Solar Analemma in Stellarium Part 1 - Observations

heartifact · May 28, 2024, 12:33am

This topic explores the analemma of the sun, which is the pattern the sun makes in the sky if you were to photograph it daily at the same time from the same place over the course of a year.

Sky Observations of the Analemma

Figure 1 shows how the analemma appears in Stellarium, an open source planetarium software. The viewing location is from Bozeman, Montana at a latitude of N 45° 40' 46.74". The time which you decide to take the picture of the sun each day affects how high it appears in the sky. It also depends on the latitude of the observer.

Figure 1. Analemma viewed from Bozeman

Figure 2 is 25˚ farther to the south at Mauna Kea, Hawaii at a latitude of N 19° 49' 28.00". Looks very similar, just higher in the sky.

Figure 2. Analemma viewed from Mauna Kea

When viewed in the southern hemisphere, the analemma appears in the northern sky instead of the south. Figure 3 shows it from the Mount John University Observatory in New Zealand at a latitude of S 43° 59' 12.00". At first glance the analemma looks to be upside down relative to the previous locations, but this is only a matter of perspective because the observer has reversed directions and is looking to the north. Notice that the larger loop of the analemma points south for all the observations.

Figure 3. Analemma viewed from Mount John University

A Closer Look at the Analemma

The viewing location and time plays a big part in how the analemma appears in the sky. One way to eliminate these variables is to find the location on Earth where the sun appears directly overhead at the zenith, repeated daily. That way the path of the analemma can be conceptualized as the path the sun takes relative to the Earth. This is where Stellarium comes in to play, as I can write a script to automate the process of finding the lat/long coordinates of where the sun is directly overhead at a given time, then repeat for each day over the course of a year, and then plot those coordinates on a map.

Start & End Dates

The first step is selecting a start date. I chose to use the current year starting from when the sun is at its southern-most latitude, which occurs on the December solstice. I can find when the minimum occurs by checking several times near the solstice. The final results are shown in table 1 (times in UTC).

Table 1. 2023 & 2024 Minimum Latitudes

Date	Time	Latitude	Longitude	Day
12/22/23	3:18:49	-23.438307	129.858627	0
12/21/24	9:27:58	-23.438398	37.5679626	365.256354

Notice that the delta between these times comes out to approx 365.25 days, which is expected. This 0.25 day difference corresponds to the approx 90˚ difference in longitude.

Analemma Data

Table 2 gives the abbreviated analemma data from December 2023 to December 2024 from Stellarium. Full data here: (cannot upload csv files)

Table 2. Solar Analemma Zenith Coordinates

Date	Time	Latitude	Longitude
12/22/2023	3:18:49	-23.438307	129.858643
1/22/2024	3:18:49	-19.807928	133.128906
2/22/2024	3:18:49	-10.408749	133.685547
3/21/2024	3:18:49	0.39851061	132.075684
4/21/2024	3:18:49	12.00142	129.964722
5/21/2024	3:18:49	20.2701874	129.449219
6/21/2024	3:18:49	23.437973	130.756836
7/21/2024	3:18:49	20.3850727	131.90918
8/21/2024	3:18:49	11.9705486	131.073975
9/21/2024	3:18:49	0.54159391	128.547852
10/21/2024	3:18:49	-10.84113	126.441406
11/21/2024	3:18:49	-19.999815	126.763672
12/21/2024	3:18:49	-23.438141	129.823608

These coordinates can then be plotted on a map as shown in figures 4 & 5.

Figure 4. Solar Analemma plotted on an equirectangular map

Figure 5. Solar Analemma plotted on an azimuthal equidistant map

Note: The stellarium measurements are in reference to the view of an observer on the earth (stationary & geocentric). It is possible to convert the measurements to a heliocentric model viewpoint, but I prefer to keep the measurements in their original form. I leave such conversions as an exercise to the reader if motivated to do so.

Figure 6 shows a closer look at the AE map re-oriented so that north is up. The latitude/longitude grid uses 5˚ major increments and 1˚ minor increments. The dashed line shows longitude 129.8586˚, which is the starting longitude on the 2023 December solstice. The equator is shown in orange and the tropics are yellow.

