In celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing from apoapsis to periapsis and with...

equivalent to the dimensionless eccentricity vector of celestial mechanics. Various generalizations of the LRL vector have been defined, which incorporate...

developed. The eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector: e = | e | {\displaystyle...

eccentricity of a circle is 0. The eccentricity of a non-circular ellipse is between 0 and 1. The eccentricity of a parabola is 1. The eccentricity of...

direction of the periapsis of the orbit. We can then define the eccentricity vector associated with the orbit as: e ≜ c α = r ˙ × H α − u = v × H α −...

current position of an object on its orbit Eccentricity vector, in celestial mechanics, a dimensionless vector with direction pointing from apoapsis to...

Solar radiation pressure will in general perturb the eccentricity (i.e. the eccentricity vector); see Orbital perturbation analysis (spacecraft). For...

eccentricity vector caused by the J 2 {\displaystyle J_{2}\,} is shown to be: where: The first term is the in-plane perturbation of the eccentricity vector...

is the eccentricity of the orbit, the stated result is reached. The flight path angle is the angle between the orbiting body's velocity vector (equal...

or line of apsides, is an imaginary line defined by an orbit's eccentricity vector. It is strictly defined for elliptic, parabolic, and hyperbolic orbits...

where: n is a vector pointing towards the ascending node (i.e. the z-component of n is zero), e is the eccentricity vector (a vector pointing towards...

Therefore, the ascending node vector can be defined by the cross product of these two vectors. Compute the eccentricity vector e → {\displaystyle {\vec {e}}}...

where: v is the orbital velocity vector of the orbiting body, e is the eccentricity vector, r is the orbital position vector (segment FP in the figure) of...

{\displaystyle J_{n}(x)} is the Bessel function of the first kind. Eccentricity vector Orbital eccentricity George Albert Wentworth (1914). "The ellipse §126". Elements...

_{2})\right)}{\left|\mathbf {r} _{2}-\mathbf {r} _{1}\right|^{2}}}} The eccentricity vector e {\displaystyle \mathbf {e} } is given by e = ( ( | r 1 | − | r...

the mean anomaly. Eccentricity vector – In celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing...

{\hat {p}} } coordinate must be aligned with the eccentricity vector. Circular orbits, having no eccentricity, give no means by which to orient the coordinate...

and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position ( r {\displaystyle \mathbf {r}...

body divided by its mass. In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum, divided...

surface, and the reference vector points to true north. The azimuth is the angle between the north vector and the star's vector on the horizontal plane....

an ellipse is related to the semi-minor axis's length b through the eccentricity e and the semi-latus rectum ℓ {\displaystyle \ell } , as follows: b =...

historically with the concept of angular momentum) is constant. The eccentricity of the orbit of the Earth makes the time from the March equinox to the...

particular use case. Eccentricity (e) — shape of the ellipse, describing how much it deviates from a perfect a circle. An eccentricity of zero describes...

At the present epoch, Mars has the next largest eccentricity while the smallest orbital eccentricities are seen with Venus and Neptune. As two objects...

precession, the angular momentum is a constant, but the angular velocity vector changes orientation with time. What makes this possible is a time-varying...

a circle), a line segment is called a chord (of that curve). If V is a vector space over ⁠ R {\displaystyle \mathbb {R} } ⁠ or ⁠ C , {\displaystyle \mathbb...

orbit is tipped. This maneuver requires a change in the orbital velocity vector (delta-v) at the orbital nodes (i.e. the point where the initial and desired...

semi-major axis a and semi-minor axis c, therefore e may be identified as the eccentricity. (See ellipse.) A prolate spheroid with c > a has surface area S prolate...

overall circular motion leaves the eccentricity of the ellipse-shaped trajectory. the center of the eccentricity is located at a distance of ( a + b...

points are the same. The elongation of an ellipse is measured by its eccentricity e {\displaystyle e} , a number ranging from e = 0 {\displaystyle e=0}...