2AI Labs | Speedrun | CAN A HUMAN JUMP OFF AN ASTEROID?

CAN A HUMAN JUMP OFF AN ASTEROID?

Before we can answer this, plese be sure to read: Jumping on Mars

Now then...

Q: Can a human jump off an asteroid?

A: Yes! Though it needs to be quite small. Under 14km (9mi) in diameter.

To get an upper bound on human launch velocity, suppose local gravity gx is zero.

vx2 ≤ 2 · he · ge + 2 · L · ( ge - gx )
      = 2 · 1.16m · 9.807m/s2 + 2 · ½m · ( 9.807m/s2 - 0.00m/s2)
      = 32.56m2/s2

vx ≤ 5.71m/s = 12.77mph

This means the fastest any human can launch by jumping, even in zero gravity, is 5.71m/s. That is the escape velocity of a rocky body of typical density (Ceres is 2080kg/m3) with a diameter of 11.0km. Anything more dense, or more massive than that and no human could jump off it.

The two moons of Mars, Phobos and Deimos, are quite small. Phobos has a diameter of 23km (14mi) and an escape velocity of 18m/s (41mph). That's too big. However, Deimos is oblong, at 15km x 12km x 11km. Standing at the end of its longest axis, the escape velocity drop just barely below 5.7m/s. So in fact it is possible that a human could jump off straight off of Deimos, and right into orbit around Mars.

Q: Can a human jump from Deimos to Phobos?

A: No way. Deimos itself moves at nearly 5000kph. Your jump may exit you from the Deimos gravity well, but your orbital velocity is almost exactly the same. You won't pass through the 7700kph orbit of Phobos.

 


Dr. Timothy P. Barber / 2AI © 18 MAY 2020