Figure 6. Detailed view of the solar analemma

Notice how the southern loop of the analemma is much bigger than the northern loop. The figure-eight shape crosses north of the equator at around 8.945˚, near April 12 and August 30. It takes 140 days for the sun to make the northern loop and 225 days to make the southern loop.

There’s a slight tilt to the analemma where the point at maximum latitude (occurring on the summer solstice) is 0.88 degrees to the east of the starting longitude. It can be estimated where this maximum point occurs by interpolating between nearby analemma points with the end result in table 3.

Date	Time	Latitude	Longitude*
6/20/24	20:46:26	23.4279671	130.648438

Table 3. Maximum Latitude

*This is the interpolated longitude along the path of the analemma, not the sun’s actual longitude at this time.

Longitudinal Variation

The deviation from the starting longitude can be plotted for all the points along the analemma as shown in figure 7. The sun reaches its east-most longitude on Feb 12 (133.845˚, delta of +3.986˚) and the west-most on November 2 (126.183˚, delta of -3.676˚). In the north loop the east-most longitude is reached on July 26 (131.933˚. delta of +2.074˚) and the west-most on May 13 (129.383, delta of -0.476˚).

Figure 7. Change in longitude of the solar analemma

The reason why these deviations in longitude occur is because the angular velocity of the sun varies throughout the year, as will be explored in the next section.

Solar Transits

The analemma is created by observing the change in position of the sun at a fixed time each day. Similarly, the reverse can be done observing the change in time (and also latitude) from when the sun crosses a fixed longitude each day. If the time between crossings is less than 24 hours then the sun has a faster angular velocity, and if more than 24 hours then the sun is traveling slower.

Table 4. Sun Transit Times for Longitude 129.8586

Date	Transit Time
12/22/23	03:18:49
1/22/24	03:31:53
2/22/24	03:34:06
3/21/24	03:27:40
4/21/24	03:19:13
5/21/24	03:17:10
6/21/24	03:22:24
7/21/24	03:27:00
8/21/24	03:23:40
9/21/24	03:13:34
10/21/24	03:05:09
11/21/24	03:06:25
12/21/24	03:18:40

Full data here: (unable to upload csv file)

The time between transits of the sun varies from 30 seconds longer on the December solstice to 21.5 seconds shorter on September 17 (in general fastest on the solstices and slowest a few days offset from the equinoxes). A complete plot is shown in figure 8.

Figure 8. Change in Sun Transit Times

The data can be converted to show angular speed as degrees longitude per hour, where a baseline speed of 15 degrees per hour equates to a time of 24 hours between transits. This plot is shown in figure 9.

Figure 9. Sun Daily Angular Speed

A difference of a few thousands of a degree per hour might not seem like a lot, but it is cumulative to where it can add up to a few degrees of longitude difference over a few months. To prove it you can integrate to find the area under the curve, and it matches the change in longitude plot looked at earlier in figure 7.

Lastly the angular speed can be plotted against latitude as shown in figure 10. As expected the minimums occur on the solstices (at both tropics), and the maximums occur at approximately 2.25˚ north of the equator (a few days past the spring equinox and a few days before the fall equinox).

Figure 10. Angular Speed vs Latitude

What’s Next?

Part 2 will examine the sun’s sidereal motion and how it relates to the analemma.

Shane_St_Pierre · May 28, 2024, 1:16am

YOO. This is a ton of work. Great to see man…
love the stellarium exports and the overall depth of detail.
Impressed …
That being said, are you refuting that its latitude dependent?

heartifact · May 28, 2024, 2:53am

The analemma as viewed in the sky absolutely is latitude dependent, but that’s because the apparent position of the sun as viewed in the sky is latitude dependent. At any given moment, however, there is only one location on earth that has the sun at the zenith position, so that isn’t latitude dependent.

