Why does the sun move in different directions in the starry sky throughout the year?
Calculate the background direction of the sun as seen from the center of the Earth, with the date fixed.
The sun is so bright during the day that we cannot usually see the stars behind it; but we can calculate its position relative to the celestial coordinate grid. Drag the date of the year to see the ecliptic longitude turn around and the declination change from north to south. This is not a live positioning telescope.
Guess first
Is the sun's ecliptic longitude the angle it faces east or west when you stand on the ground?
Show answer and explanation
No, it’s the celestial sphere background coordinates — The ground orientation also requires the location and the earth's rotation time. This lesson first calculates the geocentric celestial position of the sun.
Then connect experience and science
Use dates to record the position of the sun
The direction of the sun relative to the background stars changes slowly over the year, rather than rising in the east and setting in the west throughout the day.
T = (JDE − 2451545.0)/36525
Start with average exercise
The sun's mean celestial longitude and periapsis angle are calculated based on dates; the earth's orbit is not a perfect circle, and the center difference needs to be added.
True Geometry Θ = L₀ + C
Then change to right ascension and declination
The ecliptic angle turns the ecliptic direction into the equatorial direction. The sun's declination changes from north to south within a year, which is related to seasonal sunshine.
α = atan2(cos ε sin λ, cos λ)
The accuracy should match the purpose
Switches between the elliptic approximation and the periodic term method of Appendix III. The latter route calculates the earth's yellow latitude, FK5 correction, nutation and optical aberration, and then obtains the solar apparent coordinates; it is still not a complete VSOP87.
Appendix Truncated Periodic Term ≠ Full VSOP87
Expand the calculation
T = (JDE−2451545)/36525 L₀ = 280.46646 + 36000.76983T + 0.0003032T² M = 357.52911 + 35999.05029T − 0.0001537T² C = (1.914602−0.004817T−0.000014T²)sin M + (0.019993−0.000101T)sin(2M) + 0.000289sin(3M) e = 0.016708634−0.000042037T−0.0000001267T² Θ = L₀+C；ν = M+C R = 1.000001018(1−e²)/(1+e cos ν) Ω = 125.04−1934.136T lambda view = Θ−0.00569−0.00478sin Ω εaverage = (84381.448−46.815T−0.00059T²+0.001813T³)/3600 ε = εaverage+0.00256cos Ω α = atan2(cos ε sin lambda view,cos lambda view) δ = asin(sin ε sin lambda view)
The above expands the low-precision branch: angle cost, ε adopts low-precision visual intersection angle; L₀, M, Θ, and λ are normalized. The high-precision branch is also calculated by appendix III to truncate the periodic term, instead of retaining more decimals on this chain.
give it a try
Compare the months around March, June, September and December; the "original book calculation example" goes back to October 13, 1992 for checking the algorithm.
No need to memorize symbols
- JDE / TD
- Number of consecutive days in dynamic time / How to write time scale in the original book
- L₀ / M / C
- Mean ecliptic longitude / mean periapsis angle / central deviation
- Θ / λ
- True Geometric Yellow Meridian / Approximate Retinal Meridian
- α / δ / R
- Right Ascension / Declination / Earth-Sun Distance (AU)
Algorithm, accuracy and scope of application
Two independent routes: low-precision calculation of elliptical motion according to Equation 25.1–25.8; higher precision calculation of the earth’s L0–L5, B0–B1, R0–R4 periodic terms in Appendix III (time unit is Julian thousand years, angle result is radians), taking the geocentric sun L +180°, −B, then use 25.9 for FK5 correction, the 63 nutations of 22.A and the 20.4898″/R optical aberration of 25.10 to obtain the apparent longitude, and use the true yellow declination angle to convert the apparent right ascension and declination. Coefficient facts and local AAEart h/AANutation table check, the algorithm is implemented independently in this file; the homepage approximate ephemeris is not used. The universal FK5 longitude correction of AA+ has an extra minimum term multiplied by tanβ, which is omitted in solar equation 25.9 in the book; date equator comparison. It also clarifies the difference between 22.2 and AA+ long-form 22.3 yellow-red intersection angle. The interface is only the 2000 and 1992 examples of the original book, and does not include the complete 2425-item VSOP87 and 25.11 extremely high-precision optical aberration branches.
my understanding check
Can showing a few more decimal places turn a low-precision model into a high-precision theory?
cannot — Physical terms omitted by the algorithm cannot be recovered by the output format.
Would the eccentricity of the Earth's orbit make the Sun's motion completely uniform relative to the background?
Won't — The low-precision method uses center differences to correct uniform average motion.
What time stamp is used for the dates here?
TD/JDE in the book — Dynamic time date not converted to local time zone.
First calculate the position of the sun in the celestial coordinate network, and then combine it with your location and time to know where it is in front of you.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 25 chapter