The orbital period is the time taken for a given object to make one complete orbit about another object. Periodicity is the quality of occurring at regular intervals or periods (in Time or Space) and can occur in different contexts A Clock marks In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star
When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars. A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth
There are several kinds of orbital periods for objects around the Sun:
Copernicus devised a mathematical formula to calculate a planet's sidereal period from its synodic period. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Mathematics and in the Sciences a formula (plural formulae, formulæ or formulas) is a concise way of expressing information
Using the abbreviations
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. The sidereal year is the time taken for the Sun to return to the same position with respect to the Stars of the Celestial sphere. A tropical year (also known as a solar year) is the length of time that the Sun takes to return to the same position in the cycle of seasons as seen from Earth This article describes the unit of angle For other meanings see Degree.
Let us consider the case of an inferior planet, i. The terms " inferior planet " and " superior planet " were originally used in the Ptolemaic Cosmology to differentiate those planets e. a planet that will complete one orbit more than Earth before the two return to the same position relative to the Sun.
and using algebra we obtain
For a superior planet one derives likewise:
Generally, knowing the sidereal period of the other planet and the Earth, P and E, the synodic period can easily be derived:
which stands for both an inferior planet or superior planet. Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. The terms " inferior planet " and " superior planet " were originally used in the Ptolemaic Cosmology to differentiate those planets The terms " inferior planet " and " superior planet " were originally used in the Ptolemaic Cosmology to differentiate those planets
The above formulae are easily understood by considering the angular velocities of the Earth and the object: the object's apparent angular velocity is its true (sidereal) angular velocity minus the Earth's, and the synodic period is then simply a full circle divided by that apparent angular velocity.
Table of synodic periods in the Solar System, relative to Earth:
|Sid. P. (a)||Syn. In Astronomy, a Julian year (symbol a) is a unit of measurement of Time defined P. (a)||Syn. P. (d)|
|Mercury||0. A day (symbol d is a unit of Time equivalent to 24 Hours and the duration of a single Rotation of planet Earth with respect to the 241||0. 317||115. 9|
|Venus||0. The VENUS ( V ictoria E xperimental N etwork U nder the S ea project is a cabled sea floor observatory operated by the University 615||1. 599||583. 9|
|Moon||0. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 0748||0. 0809||29. 5306|
|Mars||1. 881||2. 135||780. 0|
|4 Vesta||3. TemplateInfobox Planet. --> 4 Vesta (ˈvɛstə Vesta is the second most massive object in the Asteroid belt 629||1. 380||504. 0|
|1 Ceres||4. Ceres (ˈsɪəriːz 600||1. 278||466. 7|
|10 Hygiea||5. 557||1. 219||445. 4|
|Jupiter||11. 87||1. 092||398. 9|
|Saturn||29. 45||1. 035||378. 1|
|Uranus||84. 07||1. 012||369. 7|
|Neptune||164. Neptune ( English|AmE] ] is the eighth and farthest Planet from the Sun in the Solar System. 9||1. 006||367. 5|
|134340 Pluto||248. 1||1. 004||366. 7|
|136199 Eris||557||1. 002||365. 9|
|90377 Sedna||12050||1. TemplateInfobox Planet.--> 90377 Sedna (ˈsɛdnə) is a Trans-Neptunian 00001||365. 1|
In the case of a planet's moon, the synodic period usually means the Sun-synodic period. A natural satellite or moon is a Celestial body that Orbits a Planet or smaller body which is called the primary. That is to say, the time it takes the moon to run its phases, coming back to the same solar aspect angle for an observer on the planet's surface —the Earth's motion does not affect this value, because an Earth observer is not involved. For example, Deimos' synodic period is 1. TemplateInfobox Planet.--> Deimos (ˈdaɪməs; also /ˈdiːməs/ 2648 days, 0. 18% longer than Deimos' sidereal period of 1. 2624 d.
In astrodynamics the orbital period (in seconds) of a small body orbiting a central body in a circular or elliptical orbit is:
Using the Law of Exponents, this equation can also be written as (rmfr):
Note that for all ellipses with a given semi-major axis, the orbital period is the same, regardless of eccentricity.
For the Earth (and any other spherically symmetric body with the same average density) as central body we get
and for a body of water
T in hours, with R the radius of the body.
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. A time standard
For the Sun as central body we simply get
T in years, with a in astronomical units. The astronomical unit ( AU or au or au or sometimes ua) is a unit of Length based on the distance from the Earth to the This is the same as Kepler's Third Law
In celestial mechanics when both orbiting bodies' masses have to be taken into account the orbital period can be calculated as follows:
Note that the orbital period is independent of size: for a scale model it would be the same, when densities are the same (see also Orbit#Scaling in gravity). In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star
In a parabolic or hyperbolic trajectory the motion is not periodic, and the duration of the full trajectory is infinite.
the Earth's surface
|speed||period/time in space||specific orbital energy|
|minimum sub-orbital spaceflight (vertical)||6500 km||100 km||0. Distance is a numerical description of how far apart objects are The orbital speed of a body generally a Planet, a Natural satellite, an artificial satellite, or a Multiple star, is the speed at which it In Astrodynamics the specific Orbital energy \epsilon\\! (or vis-viva energy) of an Orbiting body traveling through Space A sub-orbital spaceflight (or sub-orbital flight is a Spaceflight in which the Spacecraft reaches space, but its Trajectory intersects 0 km/s||just reaching space||1. 0 MJ/kg|
|ICBM||up to 7600 km||up to 1200 km||6 to 7 km/s||time in space: 25 min||27 MJ/kg|
|LEO||6,600 to 8,400 km||200 to 2000 km||circular orbit: 6. A Low Earth Orbit (LEO is generally defined as an Orbit within the locus extending from the Earth’s surface up to an altitude of 2000 km 9 to 7. 8 km/s|
elliptic orbit: 6. 5 to 8. 2 km/s
|89 to 128 min||32. 1 to 38. 6 MJ/kg|
|Molniya orbit||6,900 to 46,300 km||500 to 39,900 km||1. A Molniya orbit is a type of Highly elliptical orbit with an Inclination of 63 5 to 10. 0 km/s||11 h 58 min||54. 8 MJ/kg|
|GEO||42,000 km||35,786 km||3. A geostationary orbit (GEO is a Geosynchronous orbit directly above the Earth 's Equator (0° Latitude) with a period equal to the Earth's 1 km/s||23 h 56 min||57. 5 MJ/kg|
|Orbit of the Moon||363,000 to 406,000 km||357,000 to 399,000 km||0. The orbit of the Moon around the Earth is completed in approximately 27 97 to 1. 08 km/s||27. 3 days||61. 8 MJ/kg|