What is apogee?

A satellite in an oval orbit is not travelling at a steady speed. It slows as it climbs towards apogee and speeds up as it falls back towards the near point — for the same reason a ball thrown upwards is slowest at the top. All of that is the same trade between height and speed, running continuously.

That makes apogee a useful place to fire an engine. A push there raises the opposite side of the orbit, which is how a spacecraft turns a stretched oval into the circle it actually wants. Launches often use this deliberately: the rocket puts the payload into an oval, coasts to apogee, and only then burns again to circularise.

It works the other way too. Firing against the direction of travel at apogee lowers the far side, and that is one way of beginning a controlled return.

A useful sanity check: apogee and perigee are measured from the centre of the Earth in the mathematics, but almost always quoted as heights above the surface in conversation. The difference is Earth’s radius, 6,371 km, which is far from negligible.

The word only applies to orbits around Earth. Around the Sun it is aphelion; around the Moon, apolune. The pattern is the same everywhere — every orbit has a far point unless it is a perfect circle.