08e25680-5c37-4e20-b5f3-14e28445cbdb 51 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

The Analemma

t0 1 time :

You must visit the web for many descriptive Analemma photos. In short: Analemma is the observed path of the sun through the year. ... EOT(N) & δ(N) sources not recorded.

L H N xd i 1 N range x i el L i H L - N / * + : for x 21 line :

X 0366366 xd :

N EOT 7.9 2 π * N 3 - (* 365 / sin * 9.9 22 π * N 355 - (* 365 / (* sin * + (- :

EOT i 1366 range vx i el i : vy i el i EOT eval : 21 line for vx vy augment 21 line :

1rst/last day minutes

N Day number ≡

EOT 12 el EOT 3662 el 21 mat 3.3883 - 3.3883 - 21 mat

minmax 16.778 14.616 - 21 mat ≡

EOT minutes ≡

EOT(N) = Equation of Time ...min/day

EOT 0 2 1 sys

δ(n) is the current declination of the sun. Note that the sun declination is related to the local latitude and converted in clock hour provides the local daylight.

N δ 23.44 deg * - sin 360 deg * 365.24 / N 10 + (* 360 deg * π / 0.0167 * 360 deg * 365.24 / N 2 - (* sin * + cos * asin :

Sun i 1366 range vx i el i : vy i el i δ deg / eval : 21 line for vx vy augment 21 line :

box 14.616 - 23.44 16.778 23.44 16.778 23.44 - 14.616 - 23.44 - 14.616 - 23.44 52 mat :

A EOT 2 col Sun 2 col augment :

----------------day explore-----------------=>

J 90 :

XY A J 1 el A J 2 el . 14 black 15 mat :

J A J 1 el A J 2 el Sun J 1 el Sun J 2 el 22 mat 12 mat 90 4.9414 - 4.1476 90 4.1476 22 mat 12 mat

xy Sun J 1 el Sun J 2 el + 14 black 15 mat :

δ(N) = declination of the sun °deg/day

Sun 0 xy 3 1 sys

Analemma

A box XY 3 1 sys

The longest/shortest daylight

θLat 45.8833 :

Lat Local latitude ° ≡

θt 23.4382 :

θt Earth max inclination ° ≡

J π 182.625 / :

J Day cosine factor ≡

x m 1 θLat deg * tan θt deg * J x * cos * tan * - :

x b 1 x m - acos π / 24 * :

daylight D 13662 range : i 1 D rows range vx i el D i el : vy i el D i el b eval : 21 line for vx vy augment 31 line :

daylight 12 - 0 2 1 sys

daylight 2 col max daylight 2 col min 21 mat 15.541 8.4589 21 mat

1 time t0 - 11 s *

project Analemma on the sphere.

Analemma is an observed phenomenon, projection is decorative. Smath will allow this kind of projection by converting Analemma in the spherical coordinates system. For this part of the project evaluate 'N', copy/paste 'A & N' You may as well isolate 'M' so that if you play with Euler system, computation will be minimal.

A:=>

Analemma in spherical coordinates N λon A 1 col : λat A 2 col 90 - : i 1366 range X i el λat deg * i el sin λon deg * i el cos * eval : Y i el λat deg * i el sin λon deg * i el sin * eval : Z i el λat deg * i el cos eval : 31 line for X Y Z augment 21 line 31 line :

Analemma

λongitude λatitude

Sphere u v f u sin v cos * u sin v sin * u cos 31 mat :

N N :

M u v f 02 π * 02 π * 2424 CreateMesh :

angle Ω1 1000 angle cos angle sin - 0 angle sin angle cos 33 mat :

0 (π * 4 / 1 (π * 4 / 1 (π * 4 / 13 mat

Матрица преобразования для поворота вокруг оси y angle Ω2 angle cos 0 angle sin 010 angle sin - 0 angle cos 33 mat :

Матрица преобразования для поворота вокруг оси z angle Ω3 angle cos angle sin - 0 angle sin angle cos 000133 mat :

α 0 (π * 4 / :

β 1 (π * 4 / :

φ 1 (π * 4 / :

γ α Ω1 β Ω2 * φ Ω3 * eval :

γ 0.5 0.5 - 0.7071 0.7071 0.7071 0 0.5 - 0.5 0.7071 33 mat

N γ * 1 1 sys

image

1 time t0 - 47 s *

2d rotation of a data set

L H N xd i 1 N range x i el L i H L - N / * + : for x 21 line :

θ rot θ cos θ sin - θ sin θ cos 22 mat :

θ π - 2 / :

θ 1.5708 -

t 02 π * 50 xd :

a 0.5 :

G i 1 t rows range vx i el a t i el sin * : vy i el a t i el sin * t i el cos * : 21 line for vy vx augment 21 line :

Rot G θ rot * :

G Rot 2 1 sys

The 2d incremental plots in Smath native 3D

G Rot 2 1 sys