Orbital time

The orbital period or revolution period in astronomy is the time in which a celestial body completes its orbit around a reference point (has passed through its orbit once), i.e. the duration of a revolution.

Basics

It should be noted that there can be different reference points to which the complete 360 ° circuit is measured. B. the period of revolution of the moon with or without taking into account the simultaneous movement of the earth around the sun .

The astronomical coordinate systems are generally not fixed to each other in space. Therefore, the period of rotation is given against a reference system that is as static as possible :

Either the starry sky is used for this , such an orbital period is called the sidereal period (relative to the stars).

Or the orbital time is measured in the plane of the orbit in relation to the pericenter (the point of the orbit ellipse closest to the center), that is the anomalistic period , the orbital period , as it results from the third Kepler law .

The tropical period is particularly important for the earth , it takes into account the drift of the vernal equinox , which is the base reference point for all geocentric coordinate systems

For long-term calculations of galaxies , their center is decisive, for example the galactic center ( galactic coordinate system ) for the Milky Way .

The reference can also be the (apparent) position of the sun ( synodic period ), the knot of individual planetary orbits ( draconic period ), the center of gravity of the entire solar system , its total center of mass ( barycentric period ) or the "rest of the universe " (see inertial system ).

Table: Orbital times in the solar system

In the special case of the earth's orbit around the sun, the length of the revolution period is one year ; this expression is generalized, for example to a "Mars year", a "Venus year" etc.

The orbital times follow Newton's law of gravitation :

{\ displaystyle U = {\ sqrt {\ frac {4 \ pi ^ {2} a ^ {3}} {G \ left (M_ {1} + M_ {2} \ right)}}}}

With

U is the period of revolution,
a is the semi-major axis ,
M ₁ and M _{2 are} the masses of the central body and the satellite,
G is the gravitational constant .

The orbital times of the planets are related to one another according to Kepler's third law :

The squares of the periods of revolution are in the same ratio as the cubes of the major semi-axes.

The following table contains the times for the synodic, sidereal or anomalistic periods of rotation of the planets of the solar system , a body in the asteroid belt and of trans-Neptunes , as well as the earth's moon, satellites and the sun (given in days and calendar years ):

Except for the Earth's moon, the difference between the anomalistic orbital period and the sidereal orbital period is negligible in this accuracy, because the pericentres of the planets and asteroids shift only minimally compared to the period of orbit ( pericenter rotation ).
In contrast to the moon, the synodic orbital times for Mercury and Venus are significantly longer , but for Mars and the outer planets (the term “inside / outside” refers to the asteroid belt, not the earth), it is increasingly shorter . The exact explanation for this see in the section Planets of the article Synodic Orbital Period .

object	Sidereal anomalous orbital period "in relation to the fixed stars / the orbit geometry"	Synodic period "in relation to earth and sun"
ISS	00001.51 hours ^I1	0001.53 hours ^I2
Geosynchronous	00023.93 hours ^G1	0024.00 hours
Moon ^M1	000027,322 days / 000027,554 days ^M2	0029.53 days
Mercury	000087,969 days	0115.88 days
Venus	000224,701 days	0583.92 days
Earth ^E1	000365.256 days	000-
Mars	000686,980 days	0779.94 days
Ceres	000004.605 years	0466.72 days
Jupiter	000≈11,862 years	0398.88 days
Saturn	000≈29,458 years	0378.09 days
Uranus	000≈84.014 years	0369.66 days
Neptune	00≈164.793 years	0367.49 days
Pluto	00≈247.94 0years ^NP	0366.73 days
Orcus	00≈247.97 0years ^NP	000-
Varuna	00≈283.56 0years ^NP	000-
Haumea	00≈284.61 0years ^NP	000-
Quaoar	00≈285.09 0years ^NP	0366.54 days
Makemake	00≈309.41 0years ^NP	000-
Eris	00≈557.4 00years ^NP	000-
Sedna	≈10704 , 000years ^NP	0365.29 days
Sun ^S	00≈230 million years	000-

