Orbits & satellites

Circular orbits around a spinning planet: how speed, period and energy depend on radius

A Level Physics 9702 · 13 Gravitational fields

r = 2.00 R⊕ geostationary: stays over the ground station polar orbit: sweeps the whole surface

Kepler’s third law · T² ∝ r³

Jump to a real orbit

Orbit radius r2.00 R⊕

Inclination (tilt of orbit)0°

Planet mass M1.00 M⊕

Satellite mass m1000 kg

orbital speed v

…

km s⁻¹

period T

…

hours

angular speed ω

…

rad s⁻¹

centripetal accel.

…

m s⁻²

● kinetic E_K = GMm/2r…

● potential E_P = −GMm/r…

● total E = −GMm/2r…

Resistive forces remove energy: watch r fall while the satellite speeds up and the total energy drops (the paradox behind re-entry).

v = √(GM/r) = …

T = 2π√(r³/GM) = …

E = −GMm/2r = …

geostationary radius (T = 24 h): …