# Universal Gravitation

by dekoi
Tags: gravitation, universal
 P: n/a 1.) Consider attached image (P13.41). Determine the escape speed for a rocket on the far side of Ganymede. The escape speed from Ganymede without Jupiters influence would be $$\sqrt{\frac{2GM_{gan.}}{r_{gan.}}}$$. Now the ship will have a velocity equal to that of the escape velocity needed to escape Ganymede when it leaves Ganymede, so in order to escape Jupiter's gravitational field, we would need a velocity which is less. That is: $$v_{esc} = v_{gan.} - v_{jup.}$$ To calculate v_jup, we would use the distance from ganymede to Jupiter. Im not sure why my method is incorrect. 2.) A 1000kg sattelite orbits the Earth at a constant altitude of 100km. How much energy must be added to the system to move the sattellite into a circular obrit with altitude 200km? $$W = \Delta U = U_{new} - U_{original}$$ Now this turns into: $$W = \frac{-GMm}{2} (\frac{1}{r_{new}} - \frac{1}{r_{original}}$$ . This, once again, does not give me the correct answer. Thanks.