The orbit in time, part 2: a position angle that changes linearly in time.
Why Another Anomaly
- The true anomaly is useful geometrically, but its time dependence is unknown
- The mean anomaly will change linearly in time
Areal Angle
- Define as the fraction of the ellipse’s area swept out since perigee, times (an “areal angle”):
- By Kepler’s second law grows linearly in time, so
Mean Motion
- Mean motion is a constant
Mean Anomaly in Time
- Measuring time from perigee passage :
- After one orbital period the full area is swept out:
- With this is
- The relationship between mean and true anomaly is complex: it goes through the eccentric anomaly and Kepler’s Equation