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Simplified and optimized nutation formula.
While trying to convert ecliptic coordinates from mean equinox of date to true equinox of date, I ran into excessive overhead from the IAU2000B nutation model. The fact that it uses 77 trigonometric terms made the calculations a lot slower. https://apps.dtic.mil/sti/pdfs/AD1112517.pdf Page 4 in the above document mentions a shorter series “NOD version 2” that has 13 terms instead of 77 as used in IAU2000B. I had not noticed NOD2 before, because it appears only in the FORTRAN version of NOVAS 3.x, not the C version. After reading the FORTRAN code, I realized NOD2 is the same as IAU2000B, only it keeps the first 13 of 77 terms. The terms are already arranged in descending order of significance, so it is easy to truncate the series. Based on this discovery, I realized I could achieve all of the required accuracy needed for Astronomy Engine by keeping only the first 5 terms of the nutation series. This tremendously speeds up nutation calculations while sacrificing only a couple of arcseconds of accuracy. It also makes the minified JavaScript code smaller: Before: 119500 bytes. After: 116653 bytes. So that's what I did here. Most of the work was updating unit tests for accepting slightly different calculation results. The nutation formula change did trigger detection of a lurking bug in the inverse_terra functions, which convert a geocentric vector into latitude, longitude, and elevation (i.e. an Observer object). The Newton's Method loop in this function was not always converging, resulting in an infinite loop. I fixed that by increasing the convergence threshold and throwing an exception if the loop iterates more than 10 times. I also fixed a couple of bugs in the `demotest` scripts.
This commit is contained in:
Don Cross
@@ -1030,7 +1030,6 @@ class Spherical:
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class _iau2000b:
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def __init__(self, time):
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t = time.tt / 36525.0
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el = math.fmod((485868.249036 + t*1717915923.2178), _ASEC360) * _ASEC2RAD
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elp = math.fmod((1287104.79305 + t*129596581.0481), _ASEC360) * _ASEC2RAD
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f = math.fmod((335779.526232 + t*1739527262.8478), _ASEC360) * _ASEC2RAD
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d = math.fmod((1072260.70369 + t*1602961601.2090), _ASEC360) * _ASEC2RAD
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@@ -1072,508 +1071,6 @@ class _iau2000b:
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de += (73871.0 - 184.0*t)*carg - 1924.0*sarg
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arg = elp + 2.0*f - 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-516821.0 + 1226.0*t)*sarg - 524.0*carg
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de += (224386.0 - 677.0*t)*carg - 174.0*sarg
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sarg = math.sin(el)
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carg = math.cos(el)
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dp += (711159.0 + 73.0*t)*sarg - 872.0*carg
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de += (-6750.0)*carg + 358.0*sarg
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arg = 2.0*f + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-387298.0 - 367.0*t)*sarg + 380.0*carg
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de += (200728.0 + 18.0*t)*carg + 318.0*sarg
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arg = el + 2.0*f + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-301461.0 - 36.0*t)*sarg + 816.0*carg
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de += (129025.0 - 63.0*t)*carg + 367.0*sarg
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arg = -elp + 2.0*f - 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (215829.0 - 494.0*t)*sarg + 111.0*carg
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de += (-95929.0 + 299.0*t)*carg + 132.0*sarg
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arg = 2.0*f - 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (128227.0 + 137.0*t)*sarg + 181.0*carg
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de += (-68982.0 - 9.0*t)*carg + 39.0*sarg
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arg = -el + 2.0*f + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (123457.0 + 11.0*t)*sarg + 19.0*carg
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de += (-53311.0 + 32.0*t)*carg - 4.0*sarg
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arg = -el + 2.0*d
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (156994.0 + 10.0*t)*sarg - 168.0*carg
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de += (-1235.0)*carg + 82.0*sarg
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arg = el + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (63110.0 + 63.0*t)*sarg + 27.0*carg
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de += (-33228.0)*carg - 9.0*sarg