I would refute that latitude dependence as it is viewed in the sky could ever make the north loop appear larger than the south loop, because changing latitude doesn’t change the transit time of the sun. Therefore the north loop will take 140 days and the south loop will take 225 days regardless of latitude.

heartifact · May 28, 2024, 11:47am

I wasn’t able to upload the complete csv data because this forum doesn’t allow .csv or .txt uploads. I’ll try embedding it into the text of this post…

solar_analemma_2024.csv

Date,Time, Latitude, Longitude,Long/Hr
12/22/2023,3:18:49,-23.43830681,129.8586426,-14.99482727
12/23/2023,3:18:49,-23.43438148,129.9827271,-14.99483761
12/24/2023,3:18:49,-23.42261696,130.1068115,-14.99483761
12/25/2023,3:18:49,-23.40302086,130.2305908,-14.99484942
12/26/2023,3:18:49,-23.37560272,130.354126,-14.99486123
12/27/2023,3:18:49,-23.34037971,130.4772949,-14.99487305
12/28/2023,3:18:49,-23.29736519,130.5998535,-14.99489667
12/29/2023,3:18:49,-23.24657822,130.7216797,-14.99494393
12/30/2023,3:18:49,-23.18803978,130.8427734,-14.99496755
12/31/2023,3:18:49,-23.12177086,130.9628906,-14.99501481
1/01/2024,3:18:49,-23.04780197,131.0820313,-14.99508569
1/02/2024,3:18:49,-22.96616173,131.199707,-14.99513294
1/03/2024,3:18:49,-22.87688828,131.3164063,-14.99518019
1/04/2024,3:18:49,-22.78001976,131.4316406,-14.99522744
1/05/2024,3:18:49,-22.67559814,131.5454102,-14.9952747
1/06/2024,3:18:49,-22.56367493,131.6572266,-14.9953692
1/07/2024,3:18:49,-22.44430161,131.7675781,-14.99546371
1/08/2024,3:18:49,-22.31753349,131.8759766,-14.99555822
1/09/2024,3:18:49,-22.18343735,131.9819336,-14.99560547
1/10/2024,3:18:49,-22.0420742,132.0859375,-14.99569997
1/11/2024,3:18:49,-21.89351845,132.1879883,-14.99579448
1/12/2024,3:18:49,-21.73784637,132.2875977,-14.99593624
1/13/2024,3:18:49,-21.57513237,132.3847656,-14.99603075
1/14/2024,3:18:49,-21.40545845,132.4785156,-14.99612525
1/15/2024,3:18:49,-21.22890282,132.5703125,-14.99631426
1/16/2024,3:18:49,-21.04555321,132.6591797,-14.99631426
1/17/2024,3:18:49,-20.85549545,132.7451172,-14.99650328
1/18/2024,3:18:49,-20.65882492,132.828125,-14.99659778
1/19/2024,3:18:49,-20.45563507,132.9082031,-14.99678679
1/20/2024,3:18:49,-20.24602127,132.984375,-14.9968813
1/21/2024,3:18:49,-20.03008461,133.0585938,-14.99697581
1/22/2024,3:18:49,-19.80792809,133.1289063,-14.99716482
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1/25/2024,3:18:49,-19.10511398,133.3203125,-14.99754284
1/26/2024,3:18:49,-18.85906219,133.3779297,-14.99773185
1/27/2024,3:18:49,-18.60728645,133.4316406,-14.99782636
1/28/2024,3:18:49,-18.34988403,133.4824219,-14.99801537
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2/04/2024,3:18:49,-16.39922333,133.7437744,-14.99893681
2/05/2024,3:18:49,-16.10057449,133.7678223,-14.99907857
2/06/2024,3:18:49,-15.7972641,133.7885742,-14.99922033
2/07/2024,3:18:49,-15.4894104,133.8061523,-14.99933846
2/08/2024,3:18:49,-15.17713356,133.8203125,-14.99945659
