A stable orbit doesn’t have to be circular, it can be quite eccentric. Now if any orbit, circular or eccentric is in the atmosphere it will become unstable and eventually the object will fall. My point was that the blanket statement that slowing down from a circular orbit automatically meant re-entry is incorrect.
You fire your rocket along the trajectory of your existing circular orbit to insert yourself into an elliptical orbit that has a perigee equal to the distance of your original circular orbit. If you don’t fire it again, you will return to the orbital distance of your original circular orbit once each rotation. If you fire them again at perigee, you will increase the apogee of your elliptical orbit, but still return to the altitude of your original circular orbit each time around.
To circularize your elliptical orbit, you wait until you reach apogee, and again fire along the trajectory of the orbit enough to make the elliptical perigee equal to the current apogee. Now you have a higher circular orbit, but are moving along it at a reduced speed compared to the circular orbit that you started in.
To give yourself a mind picture of it, consider throwing a baseball in a vacuum. You throw it up. It slows down as it rises, and eventually, stops rising, then it starts to fall, and accelerates as is does. Same thing in orbits. You increase your velocity with a rocket, and it coasts upwards, slowing down until it reaches its new altitude. If you don’t do anything else, it then “falls” down to the original orbital altitude, gaining speed as it does. It will not remain in that old orbit, though, since it is again moving too fast, and must climb again, back to the same altitude it did before. To stop the rise and fall, you have to add velocity along the orbital trajectory at the top of the ellipse, or apogee.
In fact the rocket accelerations are not instantaneous, and different length of burn in different parts of the orbit will produce different resultant orbits. It’s rocket science, man! But smart guys with big computers do it pretty much routinely now days.
Tris
“It should be possible to explain the laws of physics to a barmaid.” ~ Albert Einstein ~
“You should see the place where Einstein used to drink!” ~ Triskadecamus ~