Question

During a solar eclipse the Moon is positioned directly between Earth and the Sun.

Find the magnitude of the net gravitational force acting on the Moon then, due to both Earth and the Sun.

The masses of the Sun, Earth, and the Moon are 1.99 Ý 1030 kg, 5.98 Ý 1024 kg, and 7.36 Ý 1022 kg, respectively.
The Moon\'s mean distance from Earth is 3.84 Ý 108 m, and Earth\'s mean distance from the Sun is 1.50 Ý 1011 m.
The gravitational constant is G = 6.67 Ý 10-11 Nm2/kg2.

Answer 1

Ft = - 23.99 10₁₉₉9 N

Step-by-step explanation:

In this exercise we will use the law of universal gravitation

F = G m₁ M₂ / r²

With Newton's second law we get

Ft = F1 - F2

Where F1 is the force of attraction between the moon and the Earth

F1 = G m₁ M₂ / r²

F1 = 6.67 10⁻¹¹ 7.36 10²² 5.98 10²⁴ /(3.84 10⁸)²

F1 = 19,909 10¹⁹ N

Let's calculate the force of attraction between the Sun and the moon (F2)

The distance from the sun to the moon is the distance from the sun to the Earth minus the distance from the earth to the moon

R = 1,496 10¹¹ - 3.84 10⁸ = (1496 - 3.84) 10⁸ m

R = 1492.2 108 m

F2 = 6.67 10⁻¹¹ 7.36 10²² 1,991 10³⁰ /(1492.2 10⁸)²

F2 = 4.3896 10²⁰

Ft = 19,902 10¹⁹ - 43,896 10¹⁹

Ft = - 23.99 10₁₉₉9 N

The negative sign indicates that the force is directed towards the sun