Volcanoes on Io?. Jupiter’s moon to has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface, to has a mass of 8.94 × 1022 kg and a radius of 1815 km. Ignore any variation in gravity over the 500-km range of the debris. How high would this material go on earth if it were ejected with the same speed as on Io?

Solution 16E The acceleration due to gravity of a planet is given by g = GM p …..(1), here M is the mass p r2 p of the planet, r is the radius of the planet. Given that, M = 8.94 × 10 22kg Io 3 Radius r = 1815 km = 1815 × 10 m 11 2 2 Gravitational constant G = 6.67 × 10 N.m /kg Substituting these values in equation (1), we can calculate the acceleration due to gravity of the planet. For Io, 6.67×1011N.m /kg ×8.94×10 22kg The acceleration due to gravity is g Io = 3 2 2 (1815×10 ) m g = 1.81 m/s 2 Io Now, given that volcanic...