Question

1. Calculate the magnitude of the gravitational force between the Earth and an m = 5.50 kg mass on the surface of the Earth. The distance to the center of the Earth from the surface is 6.37×103 km and the mass of the Earth is 5.98×1024 kg.
2. Calculate the magnitude of the gravitational force between the Moon and an m = 5.50 kg mass on the surface of the Earth nearest to the moon. The distance to the center of the Moon from the surface of the Earth is 3.76×105 km and the mass of the Moon is 7.36×1022 kg.
3. Calculate the ratio of the magnitude of the gravitational force between an m = 5.50 kg mass on the surface of the Earth due to the Sun to that due to the Moon. The mass of the Sun is 1.99×1030 kg and the distance from the center of the Sun to the surface of the Earth is 1.50×108 km.

Answer 1

1. The magnitude of the gravitational force between the Earth and an m is  54.1 N.

2. The magnitude of the gravitational force between the Moon and an m is  1.91 x 10⁻⁴ N.

3. The ratio of the magnitude of the gravitational force between an m on the surface of the Earth due to the Sun to that due to the Moon is 169.6.

Gravitational force between Earth and mass, m

The gravitational force between Earth and mass, m is calculated as follows;

F(Earth) = Gm₁m₂/R²

F(Earth) = (6.67 x 10⁻¹¹ x 5.5 x 5.98 x 10²⁴)/(6,370,000)²

F(Earth) = 54.1 N

Gravitational force between Moon and mass, m

F(moon) = Gm₁m₂/R²

F(moon) = (6.67 x 10⁻¹¹ x 5.5 x 7.36x 10²²)/(3.76 x 10⁸)²

F(moon) = 1.91 x 10⁻⁴ N

Gravitational force between Sun and mass, m

F(sun) = Gm₁m₂/R²

F(sun) = (6.67 x 10⁻¹¹ x 5.5 x 1.99x 10³⁰)/(1.5 x 10¹¹)²

F(sun) = 0.0324 N

Ratio of F(sun) to F(moon)

= 0.0324/1.91 x 10⁻⁴

= 169.6

Thus, the magnitude of the gravitational force between the Earth and an m is  54.1 N.

The magnitude of the gravitational force between the Moon and an m is  1.91 x 10⁻⁴ N.

The ratio of the magnitude of the gravitational force between an m on the surface of the Earth due to the Sun to that due to the Moon is 169.6.

Learn  more about gravitational force here: brainly.com/question/72250

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