Changing Lanes: Orbital Maneuvers Explained

If an object in orbit needs to change its trajectory or altitude, then its kinetic energy must be modified. If kinetic energy is linked to velocity, then the scalar measure of the impulse needed to change that velocity is defined as Delta-v.

If a spacecraft accelerates in the direction of its current velocity (prograde), then its total orbital energy increases. If the total energy increases, then the semi-major axis of the orbit must also increase, resulting in a higher altitude on the opposite side of the orbit.

If a spacecraft uses an elliptical trajectory that is tangent to both the starting and target orbits, then it minimizes the energy required for the transition. This specific two-impulse maneuver is the Hohmann Transfer.

If the work done by a rocket engine is the force times the displacement, then the change in kinetic energy is proportional to the spacecraft's current velocity. If velocity is highest at periapsis, then a burn at that point provides the greatest gain in orbital energy for the same amount of fuel.

If we want to find the change in velocity (Δv), then we must account for how fast the mass is being ejected and the ratio of the starting mass to the empty mass. If Δv = ve * ln(m0/mf), then these three variables are the only mathematical requirements.

If a retrograde burn decreases the spacecraft's velocity, then its total orbital energy decreases. If the energy is removed at the highest point (apoapsis), then the spacecraft will "fall" further on the opposite side, meaning the periapsis height will decrease, not increase.

If an orbit is non-circular, it has two extreme points along the major axis. If the point of minimum distance is the periapsis, then the point of maximum distance is the apoapsis.

If a plane change requires a change in the direction of the velocity vector, then the fuel required depends on the magnitude of the current velocity. If velocity is lowest at the apoapsis, then the Δv required to rotate that vector is minimized at that specific point.

If we need to compare how effectively different engines use their fuel, then we measure how much thrust is produced per second for every pound of fuel. If this value is higher, then the engine is more efficient and provides more Δv for the same mass of propellant.

If a maneuver occurs over a duration that is significantly shorter than the total orbital period, then it can be mathematically simplified as an "impulsive" or instantaneous change in velocity.

If the Vis-viva formula is v^2 = GM(2/r - 1/a), and if in a circle r = a, then the equation simplifies to v = sqrt(GM/r). If G and M are constants for the planet, then only the radius 'r' determines the speed.

If mission planners must calculate the fuel needed for launch, orbit insertion, and landing, then they must add all the individual Δv requirements together. If this total is the limiting factor for design, it is called the Delta-v budget.

If a spacecraft enters a planet's sphere of influence and is pulled along by the planet's own orbital motion, then the spacecraft can gain or lose speed relative to the Sun. If the spacecraft exits the planet's gravity, it keeps that extra velocity.

If kinetic energy is 1/2mv², then a change in velocity (Δv) at a high 'v' results in a much larger change in energy (ΔE) than the same Δv at a low speed. If the spacecraft is moving fast at periapsis, then the maneuver is more energy-efficient.

If a Hohmann transfer connects two circular orbits, then it must use an elliptical path that touches both. If the transfer starts at one circle and ends at another, then a burn is needed to enter the ellipse and another to leave it.

If the spacecraft has reached the target altitude via an elliptical path, it will fall back down unless its velocity is adjusted to match the required speed for a circle at that height. If that speed is reached, then the process is circularization.

If the target orbit is significantly further away than the starting orbit, then using an intermediate ellipse that goes very far out before returning can actually save fuel. If the radius ratio is high enough, the Bi-elliptic maneuver beats the Hohmann in efficiency.

If a burn is directed "Radial-In" (toward the planet), then it rotates the orientation of the orbit's major axis (argument of periapsis) rather than increasing the orbital energy or size. If you want to increase size, you must burn prograde.

If Δv is proportional to the log of the mass ratio, then as you add more fuel, you also add more weight that must be pushed. If the "empty" mass remains the same, each additional kilogram of fuel provides less and less additional velocity change.

If a retrograde burn reduces orbital energy, then it is the standard method for dropping altitude, entering orbit (braking), or adjusting speed to fix an orbit's shape. It cannot be used to reach a further destination like the Moon.