As a result the 2n-dimensional Coulomb equation of motion is reduced to equations for the radial and angular variables which determine a Keplerian orbit
Additionally, some sensible assumptions are made for the same purpose: (1) the center of mass of the system moves on a Keplerian orbit
, (2) the perturbations such as atmospheric drag and Earth oblateness, are negligible, and (3) the eccentricity of the orbit is small and would not induce the system into chaos motion .
For example, we could record the planet at different times and then fit a Keplerian orbit
to its observed positions around the host star.
Along with the deviations in the motion of the Moon from the Keplerian orbit
and the short-period nutation of the Earth axis, the evection mechanism is detected in spectral zenith observations of the atmosphere at Novolazarevskaya station (Antarctica).
With [epsilon] = 0, [sigma] = 0, the angle [[psi].sub.0] coincides with the true anomaly and [[THETA].sub.0] with the argument of latitude of a Keplerian orbit
. Next we calculate the orbital elements [[omega].sub.0], [[OMEGA].sub.0], and [M.sub.0] according to the following formulae:
"For a planet following a strictly Keplerian orbit
around its host star, the spacing, timing and other properties of the observed transit light curve should be unchanging in time," said Dr.
Within the solar system, one body typically produces the dominant force on any given body, and the resultant motion can be thought of as a Keplerian orbit
about a primary, subject to small perturbations by other bodies.
Outgassing forces can be particularly strong for small nuclei, pushing the nucleus away from its Keplerian orbit
and spinning it up in just a few orbits.
Nevertheless, there were reports [13-21] on a strong correlation between variation of some physical and biochemical processes and deviations of the Moon from the Keplerian orbit
(evection, variation and annual inequality; see ).
These lead to a Keplerian orbit
in three dimensions, which gives the observed values of perihelion precession and bending of light by a massive object.
As a further assumption, Jovian moons move on Keplerian orbits
(even though the proposed procedure is soon applicable to the general case that uses planetary ephemeris).
For computing impulsive propulsion [DELTA]v values for orbital changes we use the so-called vis-viva equation which is valid for elliptical Keplerian orbits