With some more detail on the mechanics: Here's a screenshot of an orbit in Kerbal Space Program, an excellent NASA-simulator game (you have a spaceport and mak

With some more detail on the mechanics: Here's a screenshot of an orbit in Kerbal Space Program, an excellent NASA-simulator game (you have a spaceport and make + fly rockets and do science): https://wiki.kerbalspaceprogram.com/wiki/File:KerbalEccentricity.jpg https://wiki.kerbalspaceprogram.com/wiki/File:KerbalEccentri... On the blue orbit, you can see Ap and Pe. Ap is the apogee; the place in the orbit where the spacecraft is closest to the earth. Pe is the perigee, the place where the spacecraft is farthest from the earth. Since the blue orbit is mostly circular, they are at about the same altitude. If you look at the large white orbit, the apogee would be the leftmost point, close to the apogee of the blue orbit. The perigee would be all the way at the right of the image. When your spacecraft is at position X, thrusting your engines will not meaningfully change your current position - the acceleration they generate is negligible to the speed at which you are moving. However, the maneuver will change your speed, which affects your orbit. At the apogee, if you thrust in the direction you are moving, your perigee will increase - the orbit will become even more eccentric. Example: at the apogee you are moving at 100 miles per second. Thrusting the engines will not change your current position much; your current position is determined by your 100 miles per second speed and where you came from. But the maneuver will change your speed to 105 miles per second, which will cause your perigee to become much farther away from the earth. However your apogee will stay in the exact same position. Why? Because in orbit you are basically flying sideways while gravity pulls you down. In a circular orbit this balances out into you flying around in a circle. But if you go faster, you're going more sideways while gravity pulls the same amount. So your orbit becomes more elongated. You can thrust in the direction of movement at any point in orbit, and it will increase the altitude of the orbit on the opposite side of where you are at - if you thrust at apogee the perigee altitude increases, and in the white elongated orbit if you thrust between the apogee and perigee your orbit will become more circular and bigger. Similarly to make an eccentric orbit circular, you get to the apogee and then use the engines to slow down, which brings down the perigee. Since thrusting changes your position on the opposite side of the orbit, the most efficient way to increase your perigee is to thrust while at the apogee. The NASA thing is basically going into an elongated orbit between the Sun and Jupiter, coming back to the apogee near the Sun, and then thrusting. The difference in efficiency between thrusting at the apogee of an orbit and just thrusting in a straight line out into space is really huge. Though I'm not sure why the extra gravity of the Sun makes the maneuver more efficient. If you're interested in this you should definitely play KSP. It's a great game and gives you a great intuitive sense of how these things work.