A spacecraft traveling along a parabolic path toward the planet Jupiter is expected to reach point A with a velocity v A of magnitude 26.9 km/s. Its engines will then be fired to slow it down, placing...

A spacecraft traveling along a parabolic path toward the planet Jupiter is expected to reach point A with a velocity v_A
of magnitude 26.9 km/s. Its engines will then be fired to slow it down, placing it into an elliptic orbit which will bring it to within 100
  10³
km of Jupiter. Determine the decrease in speed D_v
at point A which will place the spacecraft into the required orbit. The mass of Jupiter is 319 times the mass of the earth.