[A_No_Name_Mouse]

> Wait, you want to do a gravitational perturbation mission with 5kg, for a body of > 10^18kg? You'd have to do super duper precise measurements to notice anything I don't think so. We would measure the effect of 33 Polyhymnia on the probe, not the other way around. Which would work if it got just in the vicinity of the asteroid. The mass of the probe wouldn't even matter.

You're right of course about the density being a wild guess, probably not worth pursuing because the odds of finding something interesting are just about 0.