There are a number of enents that occur in the orbits of the Earth, Moon, and other planets. Here we define the events and define what the event is.
Defining a unique number to a particular orbit of a body is complicated by the fact that there are several different definitions of orbital periods.
Calendar years are used to define a particular orbital period. The calendar new year doesn’t correspond to any astronomical events. For event calculations a good choice of the orbit is the anomalistic period. This starts at perihelion that currently occurs in the first week of January.
Moon orbits are assigned lunation numbers. The Brown Lunation Number defines lunation 1 to be the first New Moon of 1923 which occured on 17 January. Again, we will define the start of a lunar orbit as perigee. The BLN number will be associated with New Moons.
The apses of an orbit are the closest and furthest points in an orbit. The closest point is perihelion for planets and perigee for the Moon. The furthest is Aphelion for planets and apogee for the Moon.
The times of these events has to be determined by iteration to find the closest and furthest distances.
In the case of the Earth, the times of the apses vary by several days from year to year. The reason for this is that it is the Earth-Moon Barycentre (EMB), not the Earth, that orbits the Sun. When the EMB is at perihelion, the Moon can be closer to the Sun than the Earth. In this case the Earth will be at peihelion a few days later.
The times and dates of the equinoxes and solstices are when the ecliptic longitude of the Sun from the Earth is a multiple of \(90^\circ\).