According to Newton's Law of Gravity, what is the magnitude of the net gravitational force exerted on the Moon by the Earth, given that the mass of the Earth is 5.97 × 10^24 kg, the mass of the Moon is 7.35 × 10^22 kg, and the average distance between the Earth and the Moon is 3.84 × 10^8 meters?

• A. 3.54 × 10^22 N
• B. 5.97 × 10^21 N
• C. 1.98 × 10^20 N
• D. 7.35 × 10^19 N

Answer: (C)

Verified step by step guidance

1. Identify the formula for gravitational force: Newton's Law of Universal Gravitation is given by the formula: $F=\frac{GmM}{r^2}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $m$ and $M$ are the masses of the two objects, and $r$ is the distance between the centers of the two objects.
2. Substitute the known values into the formula: Use the given values for the mass of the Earth $M=\; 5.97\; imes\; 10^\{24\}\; ext\{\; kg\}$, the mass of the Moon $m=\; 7.35\; imes\; 10^\{22\}\; ext\{\; kg\}$, and the distance between them $r=\; 3.84\; imes\; 10^\{8\}\; ext\{\; m\}$.
3. Use the gravitational constant: The gravitational constant $G=\; 6.674\; imes\; 10^\{-11\}\; ext\{\; N\; m\}^2/\; ext\{kg\}^2$ is a universal constant that you will use in the calculation.
4. Calculate the gravitational force: Plug the values into the formula: $F=\frac{\mathrm{6.674\; imes\; 10^\{-11\}}\times \mathrm{5.97\; imes\; 10^\{24\}}\times \mathrm{7.35\; imes\; 10^\{22\}}}{{\mathrm{3.84\; imes\; 10^\{8\}}}^2}$.
5. Simplify the expression: Perform the arithmetic operations to simplify the expression and find the magnitude of the gravitational force. This will give you the net gravitational force exerted on the Moon by the Earth.