Answer
The mass of the planet is $~~8.7\times 10^{24}~kg$
Work Step by Step
In part (a), we found that the radius of the orbit is $~~1.9\times 10^7~m$
We can use the gravitational force to find the mass of the planet:
$F = \frac{GMm}{r^2} = 80~N$
$M = \frac{(80~N)(r^2)}{Gm}$
$M = \frac{(80~N)(1.9\times 10^7~m)^2}{(6.67\times 10^{-11}~N~m^2/kg^2)(50~kg)}$
$M = 8.7\times 10^{24}~kg$
The mass of the planet is $~~8.7\times 10^{24}~kg$
