Slingshot effect and the conservation of momentum?

Darcie Peraha: But thank you. It makes sense

Logan Bero: This is a conservation of energy problem--not conservation of momentum.The simplest way to do this is to work in Saturn's frame of reference.Calculate the speed of the spacecraft with respect to Saturn.v' initial = vspacecraft - vsaturnThen, according to conservation of energy, the spacecraft leaves with the same kinetic energy (and hence speed) with which it entered, but (they tell you) it flies off in the opposite direction.v' final = -v' initialSo the last step is to convert back to the sun's reference frame:v final = v' final + vsaturn= 2 vsaturn - vspacecraftThe masses don't matter except to establish (in case you didn't know) that the mass of Saturn is much, much bigger than that of the satellite, so it doesn't pick up a significant amount of kinetic energy in the interaction.--I'm not saying momentum isn't conserved. It's just that it isn't really useful for solving this problem. Because Saturn is so ! much bigger than the satellite, you don't need it. You can just assume that the satellite doesn't lose any energy to Saturn. If they wanted to make this problem non-trivial, they could make the satellite a big moon or something with a mass which is significant compared to Saturn's. Then you have to consider conservation of momentum AND conservation of energy....Show more

Toby Caswell: Momentum is always conserved. Although energy is always conserved, it takes many different forms, unlike momentum. And considering this came straight out of a chapter all about momentum...

Pam Rampadarat: Really great Q. It bothered me until I talked to an astronomerKey ideas: The interaction is gravitational, no physical contact.Energy is conserved, Momentum (P) is conserved.Because of the huge mass difference there is no measurable change in Saturn's P or E.There is a point of view. From the sun (or earth); from Saturn and from the space craft .The laws of physics are the s! ame for all but the apparent motions differ.Point of view satu! rn: Space craft approaches at Vs (V seen by Saturn), just misses, swings around, and leaves at Vs opposite direction.PoV earth: Craft approaches Saturn at Ve , Saturn moves Vs toward the craft.they "almost collide". Craft leaves with Ve + 2Vs because it not only had to leave with the speed of saturn just to turn around it had to leave at twice its Vs approach speed to get out of Saturn's way. PoV earth the craft gained kinetic energy. How?At the expense of Saturn's, P and E but the change was too small for earth measure.The analogy is: Pitcher throws ball, Batter swings bat, ball and bat collide, P,E exchange. Mass Bat (and batter) >> ball.Ball has V pitcher + 2 V Bat., Home run. Ball went out of the park. Spaceship goes out of the solar system....Show more

Kenneth Blacker: Slingshot Effect