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arg = -el + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-57976.0 - 63.0*t)*sarg - 189.0*carg
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de += (31429.0)*carg - 75.0*sarg
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arg = -el + 2.0*f + 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-59641.0 - 11.0*t)*sarg + 149.0*carg
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de += (25543.0 - 11.0*t)*carg + 66.0*sarg
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arg = el + 2.0*f + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-51613.0 - 42.0*t)*sarg + 129.0*carg
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de += (26366.0)*carg + 78.0*sarg
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arg = -2.0*el + 2.0*f + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (45893.0 + 50.0*t)*sarg + 31.0*carg
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de += (-24236.0 - 10.0*t)*carg + 20.0*sarg
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arg = 2.0*d
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (63384.0 + 11.0*t)*sarg - 150.0*carg
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de += (-1220.0)*carg + 29.0*sarg
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arg = 2.0*f + 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-38571.0 - 1.0*t)*sarg + 158.0*carg
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de += (16452.0 - 11.0*t)*carg + 68.0*sarg
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arg = -2.0*elp + 2.0*f - 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (32481.0)*sarg
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de += (-13870.0)*carg
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arg = -2.0*el + 2.0*d
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-47722.0)*sarg - 18.0*carg
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de += (477.0)*carg - 25.0*sarg
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arg = 2.0*el + 2.0*f + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-31046.0 - 1.0*t)*sarg + 131.0*carg
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de += (13238.0 - 11.0*t)*carg + 59.0*sarg
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arg = el + 2.0*f - 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (28593.0)*sarg - carg
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de += (-12338.0 + 10.0*t)*carg - 3.0*sarg
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arg = -el + 2.0*f + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (20441.0 + 21.0*t)*sarg + 10.0*carg
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de += (-10758.0)*carg - 3.0*sarg
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arg = 2.0*el
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (29243.0)*sarg - 74.0*carg
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de += (-609.0)*carg + 13.0*sarg
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arg = 2.0*f
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (25887.0)*sarg - 66.0*carg
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de += (-550.0)*carg + 11.0*sarg
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arg = elp + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-14053.0 - 25.0*t)*sarg + 79.0*carg
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de += (8551.0 - 2.0*t)*carg - 45.0*sarg
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arg = -el + 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (15164.0 + 10.0*t)*sarg + 11.0*carg
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de += (-8001.0)*carg - sarg
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arg = 2.0*elp + 2.0*f - 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-15794.0 + 72.0*t)*sarg - 16.0*carg
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de += (6850.0 - 42.0*t)*carg - 5.0*sarg
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arg = -2.0*f + 2.0*d
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (21783.0)*sarg + 13.0*carg
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de += (-167.0)*carg + 13.0*sarg
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arg = el - 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-12873.0 - 10.0*t)*sarg - 37.0*carg
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de += (6953.0)*carg - 14.0*sarg
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arg = -elp + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-12654.0 + 11.0*t)*sarg + 63.0*carg
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de += (6415.0)*carg + 26.0*sarg
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arg = -el + 2.0*f + 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-10204.0)*sarg + 25.0*carg
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de += (5222.0)*carg + 15.0*sarg
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arg = 2.0*elp
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (16707.0 - 85.0*t)*sarg - 10.0*carg
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de += (168.0 - 1.0*t)*carg + 10.0*sarg
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arg = el + 2.0*f + 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-7691.0)*sarg + 44.0*carg
