When the moon crosses the ecliptic plane, will a solar or lunar eclipse definitely occur?
First calculate the moment when it crosses the orbital reference plane, and then distinguish its relationship with the moon phase.
The moon's orbit is tilted relative to the ecliptic plane. It will pass from the south side to the north side and back from the north side every round. But crossing the node itself does not mean an eclipse: the phase relationships of the sun, earth, and moon also need to match.
Guess first
Will an eclipse occur every time the moon passes through the ecliptic nodes?
Show answer and explanation
Not necessarily, it needs to be coordinated with the phase — The Moon may not be in the direction of the new or full moon when it crosses the nodes; this is not enough to cause an eclipse.
Then connect experience and science
Use the ecliptic plane as a reference paper
The moon crosses the ecliptic plane when the geocentric latitude is zero; this is relative to the ecliptic, not relative to the local horizon.
β = 0 at the intersection point
Distinguish between going north or south
The ascending node runs from the south side of the ecliptic to the north side, and the descending node goes in the opposite direction. The k of the two types of events are integers and half-integers respectively.
Ascending node integer k; descending node k+0.5
Add the periodic term to get the time
The mean nodal month gives only a rough rhythm. The original book uses 22 cycles to correct and improve the date, and cannot be repeated only in 27 days.
JDE = average polynomial + period correction
Crossing the intersection is not all the conditions for eclipse
A solar or lunar eclipse requires a new moon or full moon to also occur near the nodes. This lesson only seeks to cross the intersection moment, and does not automatically judge the eclipse.
Node conditions and moon phase conditions must be distinguished
The k integer is the ascending node, and the half integer is the descending node. First find the average time and basic angle, and then add period corrections item by item; β=0 describes the conditions for crossing the ecliptic, and does not represent a new moon or a solar eclipse.
give it a try
Switch the ascending/descending nodes and note the date and direction of crossing. The ascending node in the original book in May 1987 can be used as a calculation check.
No need to memorize symbols
- β
- The moon's geocentric latitude
- k
- Intersection event number, integer or half-integer
- D / M / M′
- Mean distance angle between the sun and the moon / periapsis angle between the sun and the moon
- JDE
- TT Kinetics Days
Algorithm, accuracy and scope of application
Realize Chapter 51 average event polynomial and all 22 corrections, including E, Ω, V, and P terms. k strictly takes an integer or a half-integer to distinguish the numbering system of the moon phase and the near and apogee. Example 51.a is verified with AA+ multiple groups of positive and negative k. The error in the original book is an approximation of the order of minutes. It does not claim that any date is accurate to seconds; it does not directly judge the intersection as an eclipse.
my understanding check
From which side of the ecliptic does the ascending node go?
south to north — The descending node goes from north to south.
Does crossing the ecliptic nodes mean rising from the local horizon?
no — The ecliptic reference plane is different from the observer's ground plane.
Can this page directly tell you whether the solar eclipse can be seen in your city?
cannot — Eclipses and their local visibility require additional spatial and observational calculations.
The moon's crossing point is one kind of space condition, and the moon phase is another condition; only when the two coincide appropriately can an eclipse occur.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 51 chapter