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Encyclopedia > Orbital period

The orbital period is the time it takes a planet (or another object) to make one full orbit. In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... Periodicity is the quality of occurring at regular intervals (e. ... The eight planets and three dwarf planets of the Solar System. ...

There are several kinds of orbital periods for objects around the Sun: The Sun is the star of our solar system. ...

• 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 point in the sky, relative to the Sun, as observed from Earth; i.e. returns to the same elongation. 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.

## Contents

The Pleiades, an open cluster of stars in the constellation of Taurus. ... The Sun is the star of our solar system. ... Earth (IPA: , often referred to as the Earth, Terra, the World or Planet Earth) is the third planet in the solar system in terms of distance from the Sun, and the fifth largest. ... This diagram shows the elongations (or angle) of the Earths position from the Sun. ... The ascending node is one of the orbital nodes, a point in the orbit of an object where it crosses the plane of the ecliptic from the south celestial hemisphere to the north celestial hemisphere in the direction of motion. ... The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ... The ascending node is one of the orbital nodes, a point in the orbit of an object where it crosses the plane of the ecliptic from the south celestial hemisphere to the north celestial hemisphere in the direction of motion. ... This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... The Sun is the star of our solar system. ... In geometry, the semi-major axis (also semimajor axis) a applies to ellipses and hyperbolas. ... Equatorial Coordinates Right ascension (abbrev. ... The First Point of Aries, also called the vernal equinox point, is one of the two points on the celestial sphere where the celestial equator intersects the ecliptic. ...

## Relation between sidereal and synodic period GA_googleFillSlot("encyclopedia_square");

Copernicus devised a mathematical formula to calculate a planet's sidereal period from its synodic period. Nicolaus Copernicus (in Latin; Polish Miko&#322;aj Kopernik, German Nikolaus Kopernikus - February 19, 1473 &#8211; May 24, 1543) was a Polish astronomer, mathematician and economist who developed a heliocentric (Sun-centered) theory of the solar system in a form detailed enough to make it scientifically useful. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... In mathematics and in the sciences, a formula (plural: formulae, formulÃ¦ or formulas) is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relatx E=mcÂ² (see special relativity). ...

Using the abbreviations

E = the sidereal period of Earth (a sidereal year, not the same as a tropical year)
P = the sidereal period of the other planet
S = the synodic period of the other planet (as seen from Earth)

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 for the Sun to return to the same position in respect to the stars of the celestial sphere. ... A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ... A degree (in full, a degree of arc, arc degree, or arcdegree), usually symbolized Â°, is a measurement of plane angle, representing 1ï¼360 of a full rotation. ...

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. The terms inferior planet and superior planet were coined by Copernicus to distinguish a planets orbits size in relation to the Earths. ...

$frac{S}{P} 360^circ = frac{S}{E} 360^circ + 360^circ$

and using algebra we obtain Algebra is a branch of mathematics concerning the study of structure, relation and quantity. ...

$P = frac1{frac1E + frac1S}$

For a superior planet one derives likewise:

$P = frac1{frac1E - frac1S}$

Generally, knowing the sidereal period of the other planet and the Earth, P and E, the synodic period can easily be derived:

$S = frac1{left|frac1E-frac1Pright|}$,

which stands for both an inferior planet or superior planet. The terms inferior planet and superior planet were coined by Copernicus to distinguish a planets orbits size in relation to the Earths. ... The terms inferior planet and superior planet were coined by Copernicus to distinguish a planets orbits size in relation to the Earths. ...

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. 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 136199 Eris 557 1.002 365.9 90377 Sedna 12050 1.00001 365.1

