The orbit of the moon is approximately a circle of radius 60 times the equatorial radius of the earth. Calculate the time taken for the Moon to complete one orbit, neglecting the rotation of the earth.
Equatorial radius of the earth = 6.4 *10^6m
1 day = 8.6*10^4s
Acceleration of free fall at the poles of earth = 9.8ms^-2
Newtonian law of gravity
The Attempt at a Solution
GMm/r^2 = mv^2/r and solve for v ---> v = sqrt(2GM/r)
Now it takes a period of time T fort he mion to make one full orbit. Thus it travels a distance C
C = 2*pi*r and using C = v*T --> T = C/v = 2*pi*r/sqrt(2GM/r)
Now i am told that r = 60Re where Re = radius of earth.
were i go from here since I was not given the mass of the earth. And what do i use the value of pi as ???