Orbital Motion & Satellites

Newton's Law of Gravitation: Every mass attracts every other mass with force F = Gm₁m₂/r².

The gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg².

Orbital velocity of a satellite: v₀ = √(GM/r) = √(gR²/r), where r is the orbital radius.

Escape velocity from Earth's surface: vₑ = √(2gR) ≈ 11.2 km/s. It is √2 times the orbital velocity at surface.

Kepler's Third Law: T² ∝ r³ — the square of the period is proportional to the cube of the orbital radius.

Geostationary orbit: T = 24 hours, r ≈ 42,164 km from Earth's center, above the equator.

Total energy of an orbiting satellite: E = −GMm/(2r) — it is negative (bound state).

At the surface: g = GM/R². As you go up: g decreases as GM/(R+h)². Inside Earth: g decreases linearly.