A satellite has a mass of 6173 kg and is in a circular orbit 4.71 × 105 m above the surface of a planet. The period of the orbit is 1.6 hours. The radius of the planet is 4.31 × 106 m. What would be the true weight of the satellite if it were at rest on the planet’s surface?
m=6173 kg
h=4.71•10⁵ m
R=4.31•10⁶m
T=1.6 h=1.6•3600=5760 s
mg=?
F=GmM/(R+h)²
F=mv²/(R+H)
GmM/(R+h)² =mv²/(R+H)
G M/(R+h)² = v²/(R+H)
G M/(R+h)= v²
T=2π(R+h)/v =>
v=2π(R+h)/T =>
v²=4 π²(R+h)²/T²
G M/(R+h)= 4 π²(R+h)²/T²
M=4 π²(R+h)³/GT²
mg=GmM/R²=
=4 π²Gm(R+h)³/GT²R²=
=4 π²m(R+h)³/ T²R²=
=4 π²•(4.31•10⁶+4.71•10⁵)³/(5760•4.31•10⁶)²=
=4.32•10⁴ kg