I have a question similar to one I've asked earlier (Calculating mass of an orbiting body with force and acceleration), but without a specific formula...

How can you find the mass of a satellite body (such as a moon or asteroid) without orbiting that body, or without it already having a satellite of its own? I understand that larger bodies can noticeably perturb their parent objects, but for the sake of the question lets assume that the object is vastly smaller (Such as an asteroid), and so those perturbations would be unrecognizable. The information that is available is mostly orbital (Semi-major axis, time, and so forth), but you could also use diameter/radius measurements. You don't know volume, and you don't know density either.

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    $\begingroup$ I have no idea if this actually works, but maybe the mass could be determined by looking at how much the perturbation change the orbit. For example the force caused by the Yarkovsky effect does not depend in the mass of the object. However for this you do need to know a lot of information, such as the emissivity of the surface, thermal conductivity, specific heat and the rotational velocity of the object. $\endgroup$ – fibonatic Dec 19 '15 at 0:00

You can't. Imagine that the satellite was two objects tied together -- the orbital mechanics would be the same. What answer would be correct -- the mass of one or both ? Now imagine that they weren't tied, but in close proximity -- same conclusion.

Basically, if the satellite has no measurable influence on the host, it's mass has no effect, and can't be measured.

  • $\begingroup$ Thanks for clarifying- I just wasn't putting the pieces together it seems... $\endgroup$ – Sigismund Dec 19 '15 at 2:45

Once you put in the constraint that the satellite doesn't disturb its host, its mass no longer has any bearing on its orbit (it's now a 'test mass' in a potential). So throw out all your orbital measurements, they're of no use.

Without knowing anything about the composition (density) of the object this is going to be difficult. The best I can think of is to try and use the tidal forces exerted by the host and the fact that the satellite hasn't been destroyed to try and put a lower limit on its mass (something is holding it together, which will be some combination of self-gravity and tensile strength if it's a solid). But this will only be a useful constraint if the tides are strong; if the tides are very weak you'll basically just get $M>0$. Might be a bit better if you can measure the diameter accurately enough to measure tidal deformation. If the satellite is a liquid/gas this could even give a decent mass estimate, but if its solid you'd want to know something about the composition again.

  • $\begingroup$ Very interesting! Though if you could find the composition you could find the mass much easier... Thank you anyway. $\endgroup$ – Sigismund Dec 19 '15 at 22:06

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