Question

1. During a solar eclipse, the Moon, Earth, and Sun all lie on the same line, with the Moon between the Earth and the Sun.

(a) What force is exerted by the Sun on the Moon?
_____ N

(b) What force is exerted by the Earth on the Moon?
_____N

(c) What force is exerted by the Sun on the Earth?
_____N

2. An artificial satellite circles the Earth in a circular orbit at a location where the acceleration due to gravity is 5.29 m/s². Determine the orbital period of the satellite.

_____min

Answer 1

We have

Earth to Sun distance = (1.496x10¹¹m)

Earth to Moon distance = (3.84x10⁸m)

Moon to Sun distance = 1.496x10¹¹m - 3.84x10⁸m = (1.49216x10¹¹m)

Mass of Earth = (5.98x10²⁴kg)

Mass of Moon = (7.36x10²²kg)

Mass of Sun = (1.991x10³⁰kg)

G = Universal Gravitational Constant = (6.673x10^-11N-m²/kg²)

Solution :-

(a)

F_SonM = GM_sM_m/r²

F_SonM = (6.673x10^-11N-m²/kg²)(1.991x10³⁰kg)(7.36x10²²kg) / (1.49216x10¹¹m)²

F_SonM = 43.91768219x10¹⁹ N

F_SonM = 4.39x10²⁰ Newtons (Toward the Sun)

(b)

F_EonM = GM_sM_m/r²

F_EonM = (6.673x10^-11N-m²/kg²) (5.98x10²⁴kg)(7.36x10²²kg)/(3.84x10⁸m)²

F_EonM = 19.917630649x10¹⁹ N

F_EonM = 1.99x10²⁰ Newtons (Toward the Earth)

(c)

F_SonE = GM_sM_m/r²

F_SonE = (6.673x10^-11N-m²/kg²)(5.98x10²⁴kg)(1.991x10³⁰kg) / 1.496x10¹¹m)²

F_SonE = 35.50016583x10²¹ N

F_SonE = 3.55x10²² Newtons (Toward the Sun)

2)