Definition
The inclination i is the angle between the plane of an orbit and a reference plane. For bodies orbiting the Sun the reference is the ecliptic, the plane of the Earth's orbit; for artificial satellites it is the Earth's equator; for the moons of other planets it is often the planet's equator or its orbital plane.
Inclination is one of the six Keplerian elements. It ranges from 0° to 180°: from 0° to 90° the body moves in the same direction as the Earth (prograde orbit), from 90° to 180° in the opposite direction (retrograde orbit). The two places where the orbit crosses the reference plane are the ascending and descending nodes.
Inclinations of the planets
| Body | Inclination to the ecliptic |
|---|---|
| Mercury | 7.00° |
| Venus | 3.39° |
| Earth | 0° (by definition) |
| Mars | 1.85° |
| Jupiter | 1.30° |
| Saturn | 2.49° |
| Uranus | 0.77° |
| Neptune | 1.77° |
| Moon (around the Earth) | 5.15° |
| Pluto | 17.1° |
| Halley's comet | 162° (retrograde) |
All the planets move within a few degrees of the ecliptic, a fossil of the flat disc of gas and dust from which they formed. This is why the planets are always found along the zodiac band in the sky.
The ecliptic is a convenient but not a privileged plane. The invariable plane, perpendicular to the total angular momentum of the solar system and dominated by Jupiter, is a more natural reference: the Earth's orbit is tilted by about 1.6° to it.
Why eclipses and transits are rare
If the Moon's orbit lay in the ecliptic, there would be a solar eclipse at every new Moon and a lunar eclipse at every full Moon. Because of its 5.15° inclination, the Moon usually passes above or below the Sun or the Earth's shadow. An eclipse needs a new or full Moon close to one of the nodes, which happens only during two eclipse seasons a year.
The same geometry makes transits rare. Venus overtakes the Earth every 584 days, but because its orbit is inclined by 3.4° it usually passes up to about 8° north or south of the Sun. Transits of Venus only happen when inferior conjunction falls near a node, in June or December: the last were in 2004 and 2012, the next in December 2117.
The Moon's changing tilt to the equator
Relative to the ecliptic the Moon's inclination stays close to 5.15°, but its nodes regress around the ecliptic in 18.6 years. Relative to the Earth's equator, the tilt therefore varies between 23.44° − 5.15° = 18.3° and 23.44° + 5.15° = 28.6°.
At the maximum, called a major lunar standstill, the Moon's declination swings each month from −28.6° to +28.6°: it rises and sets at extreme azimuths and stands very high or very low at culmination. The last major standstill was centred on early 2025; the next is around 2043.
Inclination of artificial satellites
For Earth satellites the inclination is measured from the equator, and it decides which latitudes the satellite flies over: a satellite never passes over latitudes higher than its inclination (or 180° − i for a retrograde orbit).
| Orbit | Typical inclination | Why |
|---|---|---|
| Geostationary | 0° | Stays above one point of the equator |
| International Space Station | 51.6° | Reachable from Baikonur; covers most inhabited areas |
| Polar | about 90° | Overflies the whole Earth as it turns underneath |
| Sun-synchronous | about 98° | The equatorial bulge turns the orbit plane once a year, keeping a fixed local time |
| Molniya | 63.4° | The apogee stays over the northern hemisphere |
A launch site at latitude φ reaches inclinations of at least φ without an expensive change of plane. This is why launches to geostationary orbit favour sites close to the equator.
Inclination in the computations
To turn orbital elements into a position, the inclination enters the rotation from the orbital plane to the ecliptic. With the argument of latitude u (angle from the ascending node along the orbit), the heliocentric ecliptic latitude is:
sin b = sin i · sin uThe latitude is therefore zero at the nodes (u = 0° or 180°) and reaches ±i half-way between them. In Astronomical Algorithms, Meeus gives the inclinations of the planets as slowly varying polynomials in time, referred either to the ecliptic of date or to the fixed ecliptic of J2000.0.
Explore it on AstroAlgos
Frequently asked questions
Which planet has the most inclined orbit?
Mercury, with 7.0° to the ecliptic. All the other planets are within 3.4°. Pluto, now a dwarf planet, is inclined by 17°.
What does an inclination above 90° mean?
That the orbit is retrograde: the body moves around the Sun, or around its planet, in the opposite direction to the Earth. Halley's comet (162°) and Neptune's moon Triton are well-known examples.
Why don't we have an eclipse every month?
Because the Moon's orbit is inclined by about 5° to the ecliptic. At most new and full Moons the Moon passes north or south of the Sun or of the Earth's shadow; eclipses only occur when the Moon is close to a node.
