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In mathematics, specifically in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. It can be understood as the subset of phase space covered by the trajectory of the dynamical system under a particular set of initial conditions , as the system evolves.
Conversely, the closed trajectory is called a subharmonic orbit if k is the inverse of an integer, i.e., if m = 1 in the formula k = m/n. For example, if k = 1/3 (green planet in Figure 5, green orbit in Figure 10), the resulting orbit is called the third subharmonic of the original orbit. Although such orbits are unlikely to occur in nature ...
From a circular orbit, thrust applied in a direction opposite to the satellite's motion changes the orbit to an elliptical one; the satellite will descend and reach the lowest orbital point (the periapse) at 180 degrees away from the firing point; then it will ascend back. The period of the resultant orbit will be less than that of the original ...
A celestial object's axial tilt indicates whether the object's rotation is prograde or retrograde. Axial tilt is the angle between an object's rotation axis and a line perpendicular to its orbital plane passing through the object's centre. An object with an axial tilt up to 90 degrees is rotating in the same direction as its primary.
Therefore, the speed of travel around the orbit is = =, where the angular rate of rotation is ω. (By rearrangement, ω = v / r .) Thus, v is a constant, and the velocity vector v also rotates with constant magnitude v , at the same angular rate ω .
Semi-major axis (a) — half the distance between the apoapsis and periapsis. The portion of the semi-major axis extending from the primary at one focus to the periapsis is shown as a purple line in the diagram; the rest (from the primary/focus to the center of the orbit ellipse) is below the reference plane and not shown.
Orbit modeling is the process of creating mathematical models to simulate motion of a massive body as it moves in orbit around another massive body due to gravity. Other forces such as gravitational attraction from tertiary bodies, air resistance , solar pressure , or thrust from a propulsion system are typically modeled as secondary effects.
A synchronous orbit is an orbit in which an orbiting body (usually a satellite) has a period equal to the average rotational period of the body being orbited (usually a planet), and in the same direction of rotation as that body.