The gravitational slingshot effect. Figure shows the planet Saturn moving in the negative 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 approaches Saturn. When far from Saturn, it moves in the 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.

FIGURE 7-47 Problem 81

Equation Transcription:

Text Transcription:

9.6 km/s

5.69 x 10^26 kg

10.4 km/s

Solution 81GP:

We have to determine the final speed with which spacecraft was moving, as its direction of motion was reversed due to gravitational attraction between the spacecraft and Saturn.

Step 1 of 5

Concept:

The interaction between the Saturn and the spacecraft is elastic, because the force of gravity is conservative. Thus kinetic energy is conserved in this interaction.

Relative velocity of body A with respect to body B having velocity respectively, is given as,