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Remember that this change in velocity, ∆V, is only the amount required to change the spacecraft from its original orbit to the phasing orbit.A second change in velocity equal to the magnitude but opposite in direction of the first must be done after the spacecraft travels one phase orbit period to return the spacecraft from the phasing orbit to the original orbit.
The integration of the "matrix element" over the multidimensional internal parameters phase space provides the total and differential cross-sections. Each point of this phase space is associated to an event probability. This is used to randomly generate events closely mimicking experimental data.
At this point the phase space changes qualitatively and the dynamical system is said to have gone through a bifurcation. Bifurcation theory considers a structure in phase space (typically a fixed point, a periodic orbit, or an invariant torus) and studies its behavior as a function of the parameter μ. At the bifurcation point the structure may ...
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical concerning the motion of rockets, satellites, and other spacecraft.
An event in the universe is caused by the set of events in its causal past. An event contributes to the occurrence of events in its causal future. Upon choosing a frame of reference, one can assign coordinates to the event: three spatial coordinates x → = ( x , y , z ) {\displaystyle {\vec {x}}=(x,y,z)} to describe the location and one time ...
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.
The solution then becomes a curve in the phase space, parametrized by time. The curve is usually called a trajectory or an orbit. The (vector) differential equation is reformulated as a geometrical description of the curve, that is, as a differential equation in terms of the phase space variables only, without the original time parametrization.
SPICE data files are usually referred to as "kernels." These files provide information such as spacecraft trajectory and orientation; target body ephemeris, size and shape; instrument field-of-view size, shape and orientation; specifications for reference frames; and tabulations of time system conversion coefficients.