T2/r3 for the old moon= T2/r3 for the new moon
(27.3)2/(3.84E8)3 = T2/(2 * 3.84E8)3
solve for T...
T=77.2days
The two balancing forces on a planet are GRAVITY and CENTRIPETAL
Fg = Gmplanet msun/r2 = Fc = mplanet 4p2r/ T2
Setting these equal to each other.....
Gmplanet msun/r2 = mplanet 4p2r/T2
The planet mass cancels out, leaving.....
Gmsun/r2 =4p2r/T2
Cross multiply .....
GmT2 = 4p2r3 Where m is the mass of the sun.
T and r can be observed using telescopes. Then we can solve for the mass of the sun! The T2 and r3 terms of this equation could be for any planet, so we can write the following
T2/r3 for one planet = T2/r3 for any other planet
A new moon is discovered
orbiting the earth that is twice as far away.
How long does it take to go around the Earth?
Tmoon= 27.3 days, rmoonorbit=3.84E8
meters.
T2/r3 for the old moon= T2/r3 for the new moon
(27.3)2/(3.84E8)3 = T2/(2 * 3.84E8)3
solve for T...
T=77.2days