The moon orbits the earth at a distance of 3.85x10^8 m. The moon orbits the earth at a distance of 3.85x10^8 m. Assume that this distance is between the centers of the earth and the moon and that...
The moon orbits the earth at a distance of 3.85x10^8 m.
The moon orbits the earth at a distance of 3.85x10^8 m. Assume that this distance is between the centers of the earth and the moon and that the mass of the earth is 5.98x10^24 kg. Find the period for the moon's motion around the earth. Express the answer in days and compare it to the lenght of a month.
1 Answer
jeew-m | College Teacher | (Level 1) Educator Emeritus
The moon is rotating around earth. So in the moon there is a centrifugal force acting towards earth.
`F = mv^2/r`
m = mass of moon
r = distance between moon and earth
v = velocity of moon
Earth exerts a gravitational force on earth as given by Newtons low of gravity.
`F = G(Mm)/r^2`
M = mass of earth
G = Newtonian gravity constant
But by both these equations it expresses the same thing.
Therefore;
`GMm/r^2 = mv^2/r`
` v = sqrt((GM)/r)`
`= sqrt(6.67xx10^(-11)*(5.98xx10^24)/3.85xx10^8)`
`= 1.02xx10^3`
So the linear velocity of moon is 1020m/s.
For one round around earth the moon travels `2pir` distance.
This distance is equal to time*velocity of moon.
`2*pi*3.85x10^8 = 1020*t`
`t = 2.38xx10^6s`
Number of days `= (2.38xx10^6)/(60xx60xx24) = 27.5`
So it will take 27.5 days to complete full motion around earth.