01
Newtonian Gravity
F = Gm₁m₂/r²
Gravitational attraction provides the dominant force governing many spacecraft and celestial trajectories.
02
Kepler's Laws
- Bound planetary orbits are ellipses in the ideal two-body approximation.
- A line from the central body to the orbiting body sweeps equal areas in equal times.
- Orbital period relates systematically to the size of the orbit.
T² ∝ a³
03
Escape Velocity
v_escape = √(2GM/r)
Escape velocity is the speed required at a given distance to reach zero asymptotic speed relative to the central body in the ideal two-body model.
04
Orbital Transfers
- Hohmann transfers change orbit using two idealized burns.
- Bi-elliptic transfers use three impulses.
- Gravity assists exchange orbital energy and momentum with moving bodies.
- Low-thrust propulsion can produce long-duration, continuously changing trajectories.