Mean longitude is theecliptic longitude at which anorbiting body could be found if its orbit werecircular and free ofperturbations. While nominally a simple longitude, in practice the mean longitude does not correspond to any one physical angle.^[1]

• Define a reference direction, ♈︎, along theecliptic. Typically, this is the direction of the Marchequinox. At this point, ecliptic longitude is 0°.
• The body's orbit is generallyinclined to the ecliptic, therefore define the angular distance from ♈︎ to the place where the orbit crosses the ecliptic from south to north as thelongitude of the ascending node,Ω.
• Define the angular distance along the plane of the orbit from theascending node to thepericenter as theargument of periapsis,ω.
• Define themean anomaly,M, as the angular distance from the periapsis which the body would have if it moved in a circular orbit, in the same orbital period as the actual body in its elliptical orbit.

From these definitions, themean longitude,L, is the angular distance the body would have from the reference direction if it moved with uniform speed,

${\displaystyle L=\mathrm{\Omega }+\omega +M}$,

measured along the ecliptic from ♈︎ to the ascending node, then up along the plane of the body's orbit to its mean position.^[2]

Sometimes the value defined in this way is called the "mean mean longitude", and the term "mean longitude" is used for a value that does have short-term variations (such as over a synodic month or a year in the case of the moon) but does not include the correction due to the difference between true anomaly and mean anomaly.^[3][4]Also, sometimes the mean longitude (or mean mean longitude) is considered to be a slowly varying function, modeled with aMaclaurin series, rather than a simple linear function of time.^[3]

Thetrue longitude is a separate value that corresponds to the actual angular distance from the reference direction, taking into account the varying speed and non-circular shape of the orbit. It is the analogue to thetrue anomaly, which is measured relative to periapsis like the mean anomaly.

Mean longitude, likemean anomaly, does not measure an angle between any physical objects. It is simply a convenient uniform measure of how far around its orbit a body has progressed since passing the reference direction. While mean longitude measures a mean position and assumes constant speed,true longitude measures the actual longitude and assumes the body has moved with itsactual speed, which varies around itselliptical orbit. The difference between the two is known as theequation of the center.^[5]

From the above definitions, define thelongitude of periapsis

${\displaystyle \varpi =\mathrm{\Omega }+\omega }$.

Then mean longitude is also^[1]

${\displaystyle L=\varpi +M}$.

Another form often seen is themean longitude at epoch,ε. This is simply the mean longitude at a reference timet₀, known as theepoch. Mean longitude can then be expressed,^[2]

${\displaystyle L=ϵ+n(t-t_0)}$, or

${\displaystyle L=ϵ+nt}$, ift is measured relative to the epocht₀.

wheren is themean angular motion andt is any arbitrary time. In some sets oforbital elements,ε is one of the six elements.^[2]

• Mean motion
• Orbital elements
• True longitude

• Orbits