Posted by jimmyjonas on Tuesday, February 22, 2011 at 8:48am.
Two satellites are in circular orbits around Jupiter. One, with orbital radius r, makes one revolution every 17 h. The other satellite has orbital radius 4.2r. How long does the second satellite take to make one revolution around Jupiter?

physics  tchrwill, Tuesday, February 22, 2011 at 11:11am
The orbital period is defined by
T = 2(Pi)sqrt[r^3/µ)] where T = the period in seconds, r = the orbital radius and µ = the planet's gravitational constant.
17hr = 61,200 sec.
61,200 = 2(Pi)sqrt[r^3/µ] from which µ = r^3/94,873,103
At a radius of 4.2r,
T = 2(Pi)sqrt[74.088r^3(94,873,103/r^3] = 23.288 hours.

physics  tchrwill, Tuesday, February 22, 2011 at 1:15pm
OOPS  the hand was quicker than the eye.
The orbital period is defined by
T = 2(Pi)sqrt[r^3/µ)] where T = the period in seconds, r = the orbital radius and µ = the planet's gravitational constant.
17hr = 61,200 sec.
61,200 = 2(Pi)sqrt[r^3/µ] from which µ = r^3/94,873,103
At a radius of 4.2r,
T = 2(Pi)sqrt[74.088r^3(94,873,103/r^3] = 146.32
hours.
The same result derives from Kepler's third law, T/To = [R/Ro]^(3/2) where
T/17 = [4.2R/R]^(3/2).
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