Glossary of Astronomical Terms/apogee
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Apogee is the highest altitude of a body in its orbit around the earth. The lowest point is the Perigee. The term is actually a specialized version of the more general term apoapsis, which is when two bodies are furthest apart, but is used more commonly than apoapsis.
Other, related terms include aphelion for the greatest separation an object has from the Sun, and apastron for the greatest separation an object has from any star.