Definition
Apogee is the point of an orbit around the Earth where the body is farthest from the Earth's centre, from the Greek apo, away from, and gē, Earth. It lies opposite the perigee, at the other end of the major axis. Its distance is a (1 + e), where a is the semi-major axis and e the eccentricity.
The generic word is apoapsis; around the Sun it becomes aphelion, around Jupiter apojove, around the Moon apolune. By Kepler's second law, the body moves slowest at apogee, so it spends more time in the far half of its orbit than in the near half.
The Moon at apogee
The Moon's apogee distance ranges from about 404,000 km to about 406,700 km. This range of about 2,700 km is much narrower than the range of perigee distances, about 14,000 km: the Sun's perturbation stretches and compresses the near end of the orbit far more than the far end.
At apogee the Moon's apparent diameter falls to about 29.4′, against 33.5′ at the closest perigees, and its horizontal parallax drops to about 54′. The interval between two apogees is the anomalistic month, 27.555 days on average, but individual intervals vary by more than a day.
| Distance | Apparent diameter | Disc area |
|---|---|---|
| 356,500 km (perigee) | 33.5′ | 1.30 |
| 384,400 km (mean) | 31.1′ | 1.12 |
| 406,700 km (apogee) | 29.4′ | 1.00 |
Micromoons and annular eclipses
A full Moon near apogee, sometimes called a micromoon, is the smallest full Moon of the year, about 12 % smaller in diameter than a perigee full Moon. It is also slightly fainter, and the tides at that time are weaker.
Apogee matters most for solar eclipses. The Sun's apparent diameter ranges between 31.6′ and 32.7′. When the new Moon is near perigee its disc is larger than the Sun's and the eclipse can be total; near apogee the Moon is too small to cover the Sun, and a bright ring remains around it: the eclipse is annular. Because the Moon is more often far than near, annular eclipses are slightly more frequent than total ones.
Apogee in spaceflight
In spaceflight, apogee is where orbits are reshaped most cheaply. A burn at apogee raises the perigee; a burn at perigee raises the apogee. Communication satellites are first placed on a geostationary transfer orbit, with a low perigee and an apogee near 35,786 km altitude, and an apogee engine then circularises the orbit at that altitude, where the period equals one sidereal day.
| Orbit | Perigee | Apogee | Period |
|---|---|---|---|
| Low orbit (ISS) | 410 km | 420 km | 92 min |
| Transfer (GTO) | 200–600 km | 35,800 km | 10.5 h |
| Molniya | 600 km | 39,700 km | 12 h |
| Geostationary | 35,786 km | 35,786 km | 23 h 56 min |
Molniya orbits use the long, slow passage through apogee on purpose: with the apogee placed over high northern latitudes, the satellite hangs high in the sky for about eight hours of each twelve-hour orbit, which suited Soviet communications at latitudes poorly covered by geostationary satellites.
Computing apogee
Meeus computes the lunar apogee with the same mean formula as the perigee, using values of k ending in .5, followed by a separate, shorter series of periodic terms. The periodic correction for apogee stays within about half a day of the mean instant, and the apogee parallax is given by its own series, from which the distance follows:
distance = 6378.14 km / sin(parallax)For artificial satellites, apogee and perigee are simply computed from the orbital elements: r = a (1 ± e), minus the Earth's equatorial radius, 6,378 km, to get altitudes.
Explore it on AstroAlgos
Frequently asked questions
How far is the Moon at apogee?
Between about 404,000 and 406,700 km from the Earth's centre. Its average distance is 384,400 km.
What is the difference between apogee and aphelion?
Apogee is the farthest point of an orbit around the Earth; aphelion is the farthest point of an orbit around the Sun. The Earth is at aphelion in early July, about 152.1 million km from the Sun.
Why are some solar eclipses annular?
Because the Moon is near apogee. Its disc is then smaller than the Sun's and cannot cover it completely, leaving a bright ring around the dark Moon.
