Often in designing orbits for satellites, people use what is termed a "gravitational slingshot effect." The idea is as follows: A satelite of mass m, and speed v, circles around a planet of mass m, that is moving with speed v, in the opposite direction. See the diagram below: Vs,i Although the satellite never touches the planet, this interaction can still be treated as a collision because of the gravitational interaction between the planet and satellite during the slingshot. Since gravity is a conservative force, the collision is elastic. Use an raxis with positive pointing to the right. Solve for the unknowns below algebraically first, then use the following values for the parameters. m, - 2.40E+24 kg m, - 880 kg Vu- 3.050E+3 m/s i-6.10E+3 m/s Solve for the final velocity of the satellite after the collision.

Elements Of Electromagnetics
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Gravitational Slingshot
Often in designing orbits for satellites, people use what is termed a "gravitational slingshot effect." The idea is as follows: A satellite of mass m; and speed v,i circles around a planet of mass m, that is moving with speed v in the opposite direction. See the
diagram below:
Although the satellite never touches the planet, this interaction can still be treated as a collision because of the gravitational interaction between the planet and satellite during the slingshot. Since gravity is a conservative force, the collision is elastic.
Use an x-axis with positive pointing to the right.
Solve for the unknowns below algebraically first, then use the following values for the parameters.
m, = 2.40E+24 kg
m; = 880 kg
Viz = 3.050E+3 m/s
Vpiz = -6.10E+3 m/s
Solve for the final velocity of the satellite after the collision.
Transcribed Image Text:Gravitational Slingshot Often in designing orbits for satellites, people use what is termed a "gravitational slingshot effect." The idea is as follows: A satellite of mass m; and speed v,i circles around a planet of mass m, that is moving with speed v in the opposite direction. See the diagram below: Although the satellite never touches the planet, this interaction can still be treated as a collision because of the gravitational interaction between the planet and satellite during the slingshot. Since gravity is a conservative force, the collision is elastic. Use an x-axis with positive pointing to the right. Solve for the unknowns below algebraically first, then use the following values for the parameters. m, = 2.40E+24 kg m; = 880 kg Viz = 3.050E+3 m/s Vpiz = -6.10E+3 m/s Solve for the final velocity of the satellite after the collision.
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