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Orbital parameters
For an elliptical orbit, the closest distance to the Sunthe socalled
perihelion distanceis [see Equation (4.30)]

(4.34) 
This equation also holds for parabolic and hyperbolic orbits.
Likewise, the furthest distance from the Sunthe socalled aphelion distanceis

(4.35) 
It follows that, for an elliptical orbit, the major radius,
, is simply the mean of the perihelion
and aphelion distances,

(4.36) 
The parameter

(4.37) 
is called the eccentricity and measures the deviation of the orbit
from circularity. Thus,
corresponds to a circular orbit, whereas
corresponds to an infinitely elongated elliptical orbit. Note that the Sun is displaced a
distance
along the major axis from the geometric center of the orbit. (See Section A.9 and Figure 4.3.)
Figure:
A Keplerian elliptical orbit.
is the Sun,
the planet,
the empty focus,
the perihelion point,
the aphelion point,
the major radius,
the minor radius,
the eccentricity,
the radial distance, and
the true anomaly.

As is easily demonstrated from the preceding analysis, Kepler laws of planetary motion can be written in the convenient form
where
is the mean orbital radius (i.e., the major radius),
the orbital eccentricity, and
the mean orbital angular velocity.
Next: Orbital energies
Up: Keplerian orbits
Previous: Kepler's third law
Richard Fitzpatrick
20160331