Why do lunar eclipses sometimes only dim and sometimes missing a large chunk?
Let the moon actually walk through the penumbra and umbra to see which boundary is touched.
The Earth's shadow has different areas. When the moon just passes through the penumbra, the change may be difficult to detect; it will only become obvious when it enters the umbra. Here, the shadow section is drawn according to the calculated parameters of each full moon. The moon's position and contact time come from the same model.
Guess first
When the moon enters the penumbral shadow of the earth, will it be obviously missing a piece like an umbral eclipse?
Show answer and explanation
Not necessarily, maybe just a slight dimming — The penumbral lunar eclipse is weak and difficult to detect directly.
Then connect experience and science
The full moon also needs to be close to the nodes
Just because the moon is on the side of the earth facing away from the sun doesn't necessarily mean it's in the earth's shadow. The tilt of its orbit causes most full moons to pass by the Earth's shadow.
Full moon k is an integer plus 0.5
First divide the penumbra and umbra
When the moon enters the penumbra, there may be only a weak dimming; when it enters the umbra, there is a partial umbral eclipse; when the entire lunar surface enters the umbra, it is a total lunar eclipse.
The eclipse is calculated from γ, u and the diameter of the moon
Let the moon cross the shadow
Drag "How many minutes until eclipse" and the moon will pass through the shadow section at the approximate speed of this chapter. The radius of the image and the contact time use the same set of geometry.
n=0.5458+0.0400cos M′
Find the contact moment from geometry
Penumbra, umbra and totality each have a half duration. The non-existent phase does not forge the contact time, and the result is still TT.
Contact = duration ± half duration
First select the full moon k, find γ and u and the penumbral/umbral eclipse, and then find the various semi-durations. The contact time is added and subtracted with the eclipse as the center; when a certain type of eclipse does not exist, the negative radical term should not be forced to find the duration.
give it a try
Compare the penumbral lunar eclipse of 1973 with the total lunar eclipse of 1997, and drag the time to see which shadow you enter. Gray only represents the shadow partition and does not simulate the real moon surface color.
No need to memorize symbols
- penumbra/umbra
- Areas partially covered by the sun/completely covered by the sun
- γ
- Minimum distance between the moon's center and the earth's shadow axis, unit the earth's equatorial radius
- n
- Approximate velocity of motion on cross section
- food portion
- Radial intrusion, not area coverage
Algorithm, accuracy and scope of application
Realize 54.3/54.4, penumbra/umbral radius, total and partial eclipse/penumbral half duration and corresponding TT contact time. Lunar eclipses exist independently based on penumbral eclipses, and the 1.5433+u threshold for solar eclipses is not reused; the local AA+ CalculateLunar uses the solar threshold and will miss extreme edge penumbral cases, so the corresponding differences should be determined according to the original book. Use the French rule instead of adding 1/50 to all shadow radii; approximate the shadow as a circle, and do not model the true shadow oblateness and color. After candidate k is entered as an integer, 0.5 is added internally and formatted as the full moon date; no false eclipse is displayed when there is no eclipse.
my understanding check
What are the requirements for a total lunar eclipse?
The entire lunar disk enters the umbra — The total eclipse stage occurs only when the umbra completely surrounds the disc.
How should the total eclipse contact time be displayed when there is no total eclipse phase?
Display does not exist — Contacts that do not exist cannot be faked as occurring.
What is the food and contact time shown here?
TT — Converting to UT1 or UTC requires corresponding time scale information, and the display does not automatically change to local time.
The phase of a lunar eclipse depends on which shadow the moon encounters; using the same set of geometry can match the image to the moment of contact.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 54 chapter