The moon sometimes goes very high. Can it be the same height every month?
First calculate how far north or south the moon can go, and then consider where you stand.
Sometimes the moon goes very high in the sky, and sometimes it passes low in the sky. The moon's orbit is tilted relative to the ecliptic, which in turn is tilted relative to the celestial equator. After superposition, its extreme declination changes with an 18.6-year cycle. Here we first find the northernmost or southernmost declination event in each round.
Guess first
Is the moment when the moon's declination reaches its northernmost point, exactly overhead in every place?
Show answer and explanation
no — The height of the ground also depends on the latitude and local time angle. The extreme declination cannot be directly regarded as the extreme local altitude.
Then connect experience and science
Separate "how far north you can go" from "how high you can raise your head"
Declination is the north-south angle relative to the celestial equator; local altitude also depends on latitude and the Earth's rotation.
Declination δ ≠ local height h
Find the north or south extreme value in each round
The original book gives the starting angle and period correction for north and south respectively, and finds the extreme moment and the extreme value.
44 corrections for time; 37 corrections for amplitude
Long periods change extreme ranges
The Moon's orbital node slowly moves, causing the extreme declination to vary between approximately 18° and 29°, rather than being permanently fixed at 23.4°.
Relevant to approximately 18.6 year nodal cycle
If you change your standing position, you will see a different height
The height of the midheaven at different latitudes can be very different for the same declination. The moment when the declination extreme occurs does not necessarily happen to be at the midheaven where you are.
Geometric height of Midheaven = 90° − |φ − δ|
The northward and southward extreme values are calculated separately in time and amplitude. The sign of declination cannot be directly used as the sign of time correction. Declination is the celestial coordinate, and the height of the location also needs to enter φ and H.
give it a try
Compare the northward extreme values around 1988 and 2006, and then cut to the southward direction. The side view shows the geometric height "if this declination reaches the midheaven here at you", not the real-time elevation angle at the extreme moment.
No need to memorize symbols
- δ
- The geocentric declination of the center of the moon, south is negative
- φ
- Geographical latitude, north is positive
- k
- Integer number of maximum declination event for each category
- TT / JDE
- Dynamic time labels for extreme moments
Algorithm, accuracy and scope of application
Realize the different parameters of Chapter 52 North/South, all 44 times and 37 amplitude corrections; the south direction result takes a negative sign, and k is an integer. Example 52. a/b and AA+ multiple sets of k checks. In addition, the existing Astro.horizontal(lat, δ, 0) is used to compare the mid-heaven height, and it is clear that it is not the local elevation angle at the declination extreme TT time. This lesson does not calculate real-time lunar coordinates or local highest point time, and does not use simple sine instead of periodic formula.
my understanding check
What symbol is used for maximum southward declination in this lesson?
negative number — The declination is negative toward the south, and the southward amplitude of the original formula needs to be added with a negative sign after calculation.
Does the change around 18.6 years mean that the moon reaches the same extreme declination each cycle?
no the same — The direction of the intersection slowly changes, and with it the range of extreme declinations.
Is the upper meridian height on the right the real-time elevation of your home at the extreme TT moment?
No, it’s a conditional geometric comparison — Here we only ask "how high would the midheaven be at the declination?" and do not calculate the local hour angle at that moment.
You need to first know how far north or south the moon reaches on the celestial sphere, and then combine your location and time to tell how high it is in front of you.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 52 chapter