Orbits

The word orbit refers to the path of an object around another object as a result of the combined effects of inertia and gravity. When one object orbits around another, the more massive of the two bodies is called the primary and the smaller one is called the secondary. The path of the secondary can be in the shape of one of four conic sections: the circle, the ellipse, the parabola, and the hyperbola. See: Conic Sections.

Circular orbits are rare. All of the planets in our solar system orbit the sun in an elliptical orbit. The speed needed for a secondary to leave the orbit of its primary body is called its escape velocity. Because of the mutual attraction of the two bodies, the secondary does not orbit the center of the primary, rather, it orbits the center of mass of the two bodies, a point shifted toward the secondary, which is called the barycenter. The primary also moves, but depending on how massive it is, the movement may or may not be detectable. The movement of a secondary around its primary is called a revolution and is different from a rotation. A rotation is the motion of a planet or other body turning around its axis. For any orbit, the secondary speeds up as it approaches the primary and slows down as it moves away. The point at which the secondary is moving fastest is the point in its orbit which is closest to the primary.

In an elliptical or circular orbit, the secondary is moving slower than the escape velocity. One focus of the ellipse is on or near the primary and the second focus is on an unoccupied point in space. A circular orbit is an elliptical orbit with both foci in the same place. A secondary in this type of orbit will continue to orbit the primary unless another force alters its path. All planets and moons in our solar system follow this type of orbit.

In a parabolic orbit, the secondary has reached escape velocity. A secondary with this type of orbit will never return to orbit the primary again.

In a hyperbolic orbit, which is somewhat more flattened than a parabolic orbit, the secondary is moving faster than escape velocity. A space probe leaving earth’s orbit will follow this path. In mathematics, a hyperbola consists of two curves which face each other, each extending into infinity, in a hyperbolic orbit, only one of the curves is dealt with. As in a parabolic orbit, the secondary will never again return to orbit the primary a second time. A picture of this type of orbit looks almost like a parabolic orbit but is more stretched out.

The type of orbit a secondary follows around a primary is described by its eccentricity, which is a measure of how stretched out an orbit is. The range for the eccentricities of the different types of orbits follows: circular e = 0, elliptical 0 > e < 1, parabolic e = 1, hyperbolic e > 1. An illustration of the different types of orbits follows.

Figure 1: Three types of orbits: elliptical, parabolic, hyperbolic.

Because of the many factors involved in the motion of a secondary, such as gravitational pull from other objects, the orbit of a secondary around a primary never perfectly fits one of these shapes, but in most cases it comes very close.

Elliptical Orbits

Most orbits are elliptical in nature. An elliptical orbit is described by several parameters: the length of its semimajor axis, its eccentricity, its inclination, its period, the location of its nodes, and the location of its apsides.

The length of the orbit’s semimajor axis is the average distance from the planet to its primary. It is half of the major axis. See: Conic Sections

The eccentricity for ellipses is the ratio of distance between the two foci and the length of the major axis. This is expressed in the following equation:

d is the distance between the two foci
a is the length of the major axis.
e is the eccentricity of the orbit

The inclination of an orbit is the angle between the plane of the orbit and a reference plane. For planets in the solar system, the inclination of the orbit is measured relative to the plane of the ecliptic, the plane of the earth’s orbit.

The period of an orbiting object is the amount of time it takes to complete one revolution.

The orbit’s nodes are the points where the planet passes through a reference plane, usually the ecliptic. If north and south are used for rough directions in space, then the ascending node is the point where the planet passes through the plane of the ecliptic going from south to north, the descending node is the point where the planet goes from north to south. The line intersecting both nodes is called the line of nodes.

An orbit’s apsides are the points where the secondary is closest to and farthest away from its primary. The periapsis is the point on the orbit closest to the primary and the point where the secondary is moving at its fastest rate. The apoapsis is the point farthest away from the primary and the point where the secondary is moving at its slowest rate of speed. The periapsis of an object which is orbiting the sun is called its perihelion; the apoapsis of the same object is called its aphelion. For an object orbiting earth, the point on its orbit closest to earth is called its perigee; the point farthest away from earth is called its apogee.

An orbit’s nodes and apsides are not always in the same place every time. The movement of the nodes is called the progression or regression of the nodes and it takes place on the reference plane. Progression takes place when the nodes move in the same direction as the secondary is moving; regression takes place when the rotation is in the opposite direction. The moon’s nodes regress along the plane of the ecliptic making a complete rotation every 18.61 years.

The following is an image illustrating most of the properties of an elliptic orbit. At least three observations are required before the orbit of an object can be determined.

Figure 2: The components of an orbit. The primary is the yellow sphere. The secondary is the green sphere.

An orbit can be in two directions, direct or retrograde. Direct is a counterclockwise revolution as viewed from above the north pole of the primary. Retrograde is a clockwise revolution as viewed from the same place. For planets in the solar system, the motion is as seen from the north side of the ecliptic. Note: direct and retrograde can also refer to an objects rotation direction or the apparent motion of a planet as seen from earth.

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