A certain planet is located 3.54 x 10^11 m from its sun. If its orbital period is 4.9 x 10^7 s, find the mass of its sun.
Take a good look at the one I just did for help please.
The numbers are different but the problem uses the same logic, primarily:
T^2 = (2pi)^2 * r^3 /GM
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r = .039875*10^6 +1.74*10^6 = 1.78*10^6
G = 6.67*10^-11
M = 7.35*10^22
F = m v^2/r
G M m /r^2 = m v^2/r
v^2 = G M /r
T^2 = (2pi)^2 * r^2/v^2
T^2 = (2pi)^2 * r^3 /GM
T^2 =
39.5*5.64*10^18/(6.67*10^-11*7.35*10^22)
T^2 = 4.54 * 10^7 = 45.4 * 10^6
T = 6.74 * 10^3 = 6740 seconds (about 1.8 hours)