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A rocket in free flight is approaching a planet of mass M as shown above. Free flight means that the rocket is only subjected to the force by the planet. The rocket is initially travelling on a trajectory T with eccentricity e. At A, the rocket turns on very briefly its engine to change velocities to switch to an elliptical path from A to B. Then, from A to B, the rocket is again in free flight. We are given that A is a point of closest approach for the trajectory T. Find the change of velocity at A (write it as v­final – vinitial where v­final is the velocity at A on the elliptical path A to B, and vinitial is the velocity at A on the trajectory T) Find the velocity at B.

A rocket in free flight is approaching a planet of mass M as shown above. Free flight means that the rocket is only subjected to the force by the planet. The rocket is initially travelling on a trajectory T with eccentricity e. At A, the rocket turns on very briefly its engine to change velocities to switch to an elliptical path from A to B. Then, from A to B, the rocket is again in free flight. We are given that A is a point of closest approach for the trajectory T. Find the change of velocity at A (write it as v­final – vinitial where v­final is the velocity at A on the elliptical path A to B, and vinitial is the velocity at A on the trajectory T) Find the velocity at B.

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A rocket in free flight is approaching a planet of mass M as shown above. Free flight means that the rocket is only subjected to the force by the planet. The rocket is initially travelling on a trajectory T with eccentricity e. At A, the rocket turns on very briefly its engine to change velocities to switch to an elliptical path from A to B. Then, from A to B, the rocket is again in free flight.

We are given that A is a point of closest approach for the trajectory T.

  1. Find the change of velocity at A (write it as v­final – vinitial where v­final is the velocity at A on the elliptical path A to B, and vinitial is the velocity at A on the trajectory T)

  2. Find the velocity at B.
  3.  

 

part of the ellipse going through A and B A B 0. rocket trajectory with eccentricity e R
Transcribed Image Text:part of the ellipse going through A and B A B 0. rocket trajectory with eccentricity e R
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