Why does escape speed NOT depend on mass?
Why doesn’t escape speed depend on the mass of the spacecraft?
In short: To escape, the total energy K + U must be at least zero. With K = ½mv² and U = −GMm ÷ r, setting ½mv² − GMm ÷ r = 0 makes the ship’s mass m cancel. So vesc = √(2GM ÷ r) depends only on the planet’s mass M and the starting distance r. At Earth’s surface it is about 11.2 km/s.
Common doubts
- “Wouldn’t a heavier ship need more energy to escape?” Yes, it needs more energy, but at the same speed it also has more kinetic energy. Both scale with m, so the required speed stays the same.
- “Does the ship have to keep its engines on after launch?” No. Escape speed is the launch speed needed with no further push. Gravity keeps slowing the ship, but at exactly vesc its speed only reaches zero at infinite distance.
- “What happens below escape speed?” The total energy is negative, so the ship rises to some maximum distance and then falls back.
Change the launch speed, the planet’s mass and the distance in the simulation above, press PLAY, and compare the ship’s fate with the speed ratio v₀ ÷ vesc.
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