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de += (3268.0)*carg + 19.0*sarg
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arg = -2.0*el + 2.0*f
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-11024.0)*sarg - 14.0*carg
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de += (104.0)*carg + 2.0*sarg
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arg = elp + 2.0*f + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (7566.0 - 21.0*t)*sarg - 11.0*carg
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de += (-3250.0)*carg - 5.0*sarg
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arg = 2.0*f + 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-6637.0 - 11.0*t)*sarg + 25.0*carg
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de += (3353.0)*carg + 14.0*sarg
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arg = -elp + 2.0*f + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-7141.0 + 21.0*t)*sarg + 8.0*carg
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de += (3070.0)*carg + 4.0*sarg
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arg = 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-6302.0 - 11.0*t)*sarg + 2.0*carg
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de += (3272.0)*carg + 4.0*sarg
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arg = el + 2.0*f - 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (5800.0 + 10.0*t)*sarg + 2.0*carg
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de += (-3045.0)*carg - sarg
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arg = 2.0*el + 2.0*f - 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (6443.0)*sarg - 7.0*carg
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de += (-2768.0)*carg - 4.0*sarg
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arg = -2.0*el + 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-5774.0 - 11.0*t)*sarg - 15.0*carg
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de += (3041.0)*carg - 5.0*sarg
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arg = 2.0*el + 2.0*f + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-5350.0)*sarg + 21.0*carg
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de += (2695.0)*carg + 12.0*sarg
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arg = -elp + 2.0*f - 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-4752.0 - 11.0*t)*sarg - 3.0*carg
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de += (2719.0)*carg - 3.0*sarg
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arg = -2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-4940.0 - 11.0*t)*sarg - 21.0*carg
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de += (2720.0)*carg - 9.0*sarg
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arg = -el - elp + 2.0*d
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (7350.0)*sarg - 8.0*carg
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de += (-51.0)*carg + 4.0*sarg
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arg = 2.0*el - 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (4065.0)*sarg + 6.0*carg
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de += (-2206.0)*carg + sarg
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arg = el + 2.0*d
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (6579.0)*sarg - 24.0*carg
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de += (-199.0)*carg + 2.0*sarg
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arg = elp + 2.0*f - 2.0*d + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (3579.0)*sarg + 5.0*carg
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de += (-1900.0)*carg + sarg
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arg = el - elp
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (4725.0)*sarg - 6.0*carg
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de += (-41.0)*carg + 3.0*sarg
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arg = -2.0*el + 2.0*f + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-3075.0)*sarg - 2.0*carg
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de += (1313.0)*carg - sarg
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arg = 3.0*el + 2.0*f + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-2904.0)*sarg + 15.0*carg
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de += (1233.0)*carg + 7.0*sarg
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arg = -elp + 2.0*d
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (4348.0)*sarg - 10.0*carg
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de += (-81.0)*carg + 2.0*sarg
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arg = el - elp + 2.0*f + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-2878.0)*sarg + 8.0*carg
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de += (1232.0)*carg + 4.0*sarg
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sarg = math.sin(d)
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carg = math.cos(d)
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dp += (-4230.0)*sarg + 5.0*carg
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de += (-20.0)*carg - 2.0*sarg
