Connects the physical quantities (, , , ) to the geometric ones (, , ) of the orbit.
Relation of Physical and Geometric Quantities
- Dot the eccentricity vector with itself:
- , so :
- With (Orbit Equation):
- And (Conic Sections):
- In terms of energy:
- The size of the orbit depends only on and , not on the direction of the velocity
Speed on the Orbit
- Solve the semimajor-axis relation for the speed:
Vis-Viva Equation
- Knowing the position on the orbit immediately gives the speed
- For a circular orbit :
- The inverse semimajor axis is the parameter of the Universal Variables formulation (works for every conic)