Chapter 3: Problem 25

The mass of the Moon is \(7.35 \times 10^{22} \mathrm{kg}\), while that of Earth is \(5.98 \times 10^{24} \mathrm{kg} .\) The average distance from the center of the Moon to the center of Earth is \(384,400 \mathrm{km} .\) What is the size of the gravitational force that Earth exerts on the Moon?

Short Answer

Expert verified

Answer: The approximate gravitational force between Earth and the Moon is \(1.982 \times 10^{20} \mathrm{N}\).

Step by step solution

Get the Given Values

We are given the mass of the Moon (m1) as \(7.35 \times 10^{22} \mathrm{kg}\), the mass of Earth (m2) as \(5.98 \times 10^{24} \mathrm{kg}\), and the distance (r) as \(384,400 \mathrm{km}\). Keep in mind that we need to convert the distance to meters before proceeding with the calculations.

Convert Distance to Meters

To convert the distance from kilometers to meters, we can multiply by 1,000: \((384,400 \mathrm{km}) * (1,000 \mathrm{m/km}) = 3.844 \times 10^{8} \mathrm{m}\).

Write Down the Universal Gravitational Constant

The universal gravitational constant (G) is a constant value, which is approximately \(6.674 \times 10^{-11} \mathrm{N (m/kg)^{2}}\).

Calculate the Gravitational Force

Use the universal law of gravitation to find the gravitational force (F): F = G * (m1*m2) / r^2 Plug in the given values and the constant G: F = (\(6.674 \times 10^{-11} \mathrm{N (m/kg)^{2}}\)) * ((\(7.35 \times 10^{22} \mathrm{kg}\)) * (\(5.98 \times 10^{24} \mathrm{kg}\))) / (\((3.844 \times 10^{8} \mathrm{m})^2\)) Now, perform the multiplication and division for the final answer.

Compute the Final Answer

After performing the given calculation, we obtain the gravitational force (F) between Earth and the Moon as approximately \(1.982 \times 10^{20} \mathrm{N}\). The size of the gravitational force that Earth exerts on the Moon is approximately \(1.982 \times 10^{20} \mathrm{N}\).

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The mass of the Moon is \(7.35 \times 10^{22} \mathrm{kg}\), while that of Earth is \(5.98 \times 10^{24} \mathrm{kg} .\) The average distance from the center of the Moon to the center of Earth is \(384,400 \mathrm{km} .\) What is the size of the gravitational force that Earth exerts on the Moon?

Short Answer

Step by step solution

Get the Given Values

Convert Distance to Meters

Write Down the Universal Gravitational Constant

Calculate the Gravitational Force

Compute the Final Answer

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