Orbital Elements

Introduction

Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics, these elements are generally considered in classical two-body systems, where a Kepler orbit is used. There are many different ways to mathematically describe the same orbit, but certain schemes, known as orbital element sets, are commonly used. Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects.

Keplerian Elements

The Keplerian elements are a set of six parameters that define an orbit. These parameters are semi-major axis (a), eccentricity (e), inclination (i), longitude of the ascending node (Ω), argument of periapsis (ω), and true anomaly (ν). The first two parameters relate to the size and shape of the ellipse, respectively. The next three parameters orient the ellipse in space, and the last parameter locates the spacecraft on the ellipse at a specific time.

Semi-Major Axis

The semi-major axis is the mean of the periapsis and apoapsis distances. It is the most significant of the Keplerian elements, as it determines the period of the orbit via Kepler's third law. The semi-major axis is given in units of distance.

Eccentricity

The eccentricity is a measure of how much the orbit deviates from a perfect circle. A value of 0 indicates a circular orbit, values between 0 and 1 indicate an elliptical orbit, 1 indicates a parabolic escape orbit, and greater than 1 indicates a hyperbola. The eccentricity is dimensionless.

Inclination

The inclination is the angle between the reference plane and the orbital plane. It is expressed in degrees from 0 to 180. An inclination of 0 degrees is a prograde, equatorial orbit, and an inclination of 180 degrees is a retrograde, equatorial orbit.

Longitude of the Ascending Node

The longitude of the ascending node is the angle from the reference direction, to the direction of the ascending node. The ascending node is the point where the orbit crosses the reference plane from below to above. The longitude of the ascending node is expressed in degrees from 0 to 360.

Argument of Periapsis

The argument of periapsis is the angle from the ascending node to the periapsis, measured in the orbital plane and in the direction of motion. For an equatorial orbit, it is the angle between the ascending node and the periapsis. The argument of periapsis is expressed in degrees from 0 to 360.

True Anomaly

The true anomaly is the angle between the direction of periapsis and the current position of the orbiting body, as seen from the main focus of the ellipse. The true anomaly is expressed in degrees from 0 to 360.

Orbital Plane

The orbital plane is the geometric plane in which an orbit lies. The orbital plane of all planetary and lunar orbits lies in the ecliptic, which is the plane containing Earth's orbit. However, comets may have any inclination, and their orbits may be significantly inclined to the ecliptic.

Orbital Period

The orbital period is the time taken for a given object to make one complete orbit around another object. When mentioned without further qualification in astronomy, the term is often used generically to refer to the sidereal period of an astronomical object, which is calculated with respect to the stars.

Orbital Speed

Orbital speed is the speed at which an object orbits around the barycenter of a system, usually around a more massive body. It can be calculated based on the mass of the more massive body and the radius of the orbit.

Orbital Energy

In the gravitational two-body problem, the specific orbital energy (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy and their total kinetic energy, divided by the reduced mass.