**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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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

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 7OQ

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