general physics
posted by justin on .
COMPLETELY STUCK? The period of rotation of the Moon is about 27 days, 8 hrs. The mass of the Moon is 7.35 x 1022 kg, and the radius of the Moon is 1.74 x 106 m. I wish to place a synchronous (period of orbit = period of the Moon’s rotation) satellite in orbit about the Moon.
a) Find the radius of the satellite’s orbit.
b) Find the height of the satellite above the Moon’s surface

a) the gravitational constant
G =6.67•10⁻¹¹ N•m²/kg²,
r=1.74•10⁶ m
M=7.35•10²² kg
ma=F
F =G•m•M/R²
ma=mv²/R
G•m•M/R² =mv²/R
v=sqrt(GM/R)
T=2πR/v = 2π•sqrt{R³/GM}
T²= 4π²•R³/GM
Solve for R.
b) h=Rr = …