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arg = -el - elp + 2.0*f + 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-2819.0)*sarg + 7.0*carg
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de += (1207.0)*carg + 3.0*sarg
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arg = -el + 2.0*f
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-4056.0)*sarg + 5.0*carg
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de += (40.0)*carg - 2.0*sarg
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arg = -elp + 2.0*f + 2.0*d + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-2647.0)*sarg + 11.0*carg
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de += (1129.0)*carg + 5.0*sarg
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arg = -2.0*el + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (-2294.0)*sarg - 10.0*carg
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de += (1266.0)*carg - 4.0*sarg
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arg = el + elp + 2.0*f + 2.0*om
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sarg = math.sin(arg)
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carg = math.cos(arg)
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dp += (2481.0)*sarg - 7.0*carg
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de += (-1062.0)*carg - 3.0*sarg
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arg = 2.0*el + om
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sarg = math.sin(arg)
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carg = math.cos(arg)
|
||||
dp += (2179.0)*sarg - 2.0*carg
|
||||
de += (-1129.0)*carg - 2.0*sarg
|
||||
|
||||
|
||||
arg = -el + elp + d
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (3276.0)*sarg + carg
|
||||
de += (-9.0)*carg
|
||||
|
||||
|
||||
arg = el + elp
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (-3389.0)*sarg + 5.0*carg
|
||||
de += (35.0)*carg - 2.0*sarg
|
||||
|
||||
|
||||
arg = el + 2.0*f
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (3339.0)*sarg - 13.0*carg
|
||||
de += (-107.0)*carg + sarg
|
||||
|
||||
|
||||
arg = -el + 2.0*f - 2.0*d + om
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (-1987.0)*sarg - 6.0*carg
|
||||
de += (1073.0)*carg - 2.0*sarg
|
||||
|
||||
|
||||
arg = el + 2.0*om
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (-1981.0)*sarg
|
||||
de += (854.0)*carg
|
||||
|
||||
|
||||
arg = -el + d
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (4026.0)*sarg - 353.0*carg
|
||||
de += (-553.0)*carg - 139.0*sarg
|
||||
|
||||
|
||||
arg = 2.0*f + d + 2.0*om
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (1660.0)*sarg - 5.0*carg
|
||||
de += (-710.0)*carg - 2.0*sarg
|
||||
|
||||
|
||||
arg = -el + 2.0*f + 4.0*d + 2.0*om
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (-1521.0)*sarg + 9.0*carg
|
||||
de += (647.0)*carg + 4.0*sarg
|
||||
|
||||
|
||||
arg = -el + elp + d + om
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (1314.0)*sarg
|
||||
de += (-700.0)*carg
|
||||
|
||||
|
||||
arg = -2.0*elp + 2.0*f - 2.0*d + om
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (-1283.0)*sarg
|
||||
de += (672.0)*carg
|
||||
|
||||
|
||||
arg = el + 2.0*f + 2.0*d + om
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (-1331.0)*sarg + 8.0*carg
|
||||
de += (663.0)*carg + 4.0*sarg
|
||||
|
||||
|
||||
arg = -2.0*el + 2.0*f + 2.0*d + 2.0*om
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (1383.0)*sarg - 2.0*carg
|
||||
de += (-594.0)*carg - 2.0*sarg
|
||||
|
||||
|
||||
arg = -el + 2.0*om
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (1405.0)*sarg + 4.0*carg
|
||||
de += (-610.0)*carg + 2.0*sarg
|
||||
|
||||
|
||||
arg = el + elp + 2.0*f - 2.0*d + 2.0*om
|
||||
sarg = math.sin(arg)
|
||||
carg = math.cos(arg)
|
||||
dp += (1290.0)*sarg
|
||||
de += (-556.0)*carg
|
||||
|
||||
|
||||
self.dpsi = -0.000135 + (dp * 1.0e-7)
|
||||
self.deps = +0.000388 + (de * 1.0e-7)
|
||||
|
||||
@@ -1870,7 +1367,11 @@ def _inverse_terra(ovec, st):
|
||||
# Numerically solve for exact latitude, using Newton's Method.
|
||||
# Start with initial latitude estimate, based on a spherical Earth.
|
||||
lat = math.atan2(z, p)
|
||||
count = 0
|
||||
while True:
|
||||
count += 1
|
||||
if count > 10:
|
||||
raise NoConvergeError()
|
||||
# Calculate the error function W(lat).
|
||||
# We try to find the root of W, meaning where the error is 0.
|
||||
cos = math.cos(lat)
|
||||
@@ -1881,7 +1382,7 @@ def _inverse_terra(ovec, st):
|
||||
radicand = cos2 + _EARTH_FLATTENING_SQUARED*sin2
|
||||
denom = math.sqrt(radicand)
|
||||
W = (factor*sin*cos)/denom - z*cos + p*sin
|
||||
if abs(W) < 1.0e-12:
|
||||
if abs(W) < 1.0e-8:
|
||||
# The error is now negligible
|
||||
break
|
||||
# Error is still too large. Find the next estimate.
|
||||
|
||||
@@ -1,6 +1,6 @@
|
||||
Moon horizontal position: azimuth = 274.486, altitude = 52.101
|
||||
Moon check: (1.00000000, 0.00000000, 0.00000000, 2021-03-22T02:45:00.000Z)
|
||||
Sun vector: (-0.08853032, -0.31939128, -0.93966315, 2021-03-22T02:45:00.000Z)
|
||||
Sun vector: (-0.08853032, -0.31939168, -0.93966301, 2021-03-22T02:45:00.000Z)
|
||||
Tilt angle of sunlit side of the Moon = -108.773 degrees counterclockwise from up.
