Explanation 1) Concept: Equating the gravitational force between the planet and the star and the centripetal force and putting the distance of the star (r 1 ) from C.O.M and from period of the star, we can find the mass of the planet. Comparing it with the mass of the Jupiter, we can write it in terms of M j . From r 1 , we can find r 2 using center of mass formula. 2) Given: The graph of the line of sight velocity of star vs time for the star. 3) Formulae: i) F c = M v 2 r ii) F g = G M m r 2 4) Calculations: a) The planet and the star are orbiting about their center of mass. The gravitational force of attraction between them provides the centripetal force to keep their motion in the circular orbit. It gives F = G m 1 m 2 r 2 = m 1 v 2 r 1 As both planet and star revolve about the center of mass, r 1 = ( m 1 0 + m 2 r ) m 1 + m 2 r 1 = m 2 r m 1 + m 2 r = m 1 + m 2 m 2 r 1 The orbital speed of m 1 in terms of T is written as v = 2 π r 1 T So, r 1 = v T 2 π Substituting r 1 in r r = m 1 + m 2 m 2 v T 2 π Putting r and r 1 in F 1 F = G m 1 m 2 ( m 1 + m 2 ) m 2 v T 2 π 2 = m 1 v 2 v T 2 π F = 4 π 2 G m 1 m 2 3 m 1 + m 2 2 v 2 T 2 = 2 π m 1 v T m 2 3 m 1 + m 2 2 = v 3 T 2 π G m 2 3 0.9 M s u n + m 2 2 = 70 3 1500 86400 2 3

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Chapter 13, Problem 58P

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To find:

a) The planet’s mass in terms of Jupiter’s mass Mj

b) The planet’s orbital radius in terms of Earth’s orbital radius RE.

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Chapter 13, Problem 57P

Chapter 13, Problem 59P

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Chapter 13 Solutions

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a) The planet’s mass in terms of Jupiter’s mass M j b) The planet’s orbital radius in terms of Earth’s orbital radius R E .

Solution Summary: The author explains how to find the planet's mass and its orbital radius using the center of mass formula.

Concept explainers

To find:

a) The planet’s mass in terms of Jupiter’s mass Mj

b) The planet’s orbital radius in terms of Earth’s orbital radius RE.

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Chapter 13 Solutions

a) The planet’s mass in terms of Jupiter’s mass M j b) The planet’s orbital radius in terms of Earth’s orbital radius R E .

Solution Summary: The author explains how to find the planet's mass and its orbital radius using the center of mass formula.

Concept explainers

To find: a) The planet’s mass in terms of Jupiter’s mass Mj b) The planet’s orbital radius in terms of Earth’s orbital radius RE.

Want to see the full answer?

Chapter 13 Solutions

To find:

a) The planet’s mass in terms of Jupiter’s mass Mj

b) The planet’s orbital radius in terms of Earth’s orbital radius RE.