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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.
Proposition 43; Problem 30 Diagram illustrating Newton's derivation. The blue planet follows the dashed elliptical orbit, whereas the green planet follows the solid elliptical orbit; the two ellipses share a common focus at the point C. The angles UCP and VCQ both equal θ 1, whereas the black arc represents the angle UCQ, which equals θ 2 = k ...
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 ...
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 .
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.
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
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.
The bifurcation diagram shows the forking of the periods of stable orbits from 1 to 2 to 4 to 8 etc. Each of these bifurcation points is a period-doubling bifurcation . The ratio of the lengths of successive intervals between values of r for which bifurcation occurs converges to the first Feigenbaum constant .
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