Question

The surface of a giant red star exerts a gravitational force of 2.19*10^-3 N on a 500g object. If the star's mass equals 3.98*10^31kg, what is the star's radius?

Answer 1

\[F = \frac{ GMm }{ r^2 }\]\[r=\sqrt{\frac{ GMm }{ F }}=\sqrt{\frac{ (6.67 x 10^{-11})(3.98 x 10^{31}(0.500) }{ (2.19 x 10^{-3}) }}=7.79 x 10^{11}m\]

The important thing to realize here is that the object is being acted on by the red giant on the surface of the red giant. Therefore, since the mass of the red giant is mathematically assumed to be a point mass at the center of the red giant, the distance between the red giant and the object is the radius of the star itself.