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
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?
1 answer
2 answers