Explanation A certain quaternary star system consist of three stars, each of mass m , moving in a same circular orbit of radius r about a central star of mass M . The stars orbit in the same sense and the positioned one-third of a revolution apart from one another. The diagram for the given condition is shown below. Figure (1) As the stars are moving in the same circular orbit of radius r and positioned one-third of a revolution apart from one another, their positions forms an equilateral triangle. Formula to calculate the period of the each of three stars is, T = 2 π r v (1) Here, v is the velocity of the each star and r is the radius of the circle. The net force act on the each star is, F = F 2 + 2 F 1 (2) Here, F 1 is the force exerted by the one star on the other star and F 2 is the force exerted by the star on the star placed at the center. Formula to calculate the force exerted by the one star on the other star is, F 1 = G m 2 ( d ) 2 cos θ Here, G is the universal gravitational constant, m is the mass of the star at placed at the circumference of the circle, d is the distance between the position of two stars and θ is the angle made by the force with the horizontal. Substitute 2 r cos 30.0 ° for d and 30.0 ° for θ in above expression. F 1 = G m 2 ( 2 r cos 30.0 ° ) 2 cos 30.0 ° Formula to calculate the force exerted by the star on the star placed at the center is, F 2 = G M m r 2 Here, M is the mass of the star at placed at the center of the circle and r is the radius of the circular orbit. Substitute G m 2 ( 2 r cos 30 ° ) 2 cos 30 ° for F 1 and G M m r 2 for F 2 in equation (2)

9th Edition

ISBN: 9781305804470

Author: Jewett

Publisher: CENGAGE LEARNING - CONSIGNMENT

See similar textbooks

Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force betwe…

Question

Chapter 13, Problem 13.66AP

To determine

The time period of each of three stars is T=2πr3G(M+m3).

Expert Solution & Answer

Chapter 13 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

Ch. 13 - A planet has two moons of equal mass. Moon 1 is in...Ch. 13 - Superman stands on top of a very tall mountain and...Ch. 13 - An asteroid is in a highly eccentric elliptical...Ch. 13 - Prob. 13.4QQ Ch. 13 - A system consists of five particles. How many...Ch. 13 - Rank the following quantities of energy from...Ch. 13 - Prob. 13.3OQ Ch. 13 - Suppose the gravitational acceleration at the...Ch. 13 - Imagine that nitrogen and other atmospheric gases...Ch. 13 - An object of mass m is located on the surface of a...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

The time period of each of three stars is T = 2 π r 3 G ( M + m 3 ) .

Solution Summary: The author describes a certain quaternary star system consisting of three stars, each of mass m, moving in the same circular orbit, positioned one-third of the revolution apart from one another.

Concept explainers

The time period of each of three stars is T=2πr3G(M+m3).

Chapter 13 Solutions