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**The gravitational slingshot effect. In the diagram below, the planet Saturn moving in the negative xdirection at its orbital speed (with respect to the Sun) of 9.6 km/s. The mass of Saturn is 5.96 × 1026 kg. A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the +x-direction at 10.4 km/s. The gravitational attraction of Saturn (aconservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as a dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.**

m1v1 + m2v2= m1'v1' + m2'v2'

It seems like a simple equation. I know that the speed of Saturn and the mass of Saturn are not going to change. (this is true?) So the focus of this problem should be the spacecraft.

m1v1 = m1'v1' for the spacecraft.

I'm confused about how to factor in the gravitational force of Saturn? and this is obviously (?) important for finding the final speed of the air craft.

i think this is how you would find the gravitation acceleration of saturn:

F = Gm/ r^2; where G is a constant, m= mass of Saturn, and r= the radius of Saturn

= (6.67 X 10^-11 N m^2/kg)(5.96 × 1026 kg)/ (60,268,000^2 m )

= 10.9

is this right? BTW, i'm not so sure about the radius of Saturn...I got different numbers on the web

Okay, now I dont know what to do...

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