The moon passes in the direction of the sun every month, so why isn't there a solar eclipse every month?
Look to see if the moon's shadow touches the earth, instead of just looking at "whether it's a new moon today."
At new moon, the moon is roughly between the sun and the earth, but it often passes above or below the direction of the sun. Only when the geometric conditions are right does the shadow hit the Earth. Here, we calculate each new moon candidate according to the approximate algorithm of the original book, instead of drawing a fixed occlusion animation.
Guess first
Is a solar eclipse bound to occur on a new moon?
Show answer and explanation
Not necessarily, it has to be close to the intersection of the orbits — The moon's orbit is tilted, so most new moons' shadows never hit the Earth.
Then connect experience and science
A new moon does not mean there will be a solar eclipse every month
The moon's orbit is tilted, and only a new moon close to the node can allow the moon's shadow to touch the earth. First use F for filtering, and then calculate the shadow axis distance.
|sin F|>0.36 → This algorithm determines that there is no food
Did the shadow touch the earth?
The picture is the basic plane perpendicular to the shadow axis and passing through the center of the earth. γ indicates how far the shadow axis is from the center of the earth. Whether the edge of the penumbra touches the earth determines whether there is an eclipse.
|γ| ≤ 1.5433+u
Distinguish between partial eclipse, total eclipse, annular eclipse and total annular eclipse
When the shadow axis passes through the Earth, it is a central eclipse; the size and sign of the core shadow cone help identify total or annular eclipses. There may also be non-central total eclipses/annular eclipses in the peripheral polar regions.
Center criterion |γ|<0.9972; type is judged based on u
Time is the total eclipse of the earth
This is not the start and end time of your city. Local eclipse paths must use other methods such as Besselian root numbers, and those data are not provided in this chapter.
Average New Moon + eclipse-specific period correction → JDE eclipse
First perform F screening, then use γ and u to distinguish whether there is food, centrality and type, and finally find the global food content. Passing the filter only means that the calculation needs to continue, but it does not mean that the solar eclipse can be seen from any location.
give it a try
Let’s first look at the partial solar eclipse of 1993 and the total solar eclipse of 2009, and then move the new moon to observe why the shadow axis may be staggered. The date is in TT, not the local forecast.
No need to memorize symbols
- k
- Integer candidate crescent number
- γ
- The distance between the Moon's shadow axis and the Earth's center, in units of the Earth's equatorial radius
- u
- Core shadow cone parameters on the fundamental plane
- food portion
- Occluded diameter ratio, not area ratio
Algorithm, accuracy and scope of application
According to Chapter 54 complete F screening, 54.1 time correction, P/Q/W, γ/u and center/non-center, full/ring/full ring/partial eclipse judgment and maximum partial eclipse score. The moon-phase-times.truePhase(k).mean is used as the basis for the moon-phase-times, and does not replace the moon-phase-times with the true phase-times. When the non-central core shadow touches, the total eclipse/annular eclipse is distinguished according to the original book branch, and the sqrt(1−γ²) of the central eclipse is not extrapolated when |γ|>1. The typical error of the model from 1951 to 2050 is on the order of minutes. The control is extended to about 1900 to 2100 for teaching purposes only and does not promote precise predictions. The basic plane of the diagram is an eclipse geometry section and cannot read surface paths or urban scenes.
my understanding check
What is the amount of γ in the picture?
The minimum distance from the shadow axis to the center of the earth — The unit is the earth's equatorial radius, not the local observation distance.
If the algorithm shows a total solar eclipse, does it mean that the total eclipse can be seen all over the world?
No, just the overall type of event — The totality of the eclipse is usually visible only in a very narrow area.
Can this lesson directly give you the precise path of the solar eclipse near your home?
No, you need local food algorithm and root number — Chapter 54 of the original book clearly does not count local solar eclipses.
A solar eclipse depends on whether the shadow actually touches the earth; it is a global event and cannot be directly regarded as the scene at your doorstep.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 54 chapter