How big can a moon be where you can physically jump out of its orbit, to its planet?

So, imagine a team of space marines, fighting some sort of space bug zombies on a planet's moon. Things are going pretty bad for them, and the last surviving protagonists are running for their lives. The thing is, with each step, they soar into the air, higher and higher, until the point where the planet is directly overhead. At that point, the moon's low gravity is completely counteracted by tidal forces and the space marines' jumping forces, and the marines float out into space, where they are picked up by their ship (or, alternatively, where they get caught in the planet's gravity and burn up on re-entry, depending on if this is a comedy or tragedy).

Now, I already know this is possible; if the moon weighs 1kg it wouldn't be too hard to reach escape velocity, especially when aided by the gravitational pull of an Earth-sized planet nearby. What I'm wondering is how big I can make the moon and still achieve this effect.

For the parameters, let's say the planet is Earthlike, and the moon is right at the edge of its Roche limit (which should maximize tidal forces). An average human has to be able to reach escape velocity when the planet is directly overhead, just by jumping. Assume the moon has no atmosphere and is made of similar materials to those you'd find on our Moon.

Let me know if you have any further questions.

EDIT: The human(s) used in this question can be assumed to not be augmented in any way (aside from space suits, which I'm fine with removing for the sake of simplicity), and need not actually be able to 'run' across the surface of the moon in a way resembling how they would on Earth. Perhaps in another question, I can ask about how to quickly move across the surface of a body with little to no gravity, but that is beyond the scope of this question.

posted over 8 years ago

DaaaahWhoosh‭

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