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So i'm doing this homework problem and its not working. This is it,

The radius of Saturn (from the center to just above the atmosphere) is 60300 km (60300✕103 m), and its mass is 570✕1024 kg. An object is launched straight up from just above the atmosphere of Saturn.

(a) What initial speed is needed so that when the object is far from Saturn its final speed is $24500\, m s^{-1}$ ?

(b) What initial speed is needed so that when the object is far from Saturn its final speed is $0\, m s^{-1}$ ? (This is called the "escape speed.")

I know $E_f = E_i + W$, what I don't know is how am I suppose to find kinetic energy of the object if I don't know its mass, and again how do you find gravitational potential energy if I don't know the objects mass. How far away is 'far from Saturn', so I can find radius final.

What I currently have is,

$$\frac 1 2(24500)^2 + \left(\frac {-GM} {r_f}\right) = \frac 1 2 v_i^2 + \left( \frac {-GM} {r_i}\right)$$

mostly I don't see how to get radius final.

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  • $\begingroup$ Hint: If both sodes of your equation are proportional to $m$, then mass will can el out and the final answer will not depend on $m$. $\endgroup$ – ZeroTheHero Jul 30 '17 at 3:08
  • $\begingroup$ @ZeroTheHero Ok, and how do i find radius final $\endgroup$ – michael lee Jul 30 '17 at 3:16
  • $\begingroup$ If you figure out the velocity as a function of final radius r, you will notice that it decreases as final r gets bigger. But at large r, there isn't much change. At infinite r, you reach a limiting value. The question is asking that the limiting value be 24500 m/s. In other words, the final radius is infinite. $\endgroup$ – mmesser314 Jul 30 '17 at 4:00
  • $\begingroup$ @mmesser314 thats what i needed i got it now $\endgroup$ – michael lee Jul 30 '17 at 4:10
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From above the atmosphere, you can consider Saturn a point mass. After that, it's all potential vs kinetic energy.

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  • $\begingroup$ how do i find final potential energy, i have Rf on one side and Vi on another side, i cant find one unless i know the other $\endgroup$ – michael lee Jul 30 '17 at 3:51

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