r⃗ is a vector from the chosen origin. r = |r⃗| is its length; it is not altitude.

Velocity includes direction. Speed is its nonnegative magnitude.

Rate of change of velocity. Do not confuse vector a⃗ with semi-major axis a.

r⃗ × v⃗; perpendicular to the orbit plane, constant in ideal two-body motion.

Points to periapsis; magnitude e. Zero for a circle.

Actual angle from periapsis to the spacecraft, measured at the focus.

Component along outward r⃗; positive outbound and negative inbound.

In-plane component perpendicular to r⃗. The normal direction is perpendicular to the orbit plane.

Angle of velocity above local horizontal; atan2(vᵣ,vₜ).

Kinetic plus potential energy per unit mass, with potential zero at infinity.

Closest center-to-center distance; subtract body radius for altitude.

Farthest center distance on a bound ellipse; absent for an open trajectory.

Positive for ellipses, negative for hyperbolas in this guide. Not finite for a parabola.

Short half-axis of an ellipse: a√(1−e²).

p = h²/μ = rₚ(1+e); works for all nondegenerate conics.

0 circle, between 0 and 1 ellipse, 1 parabola, above 1 hyperbola.

Angle from reference-plane normal to angular momentum, 0°–180°.

Angle in reference plane to the northward equator crossing.

Angle in orbit plane from ascending node to periapsis.

Clock-like phase n(t−tₚ). It grows uniformly for a fixed elliptic orbit.

Auxiliary ellipse angle; not uniform in time.

Fraction of sampled time bins with a satellite seeing both the lunar site and Earth.

Longest run of unserved bins within the stated analysis window, without a periodic wrap assumption.