Orbits

Orbit, path or trajectory of a body through space under the influence of forces of attraction or repulsion from a second body. In the solar system the force of gravitation causes the moon to orbit about the earth and the planets to orbit about the sun, whereas in an atom electrical forces cause electrons to orbit about the nucleus. In astronomy, the orbits resulting from gravitational forces, which are discussed in this article, are the subject of the scientific field of celestial mechanics.
An orbit has the shape of a conic section-a circle, ellipse, parabola, or hyperbola-with the central body at one focus of the curve (see Geometry: Conic Sections). When a satellite traces out an orbit about the centre of the earth, its most distant point is called the apogee and its closest point the perigee. The perigee or apogee height of the satellite above the earth's surface is often given, rather than the corresponding distances from the earth's centre. The ending -gee refers to orbits about the earth; the ending -helion refers to orbits about the sun; the ending -astron is used for orbits about a star; and the ending -apsis is used when the central body is not specified. The so-called line of apsides is a straight line connecting the periapsis and the apoapsis.

Laws of Motion
Early in the 17th century, the German astronomer and natural philosopher Johannes Kepler propounded three laws that first described the motions of the planets about the sun: (1) The orbit of a planet around the sun is an ellipse. (2) A straight line from the planet to the centre of the sun sweeps out equal areas in equal time intervals as it goes around the orbit; consequently, the planet moves faster when closer to the sun and slower when more distant. (3) The square of the period (in years) for one revolution about the sun equals the cube of the mean distance from the sun's centre, measured in astronomical units.
The physical causes of Kepler's three laws were later explained by the English mathematician and physicist Isaac Newton as consequences of Newton's laws of motion (see Mechanics) and of the inverse square law of gravity. Kepler's second law, in fact, expresses the conservation of angular momentum. Moreover, Kepler's third law, in generalized form, can be stated as follows: the square of the period (in years) times the total mass (measured in solar masses) equals the cube of the mean distance (in astronomical units). In this form the law permits the masses of the planets to be calculated by measuring the sizes and periods of their satellites' orbits.

Orbital Elements
Six elements describe an orbit (see the accompanying diagram). The first two are size and elongation. The size of the orbit is given by the periapsis distance (SP) and the elongation of the orbit is given by the eccentricity (e). For the ellipse shown, the eccentricity is the ratio CS/CP, where S is the focus and C the centre of the ellipse. For elliptical orbits, e is greater than 0, but less than 1; for circular orbits, e is exactly 0; and for parabolic orbits, e is exactly 1. A body in a hyperbolic orbit-that is, for which e is greater than 1-makes a single passage by a central body and escapes along a so-called open orbit, never to return.
The next three orbital elements are concerned with the orbit's orientation. For this discussion, however, several parameters need to be defined: the reference plane for objects orbiting the sun is the plane of the earth's orbit, also known as the plane of the ecliptic; the vernal equinox (g) is the intersection of the ecliptic and the plane of the celestial equator that the sun reaches when travelling north, at the beginning of the northern spring; and the ascending node (N) is the northbound intersection of the orbit in question and the reference plane (see Coordinate System).
The three orbital elements that describe an orbit's orientation are the inclination (i), the longitude of the ascending node (W), and the argument of the periapsis (w). The inclination is the angle between the reference plane and the orbit's plane. The longitude of the ascending node is the angle in the reference plane between the equinox and the ascending node. The argument of the periapsis is the angular displacement in the plane of the orbit between the ascending node and the line that passes through the centre of the orbit (C) and the periapsis (P). Finally, the sixth orbital element is the time at which the celestial body in question is at the periapsis.
An orbit can also be described in terms of its semimajor axis (AC, CP, or a). This axis is half the long axis (AP) of the ellipse, that is, half the distance between the periapsis (P) and apoapsis (A). The semimajor axis is longer than the periapsis distance (SP) and shorter than the apoapsis distance (AS), by an amount (CS) that is equal to the product of the semimajor axis and the eccentricity:

CS = e(AC) = e(CP) = ea

Perturbations
An orbit is described as perturbed when the forces are more complex than those between two spherical bodies. (Kepler's laws are exact only for unperturbed orbits.) The attraction between planets causes their elliptical orbits to change with time. The sun, for example, perturbs the lunar orbit by several thousand kilometres. Atmospheric drag causes the orbit of an earth satellite to shrink, and the oblate shape of the earth causes the directions of its nodes and perigee to change. The theory of relativity developed by Albert Einstein explains an observed perturbation in the perihelion of the planet Mercury.