|
||||
Moon magnitude = -10.27, phase angle = 84.22 degrees.
|
||||
Angle between Moon and Sun as seen from Earth = 95.64 degrees.
|
||||
|
||||
@@ -1,18 +1,18 @@
|
||||
2021-06-01T01:43:20.541Z : Moon leaves Capricornus and enters Aquarius.
|
||||
2021-06-03T12:20:46.838Z : Moon leaves Aquarius and enters Pisces.
|
||||
2021-06-04T04:34:27.462Z : Moon leaves Pisces and enters Cetus.
|
||||
2021-06-05T03:50:55.578Z : Moon leaves Cetus and enters Pisces.
|
||||
2021-06-06T11:54:31.605Z : Moon leaves Pisces and enters Cetus.
|
||||
2021-06-06T17:34:49.663Z : Moon leaves Cetus and enters Aries.
|
||||
2021-06-08T05:07:03.314Z : Moon leaves Aries and enters Taurus.
|
||||
2021-06-11T08:17:23.503Z : Moon leaves Taurus and enters Gemini.
|
||||
2021-06-13T13:37:29.676Z : Moon leaves Gemini and enters Cancer.
|
||||
2021-06-15T02:27:52.855Z : Moon leaves Cancer and enters Leo.
|
||||
2021-06-17T18:40:24.889Z : Moon leaves Leo and enters Virgo.
|
||||
2021-06-20T23:40:23.918Z : Moon leaves Virgo and enters Libra.
|
||||
2021-06-22T17:24:01.131Z : Moon leaves Libra and enters Scorpius.
|
||||
2021-06-23T01:36:00.285Z : Moon leaves Scorpius and enters Ophiuchus.
|
||||
2021-06-24T07:36:08.558Z : Moon leaves Ophiuchus and enters Sagittarius.
|
||||
2021-06-26T12:43:42.853Z : Moon leaves Sagittarius and enters Capricornus.
|
||||
2021-06-28T10:40:55.317Z : Moon leaves Capricornus and enters Aquarius.
|
||||
2021-06-30T19:53:26.683Z : Moon leaves Aquarius and enters Pisces.
|
||||
2021-06-01T01:43:20.607Z : Moon leaves Capricornus and enters Aquarius.
|
||||
2021-06-03T12:20:46.904Z : Moon leaves Aquarius and enters Pisces.
|
||||
2021-06-04T04:34:27.528Z : Moon leaves Pisces and enters Cetus.
|
||||
2021-06-05T03:50:55.644Z : Moon leaves Cetus and enters Pisces.
|
||||
2021-06-06T11:54:31.671Z : Moon leaves Pisces and enters Cetus.
|
||||
2021-06-06T17:34:49.729Z : Moon leaves Cetus and enters Aries.
|
||||
2021-06-08T05:07:03.380Z : Moon leaves Aries and enters Taurus.
|
||||
2021-06-11T08:17:23.569Z : Moon leaves Taurus and enters Gemini.
|
||||
2021-06-13T13:37:29.742Z : Moon leaves Gemini and enters Cancer.
|
||||
2021-06-15T02:27:52.921Z : Moon leaves Cancer and enters Leo.
|
||||
2021-06-17T18:40:24.949Z : Moon leaves Leo and enters Virgo.
|
||||
2021-06-20T23:40:23.974Z : Moon leaves Virgo and enters Libra.
|
||||
2021-06-22T17:24:01.187Z : Moon leaves Libra and enters Scorpius.
|
||||
2021-06-23T01:36:00.307Z : Moon leaves Scorpius and enters Ophiuchus.
|
||||
2021-06-24T07:36:08.596Z : Moon leaves Ophiuchus and enters Sagittarius.
