For the descent of an AES moving in a circular orbit, it must be changed so that it touches the surface of the Earth

For the descent of an AES moving in a circular orbit, it must be changed so that it touches the surface of the Earth. How can this be done in the most economical way? Determine the satellite descent time. Disregard the influence of the earth’s atmosphere.

Similar orbits were developed in celestial mechanics by Roman. In this case, it is an elliptical orbit, at apogee touching the original circular orbit, and at perigee – the surface of the Earth. To transfer to this orbit in the direction of the orbital velocity vector, a short-term braking impulse is created. For a >> R3, the semi-major axis of the new orbit will be 2 times less than the previous one, and the time of descent to the Earth is equal to half the period of the satellite’s motion in an elliptical orbit.

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