Question

A particular binary star system consists of two identical stars orbiting a point half way between them along the same circular path at constant speeds (See diagram below). If we call the mass of each star m and the radius of the circular path r. What is an expression for the speed of the stars, in terms of these symbols and fundamental constants?

• A. $v=\sqrt{\frac{Gm}{2r}}$
• B. $v=\sqrt{\frac{2Gm}{r}}$
• C. $v=\sqrt{\frac{Gm}{r}}$
• D. $v=\sqrt{\frac{Gm}{4r}}$
• E. $v=\sqrt{\frac{Gm}{2r^2}}$

Answer 1

Answer: (D)

$v=\sqrt{\frac{Gm}{4r}}$

In the given binary star system the necessary centripetal force for a star to move in a circular path is provided by the gravitational attraction force between the stars ,

centripetal force =gravitational force

or $m{v}^2/r=Gm\times m/(2r{)}^2$

or $v^2=Gm/4r$

or $v=\sqrt{Gm/4r}$