The moon moves every day, how to calculate its direction and distance at the moment?
Change the day so that the Moon's position is actually recalculated from the original book's periodic terms.
The moon moves across the starry sky, and its distance from the earth is not constant. Starting from the lunar theory in the original book, the direction and distance to the center of the earth are given at the same time; the picture only projects the calculation results, and does not use a constant velocity circle to replace the ephemeris.
Guess first
Can the position of the moon be accurately described only by "moving at a constant speed in a fixed circular orbit"?
Show answer and explanation
No, there are more variations in direction and distance — Effects such as solar and orbital eccentricity require periodic terms to be treated.
Then connect experience and science
The moon's address is more than just a circle
We want to calculate direction and distance at the same time. Ecliptic longitude and latitude are relative to the date ecliptic, with distances measured from the center of the Earth.
Output λ, β, Δ and horizontal disparity
Calculate the rhythm of the moon and the sun together
Table 47.A/B of the original book has 60 items each, using basic angles such as the lunar mean angle and the sun-lunar elongation angle; items involving the solar mean angle must be corrected according to E or E².
Σl, Σr, Σb: Keep the original book entries completely
Obtain position after adding off-balance sheet compensation
Then add the additional items listed in the original book, the longitude and latitude are output in degrees, and the distance is in kilometers. It's still the truncated moon theory in the books.
λ=L′+Σl/10⁶；Δ=385000.56+Σr/1000
To view right ascension and declination, process the datum
First add the ecliptic nutation, and then use the true ecliptic angle to convert to the equatorial coordinates. Location and refraction have not been added yet, so they are not equivalent to the compass direction of your location.
Geometric celestial longitude + Δψ → geocentric equatorial coordinates
Expand the calculation
λSpend = L′ + Σl/10⁶ βSpend = Σb/10⁶ Δkm = 385000.56 + Σr/1000 π = asin(6378.14/Δ)
Σl, Σr, and Σb respectively accumulate the original lunar periodic table and the specified additional corrections; they are not the same summation. Only the output conversion is expanded here, and the period coefficient table is not omitted to zero.
give it a try
Let’s first look at the sample questions from the original book in 1992, and then push the date back. Compare the geometric ecliptic position to the geocentric equator position, noting that their reference axes are different.
No need to memorize symbols
- λ / β
- Geocentric yellow longitude/yellow latitude, degrees
- Δ / π
- Geocentric distance km / Equatorial horizontal parallax degree
- D,M,M′,F
- basic orbital angle
- Ω
- Moon's orbit mean ascending node celestial longitude
Algorithm, accuracy and scope of application
Completely implement 60 items each of Table 47.A/B, solar eccentricity E power, additional items outside the table, parallax, mean ascending node/perigee and main true ascending node compensation. The geometric ecliptic meridian does not contain nutation, and the retinotopic meridian adds nutation and rotates to the equator in conjunction with the Laskar true intersection angle. When comparing with local AA+, please note that CAAMoon::EclipticLongitude has been nutated. The direction of the node is not the moment of passing the node, which belongs to Chapter 51.
my understanding check
What is the starting point of the distance in this lesson?
center of earth — Surface observations also require corrections such as parallax.
In the table, the term "solar periapsis angle" appears twice. How should it be corrected?
E² — The original book stipulates that the power of E is determined based on the absolute multiple of M.
Can apparent right ascension and declination be used as compass directions without conversion?
Can't — The coordinate origin, datum and local ground plane must be clearly distinguished.
The lunar ephemeris requires the direction, distance and reference system to be calculated at the same time; a circular orbit diagram cannot replace actual calculations.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 47 chapter