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Chapter 4: Problem 26

Suppose that the Earth were moved to a distance of \(3.0 \mathrm{AU}\) from the Sun. How much stronger or weaker would the Sun's gravitational pull be on the Earth? Explain.

Short Answer

Expert verified
The Sun's gravitational pull on Earth would be \(1/9\) times as strong if the Earth were moved to a distance of 3 AU from the Sun.

Step by step solution

01

Understand the Given Information

It is stated in the exercise that the Earth is moved to a distance of 3 AU from the Sun. 1 AU is the average distance from the Sun to the Earth, so 3 AU is three times the average Earth-Sun distance.
02

Apply Newton's Law of Universal Gravitation

According to Newton's Law of Universal Gravitation, the force between two objects is inversely proportional to the square of the distance between them. Therefore, if the distance increases by a factor of 3, the force decreases by a factor of \(3^2\) or 9.
03

Calculate the Change in Gravitational Force

Since the Earth is moved to 3 AU, the distance is three times greater. Therefore, the gravitational force is \(1/9\) as strong as it was at 1 AU.

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