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In a binary star system two stars orbit about their common
Chapter 12, Problem 91GP(choose chapter or problem)
Problem 91GP
In a binary star system two stars orbit about their common center of mass. Find the orbital period of such a system, given that the stars are separated by a distance d and have masses m and 2m.
Questions & Answers
QUESTION:
Problem 91GP
In a binary star system two stars orbit about their common center of mass. Find the orbital period of such a system, given that the stars are separated by a distance d and have masses m and 2m.
ANSWER:
Solution 91 GP
Step 1 of 3
We have to find the orbital period of a binary star system in which two stars orbit about their common center of mass and are separated by a distance d and have masses m and 2m.
The orbital period of a binary star system can be found by equating the centripetal force acting on one of the stars to gravitational force between the stars and using the general expression for orbital speed .
Equating the centripetal force acting on the star of mass to gravitational force between the stars of mass
and
.
. . . . . . (i)
where,
orbital speed of the star of mass
distance between the stars of mass
and
distance of the star of mass
from the
centre of mass.