In astronomy:
* Perigee: This is the point in an orbit where the object is closest to Earth.
In general usage:
* Nadir: This refers to the lowest point or the point of greatest adversity or despair.
* Low point: This is a more general term for a point of minimum achievement or success.
* Zenith: While not exactly an antonym, zenith is the opposite of nadir, meaning the highest point, which could also be considered an antonym for apogee in some contexts.
The best antonym depends on the specific meaning of apogee in the context.