Orbital period

The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars. It may also refer to the time it takes a satellite orbiting a planet or moon to complete one orbit.

Not to be confused with Rotation period.

For celestial objects in general, the orbital period is determined by a 360° revolution of one body around its primary, e.g. Earth around the Sun.

Periods in astronomy are expressed in units of time, usually hours, days, or years.

a is the orbit's

semi-major axis

G is the ,

gravitational constant

M is the mass of the more massive body.

a is the sum of the of the ellipses in which the centers of the bodies move, or equivalently, the semi-major axis of the ellipse in which one body moves, in the frame of reference with the other body at the origin (which is equal to their constant separation for circular orbits),

semi-major axes

M₁ + M₂ is the sum of the masses of the two bodies,

G is the .

gravitational constant

In celestial mechanics, when both orbiting bodies' masses have to be taken into account, the orbital period T can be calculated as follows:^[4]

where:

In a parabolic or hyperbolic trajectory, the motion is not periodic, and the duration of the full trajectory is infinite.

The synodic period is the amount of time that it takes for an object to reappear at the same point in relation to two or more other objects. In common usage, these two objects are typically Earth and the Sun. The time between two successive or two successive conjunctions is also equal to the synodic period. For celestial bodies in the solar system, the synodic period (with respect to Earth and the Sun) differs from the tropical period owing to Earth's motion around the Sun. For example, the synodic period of the Moon's orbit as seen from Earth, relative to the Sun, is 29.5 mean solar days, since the Moon's phase and position relative to the Sun and Earth repeats after this period. This is longer than the sidereal period of its orbit around Earth, which is 27.3 mean solar days, owing to the motion of Earth around the Sun.

oppositions

The draconitic period (also draconic period or ), is the time that elapses between two passages of the object through its ascending node, the point of its orbit where it crosses the ecliptic from the southern to the northern hemisphere. This period differs from the sidereal period because both the orbital plane of the object and the plane of the ecliptic precess with respect to the fixed stars, so their intersection, the line of nodes, also precesses with respect to the fixed stars. Although the plane of the ecliptic is often held fixed at the position it occupied at a specific epoch, the orbital plane of the object still precesses, causing the draconitic period to differ from the sidereal period.^[5]

nodal period

The anomalistic period is the time that elapses between two passages of an object at its (in the case of the planets in the Solar System, called the perihelion), the point of its closest approach to the attracting body. It differs from the sidereal period because the object's semi-major axis typically advances slowly.

periapsis

Also, the tropical period of Earth (a ) is the interval between two alignments of its rotational axis with the Sun, also viewed as two passages of the object at a right ascension of 0 hr. One Earth year is slightly shorter than the period for the Sun to complete one circuit along the ecliptic (a sidereal year) because the inclined axis and equatorial plane slowly precess (rotate with respect to reference stars), realigning with the Sun before the orbit completes. This cycle of axial precession for Earth, known as precession of the equinoxes, recurs roughly every 25,772 years.^[6]

tropical year

Geosynchronous orbit derivation

– time that it takes to complete one revolution around its axis of rotation

Rotation period

Satellite revisit period

Sidereal time

Sidereal year

Opposition (astronomy)

List of periodic comets

Leap year

Bate, Roger B.; Mueller, Donald D.; White, Jerry E. (1971), Fundamentals of Astrodynamics, Dover