Orbital Eccentricity - gravitational force

Description

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptical orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the galaxy.
In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit. The eccentricity of this Kepler orbit is a non-negative number that defines its shape.

The eccentricity may take the following values:
-circular orbit: e=0
-elliptic orbit: 0<e<1 (see Ellipse)
-parabolic trajectory: e=1 (see Parabola)
-hyperbolic trajectory: e>1 (see Hyperbola)

In the case of a gravitational force, the formula is as shown here.

Related formulas

Variables

eorbital eccentricity (dimensionless)
ϵspecific orbital energy (J/kg)
hspecific relative angular momentum (angular momentum divided by the reduced mass) (m2/s)
μstandard gravitational parameter (m3*s-2)