Please help with Physics Practice question.
The moon is about 3.8 x 10^5km from Earth. Show that its average orbital speed about Earth is 1026 m/s

Question

Please help with Physics Practice question.
The moon is about 3.8 x 10^5km from Earth. Show that its average orbital speed about Earth is 1026 m/s

anonymous · Answer

hmm.. i agree hold on let me see

anonymous · Answer

g (gravity) = G*M/R^2
a (centripetal) = V^2/R

G*M/R^2 = V^2/R
v = sqrt[G*M/R] 

Using M = 5.9742E+24 kg and G = 6.673E-11 
And don't forget that the radius should be in meters and not km so R = 3.8E8
We get v = 1024.3 m/s

You can also do a little more and get v in terms of the radius of the earth
At the surface of the earth: g = G*M/r^2 which gives M = g*r^2/G
v = sqrt[g*r^2/R] 
Using r = 6378.1 km gives v = 1024.8 m/s

anonymous · Answer

that  really helped put it into perspective thank you