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Gravity and Newton's Laws: How Apollo Saved Fuel to the Moon

1Why Coasting Is Free: Newton's First Law on the Way to the Moon2Gravity as a Free Engine: Newton's Law of Gravitation on the Translunar Coast3Designing the Path: Free-Return Trajectory and the Oberth Effect4The Remaining Burns: Lunar Orbit Insertion and Transearth Injection
Designing the Path: Free-Return Trajectory and the Oberth Effect

Firing Where the Spacecraft Is Fastest

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So where do you fire? On an elliptical orbit, the spacecraft moves fastest at periapsis, the closest point, and slowest at apoapsis, the farthest. That difference is the opportunity.
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Apollo applied the Oberth effect by placing its largest remaining burns near periapsis, the point in an orbit where the spacecraft moves fastest.

  • On an elliptical orbit, speed is highest at periapsis and lowest at apoapsis. A burn at periapsis therefore buys more orbital energy per kilogram of propellant.
  • The same principle applies to the departure and arrival geometry: burns timed when the spacecraft is moving fastest relative to the body it is leaving or approaching give the greatest velocity change for the propellant spent.
  • This is why burn timing, not just burn size, appears in the mission plan: the trajectory is shaped so that the critical burns occur where the spacecraft is already moving quickly.

Key point: the Oberth effect turns timing into a fuel-saving tool. The propellant saved at periapsis is propellant that stays available for the return.

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