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While visiting Planet Physics, you toss a rock straight up at 13.6 m/s and catch it 3.50 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 340.0 minutes.

What is the mass (in kg) of the planet?

The time of flight of the tossed rock is T = 2 Vo/g = 3.50 s.
Therefore the local value of g is
2 Vo/T = 7.77 m/s^2

The value of g is related to the radius R and mass M of the planet by
g = G*M/R^2

From the period of the orbit, you know that the orbital velocity is
V = 2*pi*R/P
where P is the known period, 20,400 s.
Since m V^2/R = m g,
4*pi^2*R/P^2 = 7.77 m/s^2
That equation can be solved for the orbit radius, R.
Then use g = G*M/R^2 for M

G is the universal constant of gravity,
6.67*10^-11 N m^2/kg^2

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