2.0 Definitions/Clarifications

or-bit (ôr′bit) n. [[ < L orbis, a circle ]] 1 the path of a celestial body during its revolution around another 2 the path of an artificial satellite or spacecraft around a celestial body

−vi., vt. to move in or put into an orbit

−or′bit•al adj.

me•chan′ics n.pl the science of motion and of the action of forces on bodies

dy•nam′ics n.pl 1 the science dealing with motions produced by given forces 2 the forces operative in any field

as′tro•dyn•nam′ics n.pl. the branch of dynamics dealing with the motion and gravitation of objects in space

                        − Webster’s New World Dictionary

astrodynamics has also been defined as: The practical application of celestial mechanics, astroballictics, propulsion theory, and allied fields to the problem of planning and directing the trajectories of space vehicles.

celestial mechanics: The study of the theory of the motion of celestial bodies under the influence of gravitational fields.

central force field: The spatial distribution of the influence of a central force.

central force: A force that for the purposes of computation can be considered to be concentrated at one central point with its intensity at any other point being a function of the distance from the central point. For example, gravitation is considered as a central force in celestial mechanics.

trajectory: In general, the path traced by any body moving as a result of an externally applied force, considered in three dimensions.  Trajectory is sometimes used to mean flight path or orbit, but orbit usually means a closed path and trajectory, a path that is not closed.

                            − The Dictionary of Space Technology, by Joseph Angelo, Jr.

Kepler problem (prediction problem): Given the position and velocity vectors of a satellite at a particular instant of time… determine the position and velocity vectors after an interval of time, delta t.

− Fundamentals of Astrodynamics, by Bate, R. R., Mueller, D. D., and White, J. E. (BMW)

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Orbital Paths are Conic Sections. Any two-body orbit, in the absence of external or propulsive forces, will follow an orbit that traces one of the conic sections, ellipse, parabola or hyperbola. This is not only an observed phenomenon, it has been proven mathematically. The “special case” of a linear trajectory occurs when the plane that intersects the cone passes through the apex and is tangent to the cone, and the “section” is a straight line.

Linear Trajectories. The origin of the word orbit (orbis – Latin for circle) and its definition have conditioned us to think in a certain way about orbital motion. Ancient through modern studies of the motion of bodies in space have an overwhelming emphasis on paths around another body. “Orbits” that follow a rectilinear path are real and have very straightforward mathematical derivations. However, they are not cyclic. They result in either impact into or escape from the parent body. Each linear trajectory is a special case of the general elliptic, parabolic or hyperbolic orbit. Why do I consider equations for linear motion to be important while many textbooks are mute on these orbits? They are derived from fundamental principles of mechanics just as we derive equations for general orbits, and they help us understand the full range of motion in a central force field.

Relative Orbital Motion.  On this site we model orbital motion in a Galileian system of coordinates and restrict our mechanics to that of Galilei-Newton. We apply principles that precede Einstein and consider velocities that are well below the speed of light. Any reference to a satellite moving in one orbit relative to a satellite in another orbit is within this context. That is not a serious limitation, however, because we can deal with any common orbital problem.