# Asteroid hopping

Hypothetical situation: I'm an astronaut on a celestial object and another object is passing by, quite close to me. Could I jump to the other object?

What are the two largest bodies of comparable masses/radii that could cross paths slow enough, so that I could jump between them?

Things to consider:

• The Roche Limit tearing larger objects apart
• The two objects cannot capture one another or collide.
• This Dissertation giving specifics about the impulse of a jump, which can be used for calculations.
• Can you define the requirements? What is the maximum impulse the astronaut is capable of generating relative to his mass? Are there handles on the second asteroid he can grab when he lands to keep from bouncing off? – Ben51 Jan 13 '18 at 5:39
• Handles feel like cheating, so let's just say that the astronaut has to land on his feet. – Austin A Jan 13 '18 at 7:57

(1) If one can jump with speed $v_{max}$ this is above escape velocity if $M/R<v_{max}^2/G$. This is true for a lot of small bodies.