Orbit (astronomy and physics), path or trajectory of
a body through space. A force of attraction or repulsion from a second body
usually causes the path to be curved. A familiar type of orbit occurs when one
body revolves around a second, strongly attracting body. In the solar system the
force of gravity 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. When a satellite traces out an orbit about the center 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, instead of the perigee or apogee distance from the earth's
center. The ending gee refers to orbits about the earth; perihelion and
aphelion refer 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 socalled line of apsides is a straight line connecting
the periapsis and the apoapsis.
II

LAWS OF MOTION

Early in the 17th century, the
German astronomer and natural philosopher Johannes Kepler deduced 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 center of the sun sweeps out equal areas in equal time intervals as it goes
around the orbit; the planet moves faster when closer to the sun and slower
when 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 center, 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). This last law permits the masses of the planets to be
calculated by measuring the size and period of satellite orbits.
III

ORBITAL ELEMENTS

Elements of Orbits 
Orbits of objects going around
the sun are discussed in terms of their orientation with respect to three
different planes. These are the plane of the orbit in question, the plane of
the earth’s orbit (also known as the plane of the ecliptic), and the plane of
the celestial equator. The elliptical orbit has center C and focus S. Six
elements may be used to describe an orbit: size (periapsis distance SP),
elongation (eccentricity e, which is the ratio CS/CP), longitude of the
ascending node (angle Ω), argument of periapsis (angle ω), inclination (angle
i), and the time when the orbiting body is at the periapsis.
Six orbital elements describe an orbit.
The first two elements 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 in the accompanying figure,
the eccentricity is the ratio CS/CP, where S is the focus and C
the center 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, when e
is greater than 1—makes a single close passage to a central body and escapes
along a socalled 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
around the sun is the plane of the earth's orbit, also known as the plane of
the ecliptic; the equinox (g) is the northbound intersection of the
earth's orbit and the plane of the celestial equator; 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 (Ω), and the argument of the periapsis (ω). 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 measures the angular
displacement in the plane of the orbit between the ascending node and the line
that passes through the center of the orbit (C) and the periapsis (P). Finally,
the sixth orbital element is the time when 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, or half the distance between the
points of periapsis (P) and the 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
IV

PERTURBATIONS

An orbit is 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 kilometers. Atmospheric drag causes the orbit of an
earth satellite to shrink, and the oblate shape of the earth causes the
direction of its node and perigee to change. The theory of relativity developed
by Germanborn American physicist Albert Einstein explains an observed
perturbation in the perihelion of the planet Mercury.
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