Issue 55

10 Flash Archive · Members Only

Jack’s Astro Corner: True Anomaly – “Where are we?” (Part VI)

The final Jack's Astro Corner installment explains True Anomaly, its relationship to perigee and the position vector, and how it differs from Mean Anomaly.

Author Minhas Published August 28, 2022

Over the summer, Jack Anthony broke down each of the six orbital elements required to uniquely identify a specific orbit and satellite in that orbit. This final installment examines True Anomaly. Readers who missed the earlier articles are directed to Jack’s “Orbit Element Dance” on YouTube or the previous five editions of the Final Frontier Flash. Orbit Element Dance.

This is the second P in Jack’s STP method: Size, Shape, Tilt, Twist, Position of Perigee and Position of the Satellite. True Anomaly answers the final question: where is the space object in its orbit at a particular time?

The article explains that the term “anomaly” traces back to Ptolemy’s description of non-uniform angular motion for planets in non-circular motion, later refined through Kepler’s laws of planetary motion.

The starting reference for True Anomaly is the eccentricity vector pointing toward perigee. The other reference is the satellite’s position vector at the epoch time. True Anomaly is denoted by the Greek letter Nu, ν.

If ν = 0°, the object is at perigee. If ν = 180°, the object is at apogee, where it is moving slowest in its orbit. At ν = 135° it is slowing down; at ν = 270° it is speeding up, consistent with Kepler’s Second Law.

The article also compares True Anomaly with Mean Anomaly as listed in a Two-Line Element set. Mean Anomaly is the angle the object would have if it moved on a circular path with the same semi-major axis and period. Unlike True Anomaly, Mean Anomaly increases at a constant angular rate.

Mean Anomaly lags True Anomaly on the trip from perigee toward apogee, the two are equal at apogee, and Mean Anomaly leads on the way back to perigee. They are equal again at perigee. For circular orbits, Mean and True Anomaly are equal.

This concludes Jack’s six-part series on the classical orbital elements. The STP mnemonic remains: Size, Shape, Tilt, Twist, Position Perigee, Position Satellite.

The final page offers a playful graduation message: “Congratulations, thank you for learning the 6 Orbital Elements… say, let’s see your Orbital Element Dance!” from Ferris Bueller and Barney Fife.