**AP Physics 1 Question 65: Answer and Explanation**

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**Question: 65**

**5.**

A moon has an elliptical orbit about the planet as shown above. At point A, the moon has speed v_{A} and is at a distance r_{A} from the planet. At point B, the moon has a speed of v_{B}. Which of the following correctly explains the method for determining the distance of the moon from the planet at point B in the given quantities?

- A. Conservation of angular momentum, because the gravitational force exerted by the moon on the planet is the same as that exerted by the planet on the moon
- B. Conservation of angular momentum, because the gravitational force exerted on the moon is always directed toward the planet
- C. Conservation of energy, because the gravitational force exerted on the moon is always directed toward the planet
- D. Conservation of energy, because the gravitational force exerted by the moon on the planet is the same as that exerted by the planet on the moon

**Correct Answer:** A

**Explanation:**

A By Newton's Third Law, the gravitational force exerted by the planet on the moon will equal the gravitational force exerted by the moon on the planet (eliminate (B) and (C)). Between Conservation of Angular Momentum and Conservation of Energy, the correct one to use to help us find distance is Conservation of Angular Momentum. Conservation of Energy will help us find the speed of the moon. Conservation of Angular Momentum will help us find the distance of the moon from the planet.