I am an engineer who is in charge of writing some software which makes use of those two elements. But I am a bit confused, both seem to be almost the same although there is a small difference, which one?

So what is the actual difference between mean anomaly and mean longitude?

Thank you.

  • $\begingroup$ In an AIAA paper, " Design of a Mars Rapid Round Trip Mission' by Wertz and Amade (AIAA 2010-8642) there are references to mean anomaly and mean longitude for earth and mars. There is an equation for computing mean longitude from several parameters including mean anomaly. Numerically the values for earth at Standard Julian Epoch (J2000) for mean anomaly M=357.51716 deg and for mean longitude is 100.46435 deg. They are quite different. I am a retired engineer trying to learn some astrodynamics and just stumbled across this reference in my investigations. Perhaps this helps. $\endgroup$ – tckosvic Apr 20 '15 at 15:20
  • $\begingroup$ Additional comment -- From Vallado "Fundamentals of Astrodynamics and Applications", Pg103, mean longitude is location of satellite from the vernal equinox. The calculation of mean longitude uses mean anomaly as mentioned previously. $\endgroup$ – tckosvic Apr 20 '15 at 16:19
  • $\begingroup$ One perhelion the other equinox the angle is measured from to J2000 position, analogy for other paremeters too. $\endgroup$ – marshal craft Jul 6 '18 at 17:18

The mean longitude is the sum of the right ascension of the ascending node $\Omega$, the argument of periapsis $\omega$ and the mean anomaly $M$:

$L = \Omega + M + \omega$

As $\Omega$ is measured in the equatorial plane and $\omega$ and $M$ in the orbital plane, $L$ is a broken angle and represents an angle if (and only if) the orbit is circular and equatorial (i.e. no inclination)

For a satellite on a keplerian orbit, the mean anomaly defines the position along the orbit at a given epoch. It is for instance used in the two-line element set (TLE).

So the mean longitude is a combination of measures in the equatorial plane and the orbital plane and the mean anomaly is a measure in the orbital plane only.

Hope it will help.


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