Finding the orbital state vector (position, velocity) from the classical orbital elements; the reverse of Orbital Elements from State Vector.
Two Steps
- Get position and velocity in perifocal coordinates
- Transform from perifocal to ECI with a 3-1-3 Euler angle rotation
Step 1: Perifocal State
- From Motion in Perifocal Coordinates (Curtis (4.43), (4.44)):
Step 2: Rotate 3-1-3 into ECI
- The perifocal axes are reached from ECI by rotating about , about the node line, and
about ; to go back, apply the negative angles in reverse order:
- Elementary rotation matrices:
- has the same form as
State Vector from Elements
- Worked example: Curtis example 4.7
Singular Conditions
- Circular and equatorial orbits: and/or undefined, so this route fails
- Fix: equinoctial elements to orbital state