&gt;&gt;As far as I&#x27;m aware, we have ways of measuring weight, but no way of measuring mass.<p>Then we are speaking of different things.  I understand &#x27;weight&#x27; as how heavy something is within particular gravity field (ie on a bathroom scale on earth) whereas mass is independent of local gravity.  The schemes I suggest measure mass without resort to weight.<p>&gt;&gt;I have no intuition for this. Maybe it&#x27;s valid, but your other two examples raise grave doubts about this one.<p>The motion of the more massive pair will describe a smaller circle than the lighter one.  The ratios of the two circles&#x2F;motions allows you to calculate the unknown mass from the known.