Posted by **Me** on Tuesday, November 29, 2011 at 11:45pm.

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?

- Physics help please -
**drwls**, Wednesday, November 30, 2011 at 10:40am
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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