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Problem 105 Medium Difficulty

The gravitational slingshot effect. Figure 55 shows the planet Saturn moving in the negative $x$ direction at its orbital speed (with respect to the Sun) of 9.6 $\mathrm{km} / \mathrm{s}$ . The mass of Saturn is $5.69 \times 10^{26} \mathrm{kg} .$ A spacecraft with mass 825 $\mathrm{kg}$ approaches Saturn. When far from Saturn, it moves in the $+x$ direction at 10.4 $\mathrm{km} / \mathrm{s} .$ The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as 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.

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Physics 101 Mechanics

Physics for Scientists and Engineers with Modern Physics

Chapter 9

Linear Momentum

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Video Transcript

Okay, Sir Gregory in chapter nine. Problem 105 year. So this is the gravitational slingshot effect which shows here, the planet Saturn moving in the negative X direction at its orbital speed with respect ofhis son of 9.6 kilometers per second. It says here the mass of sound is 569 times in 10 of the 26 kilograms in a spacecraft with a mass off 8 to 5 kilogram approaches Saturn. But far from sadder, it's moves in the potted vex direction at 10.4 kilometers per second. Gravitational sonic swing around and head off. We want to estimate the final speed. Okay, So the key here is that the interaction of the planet and spacecraft is elastic because the force of gravity is conservative. Someone can use equation or in Courtney, and we know that which is the A minus. Phoebe is negative. The a prime plus beauty crap. So now we know BB in the crime are the same because this has roughly no affect on side without massive ISS. So we can let V b equal evening crime of negative non great six kilometers and we know that d a here 10.4 kilometers per second. OK, so we put that in a week, a be a crime that is negative 29.6 kilometers per second. So it almost tripled the nude in the spacecraft and reverse direction says is why this back in such a useful to use?

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Two bumper cars in an amusement park ride collide…

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Physics for Scientists and Engineers with Modern Physics

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Watch More Solved Questions in Chapter 9

Video Transcript

Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics

Christina Krawiec

Liev Birman

Farnaz Mohseni

Zachary Mitchell

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Physics for Scientists and Engineers with Modern Physics

Christina Krawiec

Liev Birman

Farnaz Mohseni

Zachary Mitchell

Douglas C. GiancoliPhysics for Scientists and Engineers with Modern Physics

Christina Krawiec

Liev Birman

Farnaz Mohseni

Zachary Mitchell

Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics