This is my first topic. I'm sorry for my english: that is not my language. On the planet A, sferically symmetric and with no atmosphere, an astronaut on one pole throws in vertical upwards, a little ball giving to it a certain velocity: this ball reaches the maximum height of 25 cm. The same thing is done on another planet, B, equal in mass to the planet A, and then the ball reaches the maximum height of 4 m. Requests: (i) to calculate the planetes radii ratio (ii) to calculate the planetes densities ratio, with the hypothesis that the planets are uniform. Successively, the astronaut make the same experiment on the B planet, this time on the equator, verifying that the ball reaches the height of 8 m. (iii) calculate the rotation period of the planet, supposing that the mass of the planet is 10^27 g and its radius is 5000 km. Temptative of solution: (i) We know that E=mgh, so h=E/mg. Writing down the same equation for the two planetes, the following ratio is obtained: (hA/hB)=(R_A/R_B)^2 = 1/16 (ii) The density rho is writable as rho=M/V, where V=(4pi)/R^3, than (rhoA/rhoB)=(R_B/R_A)^3=64 Is this right? And then, how can i proceed for the third point? Thanks a lot.