2/09/2024,3:18:49,-14.8605547,133.8312988,-14.99962198
2/10/2024,3:18:49,-14.53979588,133.8388672,-14.99971648
2/11/2024,3:18:49,-14.21497917,133.8432617,-14.99990549
2/12/2024,3:18:49,-13.8862257,133.8447266,-15.00004725
2/13/2024,3:18:49,-13.55365658,133.8422852,-15.00014176
2/14/2024,3:18:49,-13.21739388,133.8369141,-15.00028352
2/15/2024,3:18:49,-12.87755966,133.8286133,-15.00042528
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3/25/2024,3:18:49,1.974111915,131.7739258,-15.00316595
3/26/2024,3:18:49,2.36643219,131.6982422,-15.00316595
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4/13/2024,3:18:49,9.197916031,130.4179688,-15.00255166
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4/28/2024,3:18:49,14.28257942,129.661377,-15.0015121
4/29/2024,3:18:49,14.59356022,129.6264648,-15.00141759
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5/10/2024,3:18:49,17.73171997,129.3964844,-15.00033077
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5/12/2024,3:18:49,18.24114799,129.3857422,-15.00009451
5/13/2024,3:18:49,18.4881916,129.3828125,-15.00009451
5/14/2024,3:18:49,18.73001289,129.3837891,-15
5/15/2024,3:18:49,18.96652985,129.3857422,-14.99990549
5/16/2024,3:18:49,19.19766808,129.390625,-14.99971648
5/17/2024,3:18:49,19.4233551,129.3984375,-14.99962198
5/18/2024,3:18:49,19.64351845,129.4072266,-14.99952747
5/19/2024,3:18:49,19.85808754,129.4189453,-14.99943296
5/20/2024,3:18:49,20.06699944,129.4326172,-14.99933846
5/21/2024,3:18:49,20.27018738,129.4492188,-14.99933846
5/22/2024,3:18:49,20.46759033,129.4667969,-14.99914945
5/23/2024,3:18:49,20.65914536,129.4873047,-14.99905494
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5/25/2024,3:18:49,21.02448463,129.5341797,-14.99896043
5/26/2024,3:18:49,21.19815063,129.5615234,-14.99886593
5/27/2024,3:18:49,21.36573792,129.5898438,-14.99877142
5/28/2024,3:18:49,21.52718735,129.6201172,-14.99867692
5/29/2024,3:18:49,21.6824398,129.6529388,-14.99860308
5/30/2024,3:18:49,21.83143806,129.6873779,-14.99852334
5/31/2024,3:18:49,21.97411919,129.7236938,-14.99845246
6/01/2024,3:18:49,22.11043167,129.7618408,-14.99838158
6/02/2024,3:18:49,22.24032021,129.8016357,-14.9983107
6/03/2024,3:18:49,22.36373711,129.8430176,-14.99823982
6/04/2024,3:18:49,22.48063278,129.8859863,-14.99815713
6/05/2024,3:18:49,22.59096527,129.9304199,-14.99810988
6/06/2024,3:18:49,22.69469452,129.9763184,-14.99808625
6/07/2024,3:18:49,22.79178047,130.0231934,-14.99801537
6/08/2024,3:18:49,22.88218498,130.0715332,-14.99796812
6/09/2024,3:18:49,22.96587372,130.1206055,-14.99792087
6/10/2024,3:18:49,23.04281425,130.1708984,-14.99787361
6/11/2024,3:18:49,23.11297607,130.222168,-14.99787361
6/12/2024,3:18:49,23.17633438,130.2734375,-14.99782636
6/13/2024,3:18:49,23.23286819,130.3261719,-14.99782636
6/14/2024,3:18:49,23.28255844,130.3789063,-14.99777911
6/15/2024,3:18:49,23.32538986,130.4321289,-14.99777911
6/16/2024,3:18:49,23.36135292,130.4858398,-14.99777911
6/17/2024,3:18:49,23.39043999,130.5400391,-14.99773185
