Gravity does negative work on the outbound leg
- Earth's pull points back toward Earth, while the spacecraft moves away. Force and displacement are opposed, so gravity removes kinetic energy from the spacecraft.
- The result is deceleration with no engine firing: the spacecraft trades speed for altitude, exactly as a ball thrown upward trades speed for height.
- The deceleration is strongest near Earth, where \(F = G m_1 m_2 / r^{2}\) is largest, and weakens as the spacecraft climbs.
Why this saves propellant
- A braking burn would have to produce the same velocity change that gravity produces for free.
- Because gravity supplies it, that velocity change never appears in the propellant budget.
- The spacecraft arrives near the Moon moving slowly — not because it braked, but because it climbed.