Perigee

Definition

Perigee is the point of an orbit around the Earth where the orbiting body is closest to the Earth's centre. The word comes from the Greek peri, near, and gē, Earth. The opposite point is the apogee. The general term for either point, whatever the central body, is an apsis; the closest point is a periapsis.

Each central body has its own word: perihelion around the Sun, perigee around the Earth, perijove around Jupiter, perilune or periselene around the Moon. The geometry is always the same: at perigee the distance is a (1 − e), where a is the semi-major axis and e the eccentricity.

The Moon at perigee

The Moon's mean distance is 384,400 km and its mean eccentricity 0.055, but the Sun's attraction constantly deforms the orbit. As a result, the perigee distance is not fixed: it ranges from about 356,400 km to about 370,400 km, depending on where the Sun is relative to the Moon's line of apsides. The closest perigees happen when perigee coincides with a new or full Moon.

The Moon returns to perigee every anomalistic month of 27.555 days, about 5.5 hours longer than the sidereal month, because the line of apsides advances eastward by a full turn in 8.85 years.

Supermoons

A full Moon near perigee is popularly called a supermoon. Compared with a full Moon near apogee, it looks about 14 % wider and about 30 % brighter. The difference is real but hard to notice without a side-by-side comparison, because there is nothing to compare the Moon to in the sky.

The full Moon of 14 November 2016, at 356,509 km, was the closest since January 1948; the next one that close will be on 25 November 2034. Since the full Moon advances by about one month along the anomalistic cycle each lunation, supermoons come in runs of three or four consecutive months, about every 13.9 months: the time for the synodic and anomalistic months to realign.

Perigean tides

The tidal force varies as the inverse cube of the distance. Between apogee and perigee the Moon's distance changes by about 12 %, so its tidal force changes by about 40 %. When perigee coincides with a new or full Moon, the solar and lunar tides add up at their strongest: these perigean spring tides give the highest tidal ranges of the year, with coastal flooding where the weather adds a storm surge.

Satellites at perigee

For artificial satellites, perigee and apogee are usually given as altitudes above the surface rather than distances from the centre. A satellite in a low, nearly circular orbit, such as the International Space Station around 400 to 420 km, has almost equal perigee and apogee. A geostationary transfer orbit has its perigee at a few hundred kilometres and its apogee near 35,786 km, where an engine burn circularises the orbit.

Perigee is where the satellite moves fastest and dips deepest into the residual atmosphere. Atmospheric drag at perigee lowers the apogee first, so orbits decaying from drag become more and more circular before reentry.

Computing the time of perigee

Meeus gives a dedicated method for the instants of lunar perigee and apogee. A mean instant comes from a linear formula in an integer k counting the anomalistic months since January 2000; k is an integer for a perigee and an integer plus 0.5 for an apogee:

JDE = 2451534.6698 + 27.55454989 k − 0.0006691 T² − …k ≈ (year − 1999.97) × 13.2555

Periodic terms in the elongation of the Moon, the mean anomaly of the Sun and the argument of latitude are then added. The perigee correction is much larger than the apogee one, up to almost two days against about half a day, because the solar perturbation acts more strongly on the perigee. Compared with a full lunar theory, the instants come out within about half an hour for perigee and a few minutes for apogee, and the parallax, hence the distance, within a fraction of an arc second.

Explore it on AstroAlgos

• Semidiameter — the Moon's apparent size from perigee to apogee
• Apogee — the farthest point from the Earth
• Perihelion — the same idea around the Sun
• All-sky disk — where the Moon is tonight