In the case of a planet's moon, the synodic period usually means the Sun-synodic period. 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 1.2648 days, 0.18% longer than Deimos' sidereal period of 1.2624 d. In astronomy, a Julian year is a unit of time defined as exactly 365. ... Water, Rabbit, and Deer: three of the 20 day symbols in the Aztec calendar, from the Aztec Sun Stone. ... Note: This article contains special characters. ... (*min temperature refers to cloud tops only) Atmospheric characteristics Atmospheric pressure 9. ... Earth (IPA: , often referred to as the Earth, Terra, the World or Planet Earth) is the third planet in the solar system in terms of distance from the Sun, and the fifth largest. ... Adjective lunar Bulk silicate composition (estimated wt%) SiO2 44. ... Mars is the fourth planet from the Sun in the solar system, named after the Roman god of war (the counterpart of the Greek Ares), on account of its blood red color as viewed in the night sky. ... 1 Ceres (IPA , Latin: ) is a dwarf planet in the asteroid belt. ... Atmospheric characteristics Atmospheric pressure 70 kPa Hydrogen ~86% Helium ~14% Methane 0. ... Atmospheric characteristics Atmospheric pressure 140 kPa Hydrogen >93% Helium >5% Methane 0. ... Atmospheric characteristics Atmospheric pressure 120 kPa Hydrogen 83% Helium 15% Methane 1. ... Atmospheric characteristics Surface pressure â‰«100 MPa Hydrogen - H2 80% Â±3. ... Atmospheric characteristics Atmospheric pressure 0. ... Eris (IPA or ), officially designated 136199 Eris, is the largest known dwarf planet in the solar system. ... 90377 Sedna is a trans-Neptunian object, discovered by Michael Brown (Caltech), Chad Trujillo (Gemini Observatory) and David Rabinowitz (Yale University) on November 14, 2003. ... Moons of the Solar System scaled to Earths Moon A natural satellite is an object that orbits a planet or other body larger than itself and which is not man-made. ... Deimos (IPA or ; Greek Î”ÎµÎ¯Î¼Î¿Ï‚: Dread), is the smaller and outermost of Marsâ€™ two moons, named after Deimos from Greek Mythology. ...

## Calculation

### Small body orbiting a central body

In astrodynamics the orbital period $T,$ of a small body orbiting a central body in a circular or elliptical orbit is: Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ...

$T = 2pisqrt{a^3/mu}$

and

$mu = GM ,$ (standard gravitational parameter)

where: In astrodynamics, the standard gravitational parameter () of a celestial body is the product of the gravitational constant () and the mass : The units of the standard gravitational parameter are km3s-2 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting...

• $a,$ is length of orbit's semi-major axis (km),
• $mu!,$ is the standard gravitational parameter,
• $G ,$ is the gravitational constant,
• $M ,$ the mass of the central body (kg).

Note that for all ellipses with a given semi-major axis, the orbital period is the same, regardless of eccentricity. The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ... In astrodynamics, the standard gravitational parameter () of a celestial body is the product of the gravitational constant () and the mass : The units of the standard gravitational parameter are km3s-2 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

For the Earth (and any other spherically symmetric body with the same average density) as central body we get

$T = 1.4 sqrt{(a/R)^3}$

and for a body of water

$T = 3.3 sqrt{(a/R)^3}$

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.

For the Sun as central body we simply get

$T = sqrt{a^3}$

T in years, with a in astronomical units. This is the same as Kepler's Third Law The astronomical unit (AU or au or a. ... This article does not cite its references or sources. ...

### Two bodies orbiting each other

In celestial mechanics when both orbiting bodies' masses have to be taken into account the orbital period $P,$ can be calculated as follows: Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ...

$P = 2pisqrt{frac{a^3}{G left(M_1 + M_2right)}}$

where:

• $a,$ 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),
• $M_1,$ and $M_2,$ are the masses of the bodies,
• $G,$ is the gravitational constant.

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). The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ...

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

Results from FactBites:

 Physics Simulation and Java - Lecture 13B: Introduction to Java Networking (232 words) is one with an orbital period equal to the period of the rotation of the Earth. A mathematical relationship exists between the orbital period and the size of the orbit, i.e., the distance between the center of the Earth and the satellite. The relationship states that the square of the orbital period is proportional to the cube of the size of the orbit.
 What is the orbital period of the Moon? (510 words) The sidereal period of the Moon is the time needed for it to return to the same position against the background of stars. The synodic period is the time required for a body within the solar system, such as a planet, the Moon, or an artificial Earth satellite, to return to the same or approximately the same position relative to the Sun as seen by an observer on the Earth. The synodic period is related to the lunar phases; it depends on the relative locations of the Sun-Earth-Moon.
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