Calculating Escape Speed and Orbital Energy in Universal Gravitation

[dekoi]

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.

 

[mezarashi]

For 1, you should try writing out the complete gravitational potential function first, then equivalate it to KE. That would make more sense to me than blind velocity subtraction/addition without solid principles.

For 2, consider both its change in gravitational potential and kinetic energies.

 

[dekoi]

I don't know how i could start the questions with the information you have given me. Could you give give some specific beginning-points please?

 

[mezarashi]

Assume that Jupiter is an absolute reference. From there, write out the gravitational potential due to Jupiter. Also, write out the potential due to the moon. How energy is needed to escape to an infinitely far away distance? Note that while on the moon, you already have some of this kinetic energy.

For 2, calculate the change in gravitational potential energy as you already have. Now calculate the change in kinetic energy. F = mv^2/r tells you the velocity (and thus corresponding kinetic energy) at any orbital distance.