The drawing (not to scale) shows one alignment of the sun, earth, and moon. the gravitational force vector f sm that the sun exerts on the moon is perpendicular to the force vector f em that the earth exerts on the moon. the masses are: mass of sun = 1.99 1030 kg, mass of earth = 5.98 1024 kg, mass of moon = 7.35 1022 kg. the distances shown in the drawing are rsm = 1.5 1011 m and rem = 3.85 108 m. determine the magnitude of the net gravitational force on the moon.

Solution:

Ms = 1.99 × 1030 kg− mass of Sun;

Me = 5.98 × 1024kg− mass of Earth;

Mm = 7.35 × 1022kg − mass of Moon;

rSM = 1.50 × 1011m − distance to the Moon from the Sun;

rEM = 3.85 × 108m − distance to the Moon from the Earth;

The gravitational force that acts on the Moon by the Earth (Law of Gravity):

The gravitational force that acts on the Moon by the Sun (Law of Gravity):

Net gravitational force on the moon:

Pythagorean theorem for a right triangle ABC:

magnitude of the net gravitational force on the moon is 4.77 × N.

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