**Problem: Satellite Orbital Period**1. A satellite of mass \( M \) moves around the Earth in a circular orbit of radius \( R \). The orbital period of the satellite is \( T \). A second satellite of mass \( 3M \) is also moving around the Earth in a circular orbit of radius \( R \). The orbital period of the second satellite is: (a) \( 3T \) (b) \( T/3 \) (c) \( T \) (d) \( 9T \) (e) \( T/9 \) ---#### Explanation:This problem involves an understanding of satellite motion, specifically the relationship between the mass of a satellite, its orbital radius, and its orbital period. The key concept to recall here is Kepler's third law which enables us to relate these aspects.**Concept:**Kepler's third law states that the orbital period \( T \) of a satellite around a planet is related to the radius \( R \) of its orbit by the equation:\[ T^2 \propto R^3 \]Interestingly, the orbital period is independent of the mass of the satellite. Therefore, the orbital periods of satellites in the same orbit (with the same radius \( R \)) remain the same regardless of their masses.**Given:**- First satellite has mass \( M \)- Orbital radius \( R \)- Orbital period \( T \)- Second satellite has mass \( 3M \)- Orbital radius \( R \)**Solution:**Since the orbital period \( T \) only depends on the radius \( R \) according to Kepler's third law, the orbital period of the second satellite will also be \( T \).**Answer: (c) \( T \)**This explanation and step-by-step approach help students to understand that the mass of the satellite does not affect the orbital period for a given orbital radius.

Answered: Image /qna-images/answer/d0242c11-8f15-49bb-9269-d420a06a7107.jpg

1. A satellite of mass M moves around the Earth in a circular orbit of radius R. The orbital period of the satellite is T. A second satellite of mass 3M is also moving around the Earth in a circular orbit of radius R. The orbital period of the second satellite is (a) 3T (b) T/3 (c) T (d) 97 (e) T/9

1. A satellite of mass M moves around the Earth in a circular orbit of radius R. The orbital period of the satellite is T. A second satellite of mass 3M is also moving around the Earth in a circular orbit of radius R. The orbital period of the second satellite is (a) 3T (b) T/3 (c) T (d) 97 (e) T/9

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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Question

**Problem: Satellite Orbital Period**

1. A satellite of mass \( M \) moves around the Earth in a circular orbit of radius \( R \). The orbital period of the satellite is \( T \). A second satellite of mass \( 3M \) is also moving around the Earth in a circular orbit of radius \( R \). The orbital period of the second satellite is:

(a) \( 3T \)
(b) \( T/3 \)
(c) \( T \)
(d) \( 9T \)
(e) \( T/9 \)

---

#### Explanation:

This problem involves an understanding of satellite motion, specifically the relationship between the mass of a satellite, its orbital radius, and its orbital period. The key concept to recall here is Kepler's third law which enables us to relate these aspects.

**Concept:**

Kepler's third law states that the orbital period \( T \) of a satellite around a planet is related to the radius \( R \) of its orbit by the equation:

\[ T^2 \propto R^3 \]

Interestingly, the orbital period is independent of the mass of the satellite. Therefore, the orbital periods of satellites in the same orbit (with the same radius \( R \)) remain the same regardless of their masses.

**Given:**
- First satellite has mass \( M \)
- Orbital radius \( R \)
- Orbital period \( T \)
- Second satellite has mass \( 3M \)
- Orbital radius \( R \)

**Solution:**
Since the orbital period \( T \) only depends on the radius \( R \) according to Kepler's third law, the orbital period of the second satellite will also be \( T \).

**Answer: (c) \( T \)**

This explanation and step-by-step approach help students to understand that the mass of the satellite does not affect the orbital period for a given orbital radius.

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