Orbital period Guide, Meaning , Facts, Information and Description
The orbital period is the time it takes a planet (or another object) to make one full orbit.
There are several kinds of orbital periods for objects around the Sun:
- The sidereal period is the time that it takes the object to make one full orbit around the sun, relative to the stars. This is considered to be an object's true orbital period.
- The synodic period is the time that it takes for the object to reappear at the same spot in the sky, relative to the Sun, as observed from Earth. This is the time that elapses between two successive conjunctions with the sun and is the object's Earth-apparent orbital period. The synodic period differs from the sidereal period since Earth itself revolves around the sun.
- The draconitic period is the time that elapses between two passages of the object at its ascending node, the point of its orbit where it crosses the ecliptic from the southern to the northern hemisphere. It differs from the sidereal period because the object's line of nodes typically precesses or recesses slowly.
- The anomalistic period is the time that elapses between two passages of the object at its perihelion, the point of its closest approach to the Sun. It differs from the sidereal period because the object's semimajor axis typically precesses or recesses slowly.
- The tropical period, finally, is the time that elapses between two passages of the object at right ascension zero. It is slightly shorter than the sidereal period because the vernal point precesses.
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2 Calculation |
Copernicus devised a mathematical formula to calculate a planet's sidereal period from its synodic period.
Using the abbreviations
Relation between sidereal and synodic period
During the time S, the Earth moves over an angle of (360°/E)S (assuming a circular orbit) and the planet moves (360°/P)S.
Let us consider the case of an inferior planet, i.e. a planet that will complete one orbit more than Earth before the two return to the same position relative to the sun.
Table of synodic periods in the Solar System, relative to Earth:
| Sid. P. (a) | Syn. P. (a) | Syn. P. (d) | |
| Mercury | 0.241 | 0.317 | 115.9 |
| Venus | 0.615 | 1.599 | 583.9 |
| Earth | 1 | — | — |
| Moon | 0.0748 | 0.0809 | 29.5306 |
| Mars | 1.881 | 2.135 | 780.0 |
| 1 Ceres | 4.600 | 1.278 | 466.7 |
| Jupiter | 11.87 | 1.092 | 398.9 |
| Saturn | 29.45 | 1.035 | 378.1 |
| Uranus | 84.07 | 1.012 | 369.7 |
| Neptune | 164.9 | 1.006 | 367.5 |
| Pluto | 248.1 | 1.004 | 366.7 |
Calculation
Small body orbiting a central body
In astrodynamics the orbital period of a small body orbiting a central body in a circular or elliptical orbit is:
where:
- is length of orbit's semi-major axis,
- is the gravitational constant,
- the mass of the central body.
For the Earth (and any other spherically symmetric body with the same average density) as central body we get
Thus, as an alternative for using a very small number like G, the strength of universal gravity can be described using some reference material, like water: the orbital period for an orbit just above the surface of a spherical body of water is 3 hours and 18 minutes. Conversely, this can be used as a kind of "universal" unit of time.
For the Sun as central body we simply get
Two bodies orbiting each other
In celestial mechanics when both orbiting bodies' masses have to be taken into account the orbital period can be calculated as follows:
- is the sum of the semi-major axes 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),
- and are the masses of the bodies,
- is the gravitational constant.
In a parabolic or hyperbolic trajectory the motion is not periodic, and the duration of the full trajectory is infinite.