Department of Physics

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A Brief Explanation of Orbital Elements

With related common astronomical terms

 

Astronomical terms can often be confusing. It sometimes seems that astronomers have purposely chosen the most difficult terms with which to describe something.

It doesn't help any when different terms are used to describe essentially the same things, which is often the case when dealing with orbits. There are several different ways to describe orbits. I have listed the orbital common terms, along with some terms that are occasionally encountered, and a brief explanation of each. I have not attempted to write an on-line tutorial on orbits or astronomical terms, but I hope that this list will prove helpful.

Also included are some astronomical terms that are useful in understanding the explanations of the orbital elements.

Many of the explanations or orbital elements refer to the figures below.

Last updated:  13 March 2006, 18:21 UTC
Thanks to Joe Heafner for bringing an error in the previous version to my attention.

FIGURE 1

orbitfig1

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FIGURE 2

orbitfig2

Standard Orbital Elements: (Sun orbiting object)

(Refer to the explanations below)

* Argument of Perihelion

* Eccentricity

* Inclination

* Longitude of the Ascending Node

* Semi-major axis of orbit

* Time of perihelion passage


Standard Orbital Elements: (Earth orbiting object)

(Refer to the explanations below)

* Argument of Perigee

* Eccentricity

* Inclination

* Longitude of the Ascending Node

* Period

* Semi-major axis of orbit

* Time of perigee passage


However: anyone interested in finding the positions of Earth orbiting satellites is likely to come upon a set of orbital parameters that are used in aerospace engineering that are slightly different from the standard set used in astronomy. The object is still at the same place, it's just specified differently.

These elements are usually:

(Refer to the explanations below)

* Argument of Perigee

* Eccentricity

* Epoch

* Inclination

* Mean Anomaly

* Mean Motion

* Right Ascension of the Ascending Node

* Argument of Latitude (not shown): The geographic latitude of an Earth orbiting satellite at a specific time (the Epoch), expressed as an angle measured from the celestial equator northward.

* Ascending Node (AN in Figure 2): The point in a satellite's orbit where it crosses the plane of the celestial equator (or ecliptic for a sun orbiting object) going north.

* Argument of Perigee (Perihelion): (w in Figure 2) : The angle between the ascending node and perigee (or perihelion for sun orbiting satellites), measured counter clockwise along the plane of the orbit.

* Apogee (Aphelion) (Figure 1): Point in orbit when the satellite is farthest from the Earth (sun).

* Celestial Equator: The plane of the Earth's equator projected onto the celestial sphere. The celestial equator is tilted 23.5 degrees in relation to the plane of the Earth's orbit (the ecliptic). The ecliptic and the celestial equator cross at two points, the vernal equinox and the autumnal equinox.

* Celestial Sphere: A imaginary sphere surrounding the Earth, at some arbitrary great distance, upon which the stars are considered to be fixed for the purpose of position measurement. Although it is the Earth that rotates, it appears to an observer on the Earth that the Celestial Sphere revolves around the Earth in one (sidereal) day.

* Eccentricity, e : Half of the distance between the foci of an ellipse divided by the semi-major axis. Think of it as a measure of how "out of round" an ellipse is. An eccentricity of 0 would be a circle.

* Ecliptic: The plane of the Earth's orbit around the sun. The ecliptic is the apparent path of the sun across the celestial sphere over the period of one year.

* Ecliptic Latitude: The angle between the position of an astronomical body at the time of interest and the plane of the ecliptic.

* Ecliptic Longitude: The angle of an astronomical body from the vernal equinox, measured EAST along the ecliptic.

* Epoch: The specific time at which the position of a satellite is specified.

* Geographic Longitude of the Ascending Node (not shown): The geographic longitude EAST of the Prime Meridian where the orbit of an Earth-orbiting satellite crosses the celestial equator. Do not confuse with Longitude of the Ascending Node.

* Inclination, (i in Figure 2): The angle between the plane of the orbit and the plane of the celestial equator for Earth orbiting satellites (or the plane of the ecliptic for sun orbiting satellites).

* Longitude of the Ascending Node, (W in Figure 2): The angle between the vernal equinox and the ascending node, measured counter-clockwise.

* Longitude of Perigee (Perihelion) The angle between the vernal equinox  and perigee (or perihelion) measured in the direction of the object’s motion.  It is equal to the sum of the Argument of Perigee and the Longitude of the Ascending Node (W + w in figure 2).

* Mean Anomaly: (Compare with True Anomaly) The angle that a satellite would have moved since last passing perigee (or perihelion), assuming that the satellite moved at a constant speed in a orbit on a circle of the same area as the actual orbital ellipse. Equal to the True Anomaly at perigee and apogee only for elliptical orbits, or at all times for circular orbits.

* Mean Motion: The reciprocal of the Period, expressed in revolutions per day

* Meridian: An imaginary line on the surface of the Earth running from the north pole to the south pole through any given point on the Earth. Also, an imaginary line on the celestial sphere running from the North Celestial Pole to the South Celestial pole directly over any given point on the Earth. These definitions are essentially the same, one line goes under you feet, one goes over your head. The Prime Meridian is the meridian the runs through Greenwich, England (0 degrees longitude).

* Obliquity of the Ecliptic: The angle between the celestial equator and the ecliptic.

* Perigee (Perihelion) (Figure 1): The point in an orbit when the satellite is closest to the Earth (sun).

* Period: The time it takes the satellite to complete one orbit.

* Right Ascension: A measure of the angle between the vernal equinox and a given astronomical object (star, planet, or satellite), as seen from the Earth. In astronomy, Right Ascension (RA) is expressed in units of time. The RA is the time that elapses between the transit of the vernal equinox across any given meridian and the transit of the given object across the same meridian, expressed in a 24 hour format. Right Ascension can also be expressed as the angle between the vernal equinox and the object, measured EAST of the vernal equinox along the celestial equator.

* Right Ascension of the Ascending Node (W in Figure 2): Another term for Longitude of the Ascending Node, It is the angle of the ascending node measured EAST of the vernal equinox along the celestial equator.

* Semi-Major Axis (a in Figure 1): The half of the longer of the two axes of the orbital ellipse.

* Semi-Minor Axis (b in Figure 1): The half of the shorter of the two axes of the orbital ellipse.

* Sidereal Day: A sidereal day is the amount of time it takes the Earth to rotate once on it axis relative to the stars. A mean sidereal day is equal to 0.99727 mean solar days, or 23 hours, 56 minutes, 4.1 seconds. The mean solar day and the mean sidereal day differ due to the fact the Earth is orbiting the sun in 365.2422 mean solar days, resulting in the sun moving slightly across the celestial sphere during one solar day (24 hours)

* Time of Perigee (Perihelion) Passage: The time at which a satellite last passed perigee (or perihelion).

* True Anomaly (q in Figure 1): The actual angle that a satellite has moved since last passing perigee (or perihelion).

* Vernal Equinox: One of two points where the ecliptic crosses the celestial equator, the other being the Autumnal Equinox. The Vernal Equinox is the point where the ecliptic crosses the celestial equator with the sun passing from south to north. Unfortunately for students of astronomy, the same term, Vernal Equinox, is used to describe both the POINT on the celestial sphere where the crossing occurs (its meaning throughout these explanations), AND the MOMENT IN TIME when the crossing occurs (the first moment of spring). Which is the intended meaning in any given sentence must be determined by the context on the statement.

 

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