Asked by John
astronomers believe the moon used to be much closer to the earth mass=5.98 x 10^24 kg. When it was at 1.92 x 10^8, half its current distance. what was its orbital period in days
Answers
Answered by
Damon
G m M / R^2 = m v^2/R
G M/R = v^2
so
v = sqrt (G M/R)
and
T = 2 pi R/v
so
T^2 = 4 pi^2 R^2/v^2
T^2 = 4 pi^2 R^2 /(G M/R) = 4 pi^2 R^3/ (GM)
T^2 = constant* R^3
if you divide R by 2
you divide T^2 by 8
so you divide T by sqrt 8
G M/R = v^2
so
v = sqrt (G M/R)
and
T = 2 pi R/v
so
T^2 = 4 pi^2 R^2/v^2
T^2 = 4 pi^2 R^2 /(G M/R) = 4 pi^2 R^3/ (GM)
T^2 = constant* R^3
if you divide R by 2
you divide T^2 by 8
so you divide T by sqrt 8