Question

1. calculate the force that the moon exerts on the earth. here are some data that might be useful:

• massmoon = 7.3 × 10²² kg
• radiusmoon = 1.74 × 10⁶ m
• massearth = 6.0 × 10²⁴ kg
• radiusearth = 6.4 × 10⁶ m
• g = 6.67 × 10⁻¹¹ nm²

kg²

• orbital radiusmoon = 3.8 · 10⁸ m

Explanation:

Step1: Write the formula for gravitational force

According to Newton's law of universal gravitation, the formula is \( F = G\frac{M_{Earth}M_{Moon}}{r_{moon}^2} \), where \( G = 6.67\times10^{- 11}\frac{Nm^{2}}{kg^{2}}\), \(M_{Earth}=6.0\times10^{24}kg\), \(M_{Moon}=7.3\times10^{22}kg\), and \(r_{moon}=3.8\times10^{8}m\)

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step3: Calculate the coefficient and the power of 10 separately

First, calculate the coefficient: \(\frac{43.8}{14.44}\approx3.03\)
Then, for the power of 10: \(10^{-11}\times10^{30}=10^{-11 + 30}=10^{19}\)
So \(F\approx6.67\times3.03\times10^{19}\)

Step4: Calculate the final result

\(6.67\times3.03\approx20.2\)
So \(F\approx2.02\times10^{20}N\)

Answer:

\(2.02\times 10^{20}N\)