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After the international physics olympiad on Bali all olympionics went relax to the beach on the south side of the island in Indonesia. They saw coral reef disappearing in the tidal wave and realized that, after full moon night and summer day, high tide happened only once (during 24-hour period). Aboriginals confirmed this observation, but could not explain it. Can you do it?

When the star is compressed (or any other body) into a sphere of radius $r_{g}$, the black hole is created. So called Schwarzschild's radius $r_{g}$ can be interpreted in classical physics as a radius of a body of mass $M$, where the exit velocity is equal to the speed of light $c)$.

Knowing the mass of the star $M$ calculate Schwarzschild radius $r_{g}$ and critical density of the star $ρ$, at which it collapses into black hole. Solve for arbitrary values and then for the masses of Earth, Sun and the galaxy nucleus 100 billions heavier than Sun.

During the long term observations of Jupiter's moon Io it was noticed that the the orbit time of the Io around Jupiter (e.g. time between two consecutive 'disappearances' of the moon behind Jupiter) is oscillating regularly between 42 h 28 min 21 s and 42 h 28 min 51 s (with the measurement error of 2 s).

Try to explain qualitatively and quantitatively observed changes. By quantity we mean to determine the magnitude of the source of this oscillations from the measurements. And of course including the estimation of the experimental error.

Check experimentally the equivalence of inertial mass (the mass in second Newton's law) and gravitational mass (the one in Newton's gravitational law).