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

 

[alphy]

I would like to clarify that the minimum number of rocket burns required to change the orbit of a satellite and rotate its major axis by 90 degrees would depend on several factors such as the mass and velocity of the satellite, the altitude of its orbit, and the type of rocket propulsion being used. It is not a simple matter of just two burns.

In general, changing the orbit of a satellite requires careful planning and precise calculations to ensure the desired outcome is achieved. Depending on the specific situation, it may take more than two burns to achieve the desired change in orbit.

Additionally, the statement that the final and initial energy must be the same is not entirely accurate. While the total energy of the satellite may remain constant, the distribution of kinetic and potential energy can vary depending on the orbital parameters.

In summary, the minimum number of rocket burns required to change the orbit of a satellite and rotate its major axis by 90 degrees cannot be determined without specific details and calculations. It is a complex process that requires careful consideration and cannot be simplified to just two burns.