^I1 Anomalistic Orbital Time: 91.4887 minutes

^I2That is the time between two sunrises for an ISS astronaut. The ISS runs prograde around the earth, so the sun comes “towards” it. It takes 1.61 hours until it arrives again over a parallel

^G1 sidereal day

^M1For the orbit period of the moon see in detail: Lunar orbit

^M2The Draconite Period is the time between two passes through the same lunar node. It plays a role for the eclipses, for the planets and minor planets it is of no particular significance

^E1For the orbit period of the earth see in detail: Earth orbit

^NPThe orbital periods of objects beyond Neptune are so long that modern astronomy has not yet fully grasped them. The values given are based on planetary theories (such as the VSOP 87 ), which then provide useful results in model calculations. The confirmation by measurement is still pending. On April 11, 2009, Neptune completed its first fully observed period, and has been fairly accurately specified ever since.

^S.About the center of the Milky Way, see The Sun in the Milky Way System

Conversion synodic - sidereal

Sidereal period (1 to 2) and synodic period (1 to 3).

{\ displaystyle T _ {\ mathrm {E}}}

= sidereal period of revolution of the earth

Outer planets:

{\ displaystyle T _ {\ mathrm {sid}} = {\ frac {T _ {\ mathrm {E}}} {T _ {\ mathrm {syn}} -T _ {\ mathrm {E}}}} \ cdot T _ {\ mathrm {syn}}}

Inner planets:

{\ displaystyle T _ {\ mathrm {sid}} = {\ frac {T _ {\ mathrm {E}}} {T _ {\ mathrm {syn}} + T _ {\ mathrm {E}}}} \ cdot T _ {\ mathrm {syn}}}

Table: Orbit times of the sun, moon, earth and derived time quantities

A table about the mean dates, standard epoch J2000.0 , and the derived quantities of the calendar calculation .

It should be noted that the "revolution time of the sun" is the apparent solar path observed from the earth . It is not created by an orbit, but by the rotation of the earth .

Day	month	year
Sidereal day	Sidereal Month ⁽¹⁾	Sidereal year
86164,099s	27.32166 d	365.256366 d
23h 56m 4.099s	27d 7h 43m 11.5s	365d 6h 9m 9s
Sidereal day ⁽²⁾	Tropical month	Tropical year
86164.091 s	27.32158 d	365.242199 d
23h 56m 4.091s	27d 7h 43m 4.7s	365d 5h 48m 46s
Sunny day ⁽³⁾	Synodic month ⁽⁵⁾	Solar year ⁽³⁾
86400s ⁽⁴⁾	29.53059 d	365.242199 d ⁽⁶⁾
24h ⁽⁴⁾	29d 12h 44m 2.9s	365d 5h 48m 46s ⁽⁶⁾
Calendar day	Calendar month	Calendar year ⁽⁸⁾
1 d = 86400 s ⁽⁷⁾	30 d / 31 d	365.2425 d
24h ⁽⁷⁾		365d 5h 49m 12s

⁽¹⁾ Cycle of the highest and lowest levels of the moon

⁽²⁾The term tropical day is not in use.

⁽³⁾The terms synodic day and synodic year are not in use.

⁽⁴⁾mean day length, cf. Mean local time

⁽⁵⁾The moon phase cycle , the single period fluctuating around the mean value, is called the lunation

⁽⁶⁾ The solar year corresponds to the tropical year.

⁽⁷⁾ The calendar day is - in general - defined via the sunny day.

^(8th)The middle year of the Gregorian calendar .

Individual evidence

↑ Gerhard Dangl: ISS - Visibility table July 22, 2009 to July 25, 2009. Retrieved on August 5, 2009 .

[1] Gerhard Dangl: ISS - Visibility table July 22, 2009 to July 25, 2009. Retrieved on August 5, 2009 .