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Two identical stars with mass M orbit around their center of mass. Each orbit is circular...

Two identical stars with mass M orbit around their center of mass. Each orbit is circular and has radius R, so that the two stars are always on opposite sides of the circle.

A) Find the orbital speed of each star and the period of the orbit.

B) Suppose each identical mass for the binary stars is halved, then the orbital period would change by:

a. Remain the same

b. Change by a factor of 1/?2

c. Change by a factor of ?2

d. None of the above

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Homework Answers

Answer #1

A) Distance between the two stars = Diameter of the circular orbit = 2R

Gravitational force of attraction between the two stars

To keep the star in circular orbit the gravitational force is balanced by

Orbital velocity of star is

Using

Time period of orbit is

B) Mass of each star is halved,

Time period of orbit is

Answer is c. Change by a factor of

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