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As previously stated, the duration of an eclipse is determined primarily by the Earth-Moon distance and the angle between the Moon's orbit and the Earth's equator. The Earth-Sun distance is a secondary factor, but still important. One would think that the maximum & minimum Earth-Moon distances at eclipse would simply be the extreme largest apogee and smallest perigee values (406720km and 356353km respectively, in 2266 AD and 1055 BC). However, as Meeus shows in Mathematical Astronomy Morsels III, this is not the case - due to the complex interactions of the orbits of Sun, Earth and Moon extreme values cannot occur at either New or Full Moon (as required for a solar or lunar eclipse respectively). Lunar orbit theory shows that the distances are affected by whether it is new Moon or full Moon, whether the Earth is at perihelion or aphelion, and by exactly how the Moon's orbit is orientated: it is one of these last dependencies that cannot be maximised at an eclipse.
The same theory allows the true distances to be calculated, however, and by using data appropriate to the conditions pertaining at eclipses we find four sets of values for maximum apogee and minimum perigee:-
| Perihelion | Aphelion | |
|---|---|---|
| New Moon (solar eclipse) | Apogee 406537km Perigee 356743km | Apogee 406475km Perigee 357349km |
| Full Moon (lunar eclipse) | Apogee 406358km Perigee 356560km | Apogee 406230km Perigee 357099km |
When experimenting with my eclipse model, I assumed the technique employed by Meeus to derive maximum durations would have resulted in the above values being used (as it was based on lunar orbit theory, not on geometry). I thus also used these values and derived appropriate "fiddle factors". I then calculated for a "maximally optimal" situation (as mentioned on the previous page), to give the results 7mins 32.2sec for totals and 12mins 29.6sec for annulars i.e almost no difference! This is due to the fact that as we are very close to the key dates of 2019 and 1922 we are currently living in a period where circumstances are almost perfect for eclipses to take the longest possible values permitted by the eccentricity. Note that this very small effect is not noticeable on Meeus' graph because he calculated for exact millenia only.