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.
  • $\begingroup$ 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? $\endgroup$ – Ben51 Jan 13 '18 at 5:39
  • $\begingroup$ Handles feel like cheating, so let's just say that the astronaut has to land on his feet. $\endgroup$ – Austin A Jan 13 '18 at 7:57

Saturn's two co-orbital moons Janus and Epimetheus are almost possible to jump between. At their closest they are 10,000 km apart and have zero relative velocity. Unfortunately escape velocity from Janus is 37.6 m/s and Epimetheus 24.6 m/s. This is about ten times terrestrial take-off velocity for jumps in the linked dissertation in the question. Maximal current human running speed is about 12.5 m/s, so even running up a ramp is not going to succeed - it is about half the required. But the moons could have been smaller; it is just bad luck that they are too heavy in this case.

The actual problems are (1) escape velocity, (2) relative velocities, and (3) hitting the target with precision.

(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.

(2) The bodies need to have near-zero relative velocity. In general relative velocities are in the range of km/s, that is, rifle-bullet speeds and faster. Just because you can jump from one small body to another doesn't mean it is survivable. This is likely to be the main constraint: velocity vectors are very unlikely to line up nicely, and even a small difference is not survivable. An important exception are objects in nearly the same orbit.

(3) If the jump could be arbitrarily long-lasting and precise one could do a clever orbital calculation and likely find a solution that intercepted another small body orbit with zero relative velocity, perhaps after a bunch of gravity assists. Typical duration would be a few orbital periods. Such orbits would stretch the concept of a "jump" to the limit. The precision required for the jump between Janus and Epimetheus is likely above what any human can do - the 10,000 km jump requires getting the angle right to 0.0688 degrees or you will miss.

To sum up, the co-orbital moons are likely close to ideal for body-jumping. There are definitely other places like between big chunks in Saturn's rings where this could be done. But beyond that you need implausible precision and durability.

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