Question

Two stars of equal mass form a binary system. If the two stars have an average separation of 7.38 x 108 km, and the magnitude of the gravitational force is 3.03×1027 N between the stars, find the mass of each star in kg. Express your result in scientific notation and to three significant digits. Be careful with units! (Please help! Correct answers will receive thumbs up)

Answer 1

Gravitational Force b/w two masses is $F=GM_1M_2/r^2$

where M₁= M₂= m ( masses of stars which are given equal)

r= distance of seperation b/w them= 7.38 *10⁸km= 7.38 * 10¹¹m

G= Gravitational Constant $= 6.67 \times 10^{-11} m^3/kgs^2$

and F= Force= 3.03 *10²⁷ N

Using all given values,

$m^2= Fr^2/G$

$m^2= (3.03 \times 10^{27})(7.38 \times 10^{11})^2/(6.67 \times 10^{-11})$

$m=\sqrt{ (24.7416 \times 10^{60})}= 4.974 \times 10^{30} kg$