Question

10. The moon is about 3.8 x’s 105 km from the Earth. Show the average orbital speed about Earth is 1026 m/s.

Answer 1

just use use the equation gravitational force by earth = centrifugal force on moon.
G*m(earth)*m(moon)/(r^2) = m(moon)*v^(2)/r
where r denotes radius. and in this equation mass of moon will get cancelled on both sides so you just need to know the mass of earth.

Answer 2

The equation for orbital speed is
\[V = \sqrt{\frac{ Gm }{ r }}\]where
r is the distance between the earth and the moon.
m is the orbital mass of in question, in our case is the earth.
G is the newtonian gravitationl constant

if
r = 3.8 x 10^7 m [distance from moon to earth]
m = 5.9 x 10^24 kg [mass of earth]
G = 6.67 x 10^-11 [constant]

then you can prove that the speed of the earth is 1026 m/s

Answer 3

@dibuaman can you show me where I'm going wrong with the equation you gave? I tried the method you have and keep getting V = 3237 m/s. here is the equation i am using with the numbers filled in:
\[(6.67*10^{-11})*(5.97*10^{24})*(7.35*10^{22})/(38000000^{2}) = (7.35*10^{22})*v^{2}/38000000, \] where am I going wrong?