1.) Consider attached image (P13.41). Determine the escape speed for a rocket on the far side of Ganymede.(adsbygoogle = window.adsbygoogle || []).push({});

The escape speed from Ganymede without Jupiters influence would be [tex]\sqrt{\frac{2GM_{gan.}}{r_{gan.}}}[/tex]. 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: [tex]v_{esc} = v_{gan.} - v_{jup.} [/tex] 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?

[tex]W = \Delta U = U_{new} - U_{original} [/tex] Now this turns into:

[tex] W = \frac{-GMm}{2} (\frac{1}{r_{new}} - \frac{1}{r_{original}}[/tex] . This, once again, does not give me the correct answer.

Thanks.

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# Universal Gravitation

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