Planet Hopper
How high could you jump on the Moon, on Mars or on a small asteroid — and is there a rock small enough to jump off into space? Enter how high you jump on Earth and compare your jump side by side.
Jumping in Low Gravity
Your leg muscles give you a certain take-off speed, about 3 m/s for a normal jump. How high that takes you depends on gravity: on the Moon, with one-sixth of Earth’s gravity, you rise six times higher and stay in the air six times longer.
On a small asteroid, gravity is so weak that your take-off speed comes close to the escape velocity. Gravity then also fades noticeably as you rise, so you go even higher than the simple formula says — and on a rock a few kilometres across, one jump sends you into space for good.
Your Jump, Side by Side
same scaleJumps Across the Solar System
0.5 m jump on Earth| Body | Gravity | Jump height |
|---|
Worked Techniques
With the same take-off speed, the jump height scales with one over gravity, and so does the time in the air.
Energy conservation with the full 1/r potential. For small h it reduces to v₀²/2g; when v₀ approaches vesc the height runs off to infinity.
For a rocky body of density ρ, the escape velocity grows in proportion to its size. Below this radius, your jump is faster than the escape velocity.
Sources & Verification
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 13 (Gravitation).
- H. D. Curtis, Orbital Mechanics for Engineering Students, 3rd ed., Butterworth-Heinemann, 2014 — Ch. 2 (The Two-Body Problem) and Ch. 3 (Orbital Position as a Function of Time).