Question

1. calculate the force that the earth exerts on the moon. 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

useful data

Explanation:

Step1: Write the formula for gravitational force

The formula for the gravitational force \( F \) between two objects is \( F = G\frac{M_1M_2}{r^{2}} \), where \( G\) is the gravitational constant, \( M_1\) and \( M_2\) are the masses of the two objects, and \( r\) is the distance between their centers.
Here, \( M_1 = M_{Earth}=6.0\times 10^{24}\text{ kg}\), \( M_2 = M_{Moon}=7.3\times 10^{22}\text{ kg}\), \( r = r_{moon}=3.8\times 10^{8}\text{ m}\), and \( G = 6.67\times 10^{-11}\frac{\text{Nm}^2}{\text{kg}^2}\)

Step2: Substitute the values into the formula

$$
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$$

Step3: Calculate the numerical coefficient and the exponent of 10

\(\frac{43.8}{14.44}\approx3.03\)

$$
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$$

Answer:

\(2.0\times 10^{20}\text{ N}\) (rounded to one significant figure considering the significant figures of the given data)