6/18/2024,3:18:49,23.41264534,130.5942383,-14.99773185
6/19/2024,3:18:49,23.42796707,130.6484375,-14.99773185
6/20/2024,3:18:49,23.436409,130.7026367,-14.99773185
6/21/2024,3:18:49,23.43797302,130.7568359,-14.99782636
6/22/2024,3:18:49,23.43266678,130.8105469,-14.99773185
6/23/2024,3:18:49,23.42049599,130.8642578,-14.99782636
6/24/2024,3:18:49,23.40146828,130.9179688,-14.99782636
6/25/2024,3:18:49,23.37558937,130.9707031,-14.99782636
6/26/2024,3:18:49,23.3428669,131.0224609,-14.99782636
6/27/2024,3:18:49,23.3033123,131.0751953,-14.99782636
6/28/2024,3:18:49,23.2569313,131.1259766,-14.99782636
6/29/2024,3:18:49,23.20374489,131.1767578,-14.99792087
6/30/2024,3:18:49,23.14376831,131.2255859,-14.99792087
7/01/2024,3:18:49,23.07702827,131.2744141,-14.99801537
7/02/2024,3:18:49,23.00355148,131.3222656,-14.99801537
7/03/2024,3:18:49,22.92337227,131.3691406,-14.99810988
7/04/2024,3:18:49,22.83652496,131.4140625,-14.99820439
7/05/2024,3:18:49,22.74304771,131.4580078,-14.99820439
7/06/2024,3:18:49,22.64297867,131.5,-14.99829889
7/07/2024,3:18:49,22.5363636,131.5410156,-14.99829889
7/08/2024,3:18:49,22.42324257,131.5805817,-14.99842293
7/09/2024,3:18:49,22.30366516,131.6181641,-14.99846723
7/10/2024,3:18:49,22.17767715,131.6539307,-14.99854697
7/11/2024,3:18:49,22.04533195,131.6877441,-14.99862966
7/12/2024,3:18:49,21.90668106,131.7197266,-14.99871236
7/13/2024,3:18:49,21.76178169,131.7496338,-14.99879505
7/14/2024,3:18:49,21.61069489,131.7773438,-14.99888955
7/15/2024,3:18:49,21.45347786,131.8029785,-14.99898406
7/16/2024,3:18:49,21.29019356,131.826416,-14.99907857
7/17/2024,3:18:49,21.12090874,131.8476563,-14.99917307
7/18/2024,3:18:49,20.94568634,131.8666992,-14.99924395
7/19/2024,3:18:49,20.76459312,131.8833008,-14.99938571
7/20/2024,3:18:49,20.57770157,131.8974609,-14.99943296
7/21/2024,3:18:49,20.38507271,131.9091797,-14.99952747
7/22/2024,3:18:49,20.18677521,131.9189453,-14.99966923
7/23/2024,3:18:49,19.9828701,131.9257813,-14.99976373
7/24/2024,3:18:49,19.77341843,131.9306641,-14.99981099
7/25/2024,3:18:49,19.55848503,131.9331055,-14.99995275
7/26/2024,3:18:49,19.33813095,131.9331055,-15.00004725
7/27/2024,3:18:49,19.11242485,131.9306641,-15.00014176
7/28/2024,3:18:49,18.88143349,131.925293,-15.00023627
7/29/2024,3:18:49,18.64523506,131.9179688,-15.00033077
7/30/2024,3:18:49,18.40390587,131.9082031,-15.00042528
7/31/2024,3:18:49,18.15753174,131.8964844,-15.00056704
8/01/2024,3:18:49,17.90619278,131.8808594,-15.00066154
8/02/2024,3:18:49,17.64997292,131.8642578,-15.00075605
8/03/2024,3:18:49,17.38895988,131.8447266,-15.00085055
8/04/2024,3:18:49,17.12323761,131.8222656,-15.00094506
8/05/2024,3:18:49,16.85289192,131.7978516,-15.00103957
8/06/2024,3:18:49,16.57801056,131.7705078,-15.00122858
8/07/2024,3:18:49,16.29867935,131.7402344,-15.00132308
8/08/2024,3:18:49,16.01498413,131.7080078,-15.00141759
8/09/2024,3:18:49,15.72701836,131.6738281,-15.0015121
8/10/2024,3:18:49,15.43486691,131.6357422,-15.0016066
