Changing the orbit of a satellite, minimum rocket burns.

[Spinnor]

Suppose we have a satellite in an elliptical orbit around the Earth with the major axis pointed towards some fixed point in the heavens. What is the minimum number of rocket burns so that the major axis is rotated 90 degrees and the final and initial energy are the same. Is the number 2?

At closest approach to the Earth, slow down, one burn, orbit circular, 90 degrees later speed back up, one more burn or at farthest approach speed up, 90 degrees later slow down, again two burns?

Thanks for any help!

 

[mfb]

While your way might be the most energy-efficient method: You can accelerate at other points, too, achieving every orbit which intersects the old orbit in one point, with a single, short burn. With a longer time for the acceleration, you can reach non-intersecting orbits, too.

 

[Spinnor]

While your way might be the most energy-efficient method: You can accelerate at other points, too, achieving every orbit which intersects the old orbit in one point, with a single, short burn. With a longer time for the acceleration, you can reach non-intersecting orbits, too.

Thank you mfb! I have to think about the above. This problem I think is related to a similar problem, given a 2 dimensional harmonic oscillator that has some "orbit", what impulses acting on the "point mass" change the orbit? Seems like there are 2 classes of change? Impulses that change the energy and orbit and impulses that only change the orbit?

If I always "push" on a satellite perpendicular to its velocity then I don't change the energy, right?

Thanks for any help!

 

[mfb]

impulses that only change the orbit?

That is just a special case in the whole range of energies which can be reached.

If I always "push" on a satellite perpendicular to its velocity then I don't change the energy, right?

Right