# Anomalous period

The anomalistic period is the length of time that a celestial body needs in its orbit to pass the pericenter again.

## Basics

In Kepler's theory of ellipses , the true anomaly describes an angle with which the position of the revolving object is related to the pericenter of its orbit. This angle is measured in one of the two focal points of the ellipse, the center of gravity. At the smallest distance from the center of gravity, the periapsis distance, the object, the point of the pathway closest to the center of gravity (the periapsis) and the center of gravity lie on one line, the apsidal line , and thus form an angle of 0 °. The period of time until the object on its orbit - passing through the point of the path furthest from the center (the apoapsis) at 180 ° - with a path angle of 360 ° again reaches its position in the periapsis is called the anomalistic period .

The anomalous period is a trajectory element of the classic trajectory determination and is generally referred to as T (for time ) or P (for period ). Anomalies (orbit angles) can be calculated from this period ; as a path-related measure, it is fundamental for all celestial mechanical calculations ( ephemeris calculation ). The anomalistic period differs from the sidereal period as a result of long-term displacement of the pericenter due to the rotation of the apse . Both are also known as the orbit period .

The anomalous orbital period results from the third Kepler law with the aid of the law of gravitation :

${\ displaystyle T = {\ sqrt {\ frac {a ^ {3} 4 \ pi ^ {2}} {G (M + m)}}}}$

for a sufficiently negligible mass of the satellite compared to its central body , as a two-body problem without orbital disturbances , with:

G: gravitational constant
a: major semi-axis of the elliptical Kepler orbit
M: mass of the central object (in this case the center of gravity )
m: mass of the satellite

However, the formula only describes an ideal case , because of the orbital disturbances by other celestial bodies, as they occur in a multi-body system. A more complex perturbation calculation results in an orbit period as an oscillating orbit element.

## Table: Anomalistic periods in the solar system

The following table shows the mean anomalistic period, the mean orbital velocity and the major semi-axis of an elliptical orbit for the planets of the solar system, furthermore for a body in the asteroid belt ( Ceres ) and also for two trans-Neptunian objects ( Quaoar and Sedna ) except Pluto .

 Object m Orbit period T mean orbit speed v major semi-axis Mercury 0000087.97 days IÄ 47.87 km / s 0.387 AU Venus 0000224.70 days IÄ 35.02 km / s 0.723 AU Earth E1 0000365.26 days 29.78 km / s 1,000 AU Mars 0000686.98 days IÄ 24.14 km / s 1.524 AU Ceres 000004,600 years 17.91 km / s 2.767 AU Jupiter 000011,869 years 13.07 km / s 5.203 AU Saturn 000029.628 years 9.67 km / s 9.583 AU Uranus 000084.665 years 6.84 km / s 19,201 AU Neptune 000165.49 0years NP 5.48 km / s 30,070 AU Pluto 000247.7 years NP00 4.75 km / s 39.482 AU Quaoar 00~ 285.97 0years 4.52 km / s 45,563 AU Sedna ~ 10040  years 000 1.36 km / s ~ 488 AU 000
The synodic orbital times for the moon, Mercury and Venus are significantly longer , from Mars and the outer planets - the term "inside / outside" refers to the asteroid belt, not the earth - however, increasingly shorter (for explanations see synodic orbital period )
E1For more details on the Earth's orbit, see Earth's orbit
NPThe orbital periods of Neptune and Pluto 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.

Since the pericentres of the planets shift only minimally during an orbit, the difference between the anomalistic and sidereal orbital times is negligible in the accuracy given here.

In contrast, the rotation of the apse leads to clearer differences when the earth's moon revolves around the earth (anomalistic period: 27.55 days; sidereal period: 27.32 days). An anomalous month is the mean length of time between two consecutive passes of the moon on its orbit through perigee . A sidereal month must be differentiated from this, followed by a synodic month ( synodic period : 29.53 days).

The sun, and with it the solar system, will move around the galactic center of the Milky Way in around 230 million years at around 220 km / s. The speed of the sun relative to the neighboring stars in the direction of the solar apex is 19.7 km / s, the relative speed of the local group of nearby galaxies in relation to the Virgo supercluster is about 1000 km / s.