|
||||
2021-06-26T12:43:42.908Z : Moon leaves Sagittarius and enters Capricornus.
|
||||
2021-06-28T10:40:55.380Z : Moon leaves Capricornus and enters Aquarius.
|
||||
2021-06-30T19:53:26.746Z : Moon leaves Aquarius and enters Pisces.
|
||||
|
||||
@@ -1,11 +1,11 @@
|
||||
search : 2015-02-28T00:00:00.000Z
|
||||
Sun : 2015-02-28T18:12:31.045Z altitude= 52.13 azimuth= 180.00
|
||||
Moon : 2015-02-28T01:58:15.631Z altitude= 77.88 azimuth= 180.00
|
||||
Mercury : 2015-02-28T16:31:18.940Z altitude= 42.57 azimuth= 180.00
|
||||
Sun : 2015-02-28T18:12:31.044Z altitude= 52.13 azimuth= 180.00
|
||||
Moon : 2015-02-28T01:58:15.630Z altitude= 77.88 azimuth= 180.00
|
||||
Mercury : 2015-02-28T16:31:18.939Z altitude= 42.57 azimuth= 180.00
|
||||
Venus : 2015-02-28T20:03:56.711Z altitude= 63.24 azimuth= 180.00
|
||||
Mars : 2015-02-28T19:52:21.643Z altitude= 62.24 azimuth= 180.00
|
||||
Jupiter : 2015-02-28T04:40:04.004Z altitude= 77.29 azimuth= 180.00
|
||||
Mars : 2015-02-28T19:52:21.644Z altitude= 62.24 azimuth= 180.00
|
||||
Jupiter : 2015-02-28T04:40:04.003Z altitude= 77.29 azimuth= 180.00
|
||||
Saturn : 2015-02-28T11:40:53.878Z altitude= 40.96 azimuth= 180.00
|
||||
Uranus : 2015-02-28T20:20:51.246Z altitude= 65.12 azimuth= 180.00
|
||||
Neptune : 2015-02-28T18:04:23.942Z altitude= 50.53 azimuth= 180.00
|
||||
Pluto : 2015-02-28T14:31:39.865Z altitude= 39.51 azimuth= 180.00
|
||||
Neptune : 2015-02-28T18:04:23.941Z altitude= 50.53 azimuth= 180.00
|
||||
Pluto : 2015-02-28T14:31:39.864Z altitude= 39.51 azimuth= 180.00
|
||||
|
||||
@@ -1,2 +1,2 @@
|
||||
Ecliptic longitude 93.6460 descends through horizon az 296.3883, alt -1.7327e-07
|
||||
Ecliptic longitude 274.9704 ascends through horizon az 115.7274, alt 2.1042e-07
|
||||
Ecliptic longitude 93.6460 descends through horizon az 296.3883, alt -1.2786e-07
|
||||
Ecliptic longitude 274.9704 ascends through horizon az 115.7274, alt 1.1404e-07
|
||||
|
||||
@@ -1,5 +1,5 @@
|
||||
search : 2018-11-30T17:55:07.234Z
|
||||
sunrise : 2018-12-01T13:22:51.098Z
|
||||
sunset : 2018-11-30T22:21:03.107Z
|
||||
moonrise : 2018-12-01T06:49:32.984Z
|
||||
moonrise : 2018-12-01T06:49:32.983Z
|
||||
moonset : 2018-11-30T19:22:02.736Z
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
March equinox : 2019-03-20T21:58:19.248Z
|
||||
June solstice : 2019-06-21T15:54:02.001Z
|
||||
September equinox : 2019-09-23T07:49:59.929Z
|
||||
December solstice : 2019-12-22T04:19:32.258Z
|
||||
March equinox : 2019-03-20T21:58:18.532Z
|
||||
June solstice : 2019-06-21T15:54:02.462Z
|
||||
September equinox : 2019-09-23T07:49:57.766Z
|
||||
December solstice : 2019-12-22T04:19:32.601Z
|
||||
|
||||
Reference in New Issue
Block a user