An astronaut is standing at the north pole of a newly discovered, spherically symmetric planet of radius R. In his hands he holds a container full of a liquid with mass m and volume V. At the surface of the liquid, the pressure is P0; at a depth d below surface, the pressure has a greater value p. From this information, determine the mass of the planet.
Step 1 of 2 we know that p p = gd pp g = 0 d (pP 0V g = md ...................................(1) Gmp But also g = 2 ...............................(2) R Equating (1)m and (2) Gm p = (pp0)V R 2 md (pp )V R m p 0 Gmd