Question

Approximate the gravitational force exerted on the moon by the earth and the sun. A) during a solar eclipse and B) during a lunar eclipse. Given the mass of sun = 2 x 10³⁰ kg mass of earth 6 x 10²⁴ kg mass of the moon 7.4 x 10²² kg radius of earth's orbit around the sun 1.5 x 10¹¹ m and radius of moon's orbit around the earth 3.8 x 10⁸ m.

Answer 1

Using the given data,

Gravitational force on moon due to earth is,

F_me = (6.67×10^-11) ×(5.98×10²⁴) ×(7.36×10²²)/(3.8×10⁸)²

=> F_me = 2.03 × 10²⁰ N

Gravitational force on moon due to sun is,

F_ms = (6.67×10^-11) ×(1.99×10³⁰) ×(7.36×10²²)/(3.8×10⁸ + 1.49×10¹¹)²

=> F_ms = 4.38 × 10²⁰ N

So, the net gravitational force on moon is,

(a) During solar ecilpse ;

$F_{net}=F_{ms}-F_{me}$

$F_{net}=2.35\times {10}^{20}N$

(b) During lunar ecilpse

$F_{net}=F_{ms}+F_{me}$

$F_{net}=6.41\times {10}^{20}N$