350 x 103 km 100 x 103 km B Jupiter VA
A spacecraft traveling along a parabolic path toward the planet Jupiter is expected to reach point vA 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 ? 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.
Given data:
The velocity at the point A is VA1=26.9 km/s.
The mass of the Jupiter is MJ=319ME
Determine the value of decrease in speed (ΔV):
From the law of conservation of angular momentum:
Where,
rA is the distance of A from the centre of the Jupiter.
rB is the distance of B from the centre of the Jupiter.
m is the mass
vA is the velocity at A.
vB is the velocity at B.
Substitute the values in the above equation.
Apply law of conservation of energy:
Energy at the point A= Energy at the point B
Where,
KEA is the kinetic energy at the point A.
PEA is the gravitational potential energy at A.
KEB is the kinetic energy at the point B.
PEB is the gravitational potential energy at B.
Substitute the values in the above equation.
Substitute equation 1 in the above equation.
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