8/11/2024,3:18:49,15.13862038,131.5966797,-15.00170111
8/12/2024,3:18:49,14.83836842,131.5546875,-15.00189012
8/13/2024,3:18:49,14.53420162,131.5097656,-15.00198463
8/14/2024,3:18:49,14.22620869,131.4628906,-15.00198463
8/15/2024,3:18:49,13.91448116,131.4140625,-15.00207913
8/16/2024,3:18:49,13.59910774,131.3623047,-15.00217364
8/17/2024,3:18:49,13.28017616,131.3092346,-15.00227405
8/18/2024,3:18:49,12.95777321,131.253479,-15.00236265
8/19/2024,3:18:49,12.63198185,131.1956787,-15.00245125
8/20/2024,3:18:49,12.30288219,131.1357422,-15.00253985
8/21/2024,3:18:49,11.97054863,131.0739746,-15.00261073
8/22/2024,3:18:49,11.6350565,131.0102539,-15.00268161
8/23/2024,3:18:49,11.29647923,130.9448242,-15.0027643
8/24/2024,3:18:49,10.95489597,130.8774414,-15.00283518
8/25/2024,3:18:49,10.61038685,130.8085938,-15.00288243
8/26/2024,3:18:49,10.26303864,130.7380371,-15.00297694
8/27/2024,3:18:49,9.912940025,130.6660156,-15.00302419
8/28/2024,3:18:49,9.560183525,130.5927734,-15.00307145
8/29/2024,3:18:49,9.204861641,130.5175781,-15.0031187
8/30/2024,3:18:49,8.847068787,130.4414063,-15.00321321
8/31/2024,3:18:49,8.486898422,130.3637695,-15.00326046
9/01/2024,3:18:49,8.124445915,130.284668,-15.00330771
9/02/2024,3:18:49,7.759805202,130.2045898,-15.00335496
9/03/2024,3:18:49,7.393072128,130.1235352,-15.00340222
9/04/2024,3:18:49,7.024340153,130.0415039,-15.00344947
9/05/2024,3:18:49,6.653705597,129.9580078,-15.00349672
9/06/2024,3:18:49,6.281261921,129.8740234,-15.00354398
9/07/2024,3:18:49,5.9071064,129.7885742,-15.00354398
9/08/2024,3:18:49,5.53133297,129.7026367,-15.00363848
9/09/2024,3:18:49,5.154036999,129.6162109,-15.00368574
9/10/2024,3:18:49,4.775313377,129.5292969,-15.00359123
9/11/2024,3:18:49,4.39525795,129.4404297,-15.00368574
9/12/2024,3:18:49,4.013966084,129.3525391,-15.00368574
9/13/2024,3:18:49,3.631531954,129.2636719,-15.00368574
9/14/2024,3:18:49,3.248049021,129.1748047,-15.00378024
9/15/2024,3:18:49,2.863609314,129.0849609,-15.00368574
9/16/2024,3:18:49,2.478301048,128.9951172,-15.00368574
9/17/2024,3:18:49,2.092211723,128.9052734,-15.00378024
9/18/2024,3:18:49,1.705418706,128.8154297,-15.00378024
9/19/2024,3:18:49,1.317999601,128.7265625,-15.00378024
9/20/2024,3:18:49,0.930031478,128.6367188,-15.00368574
9/21/2024,3:18:49,0.541593909,128.5478516,-15.00368574
9/22/2024,3:18:49,0.152771011,128.4589844,-15.00368574
9/23/2024,3:18:49,-0.236348033,128.3710938,-15.00368574
9/24/2024,3:18:49,-0.625669718,128.2832031,-15.00359123
9/25/2024,3:18:49,-1.01509738,128.1972656,-15.00359123
9/26/2024,3:18:49,-1.404527903,128.111084,-15.00354398
9/27/2024,3:18:49,-1.793869972,128.0260315,-15.00352626
9/28/2024,3:18:49,-2.183014393,127.9418945,-15.00348491
9/29/2024,3:18:49,-2.571863651,127.8588257,-15.00343766
9/30/2024,3:18:49,-2.960315704,127.7768555,-15.00340222
10/01/2024,3:18:49,-3.348267794,127.6960449,-15.00334315
10/02/2024,3:18:49,-3.735616684,127.6165771,-15.0032959
10/03/2024,3:18:49,-4.122258186,127.5383301,-15.00323683
