*** A planet's moon travels in an approximately circular orbit of radius 8.6e7 meters with a period of 7 h 53 min. Calculate the mass of the planet from this information.
_____ kg
2007-01-23 03:49:29 · 2 answers · asked by Khoi 1 in Science & Mathematics ➔ Physics
Angular velocity w = 1/t; where t = period (remember to do this in seconds)
Tangential velocity at r = 8.6 X 10^7 meters orbit = v = wr (m/sec)
Centrepital force F = mv^2/r
Weight of satellite = W = GmM/r^2
When in orbit, F = W; so that mv^2/r = GmM/r^2 and
v^2 = GM/r; so the M = rv^2/G, which presuming you know G you can solve. (Make sure you use G in kg-m-sec units to be consistent).
2007-01-23 05:57:33 · answer #1 · answered by oldprof 7 · 0⤊ 0⤋
mv^2/r = GMm/r^2
so, M = v^2xr/G
v = wr
2007-01-23 12:05:23 · answer #2 · answered by ag_iitkgp 7 · 0⤊ 0⤋