r)^2}$

now we have

$\frac{2.71}{r} = \frac{24.4}{3.84\times 10^8 - r}$

$10.4 \times 10^8 - 2.71 r = 24.4 r$

now we have

$r = 3.84 \times 10^7 m$