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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
The Remaining Burns: Lunar Orbit Insertion and Transearth Injection

Closing the Orbit with a Small Burn

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The spacecraft has arrived at the Moon on a path that gravity has already bent toward it. With no burn at all, that path would carry it past the far side and back toward Earth.
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Lunar orbit insertion (LOI) is the burn that turns a lunar flyby into a lunar orbit.

  • By the time the spacecraft reaches the Moon, the Moon's gravity has already bent its path into a bound trajectory. The spacecraft is falling toward the Moon, not racing past it under power.
  • LOI is a retrograde burn — it fires opposite the direction of motion — to remove just enough speed that the path closes into an ellipse around the Moon instead of opening back out.
  • Because gravity supplied the bending, LOI is small compared with the translunar injection burn. The engine only has to trim the orbit, not create the capture.
  • The burn is timed near closest approach (periapsis), where the spacecraft moves fastest, so the Oberth effect gives the most velocity change per unit of propellant.
  • A useful way to see it: gravity does the capture, the engine only tidies the orbit.

Key idea: LOI is small because the Moon's gravity has already done the hard part.

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