10/04/2024,3:18:49,-4.508088589,127.4616699,-15.00316595
10/05/2024,3:18:49,-4.893002987,127.3862305,-15.00309507
10/06/2024,3:18:49,-5.276895046,127.3125,-15.00302419
10/07/2024,3:18:49,-5.659653664,127.2402344,-15.00297694
10/08/2024,3:18:49,-6.041178703,127.1699219,-15.00288243
10/09/2024,3:18:49,-6.421362877,127.1010742,-15.00283518
10/10/2024,3:18:49,-6.800098896,127.0341797,-15.00274068
10/11/2024,3:18:49,-7.177279949,126.9692383,-15.00264617
10/12/2024,3:18:49,-7.552799702,126.90625,-15.00259892
10/13/2024,3:18:49,-7.926552773,126.8452148,-15.00250441
10/14/2024,3:18:49,-8.298435211,126.7861328,-15.0024099
10/15/2024,3:18:49,-8.668346405,126.7299805,-15.0023154
10/16/2024,3:18:49,-9.03619194,126.675293,-15.00222089
10/17/2024,3:18:49,-9.401869774,126.6235352,-15.00207913
10/18/2024,3:18:49,-9.76529789,126.5742188,-15.00198463
10/19/2024,3:18:49,-10.12638187,126.5273438,-15.00193737
10/20/2024,3:18:49,-10.48502636,126.4833984,-15.00179561
10/21/2024,3:18:49,-10.84113026,126.4414063,-15.00170111
10/22/2024,3:18:49,-11.1945858,126.4033203,-15.0016066
10/23/2024,3:18:49,-11.54528427,126.3681641,-15.00141759
10/24/2024,3:18:49,-11.89311314,126.3349609,-15.00132308
10/25/2024,3:18:49,-12.23795795,126.3056641,-15.00113407
10/26/2024,3:18:49,-12.57970428,126.2792969,-15.00103957
10/27/2024,3:18:49,-12.91823101,126.2548828,-15.00094506
10/28/2024,3:18:49,-13.25342751,126.2353516,-15.00075605
10/29/2024,3:18:49,-13.58517838,126.2177734,-15.00066154
10/30/2024,3:18:49,-13.91336727,126.2041016,-15.00047253
10/31/2024,3:18:49,-14.23787785,126.1933594,-15.00037802
11/01/2024,3:18:49,-14.55859375,126.1865234,-15.00018901
11/02/2024,3:18:49,-14.87539673,126.1826172,-15.00009451
11/03/2024,3:18:49,-15.18817043,126.1826172,-15
11/04/2024,3:18:49,-15.49679852,126.1855469,-14.99981099
11/05/2024,3:18:49,-15.80115891,126.1919098,-14.99968695
11/06/2024,3:18:49,-16.10113716,126.2017212,-14.99952156
11/07/2024,3:18:49,-16.39661598,126.2149048,-14.9993739
11/08/2024,3:18:49,-16.68748093,126.2315674,-14.99923214
11/09/2024,3:18:49,-16.97361755,126.251709,-14.99909038
11/10/2024,3:18:49,-17.25491142,126.2752686,-14.99894862
11/11/2024,3:18:49,-17.53125,126.3022461,-14.99879505
11/12/2024,3:18:49,-17.80252647,126.3327637,-14.99867692
11/13/2024,3:18:49,-18.06863785,126.3666992,-14.99853516
11/14/2024,3:18:49,-18.32948303,126.4040527,-14.99836977
11/15/2024,3:18:49,-18.58496475,126.4448242,-14.99822801
11/16/2024,3:18:49,-18.83498955,126.4892578,-14.99806263
11/17/2024,3:18:49,-19.07946205,126.5371094,-14.99796812
11/18/2024,3:18:49,-19.31828499,126.5883789,-14.99777911
11/19/2024,3:18:49,-19.55135345,126.6435547,-14.99763735
11/20/2024,3:18:49,-19.77856445,126.7016602,-14.99749559
11/21/2024,3:18:49,-19.99981499,126.7636719,-14.99735383
11/22/2024,3:18:49,-20.21500206,126.8286133,-14.99721207
11/23/2024,3:18:49,-20.42402267,126.8969727,-14.99711757
11/24/2024,3:18:49,-20.62677574,126.9692383,-14.99692855
11/25/2024,3:18:49,-20.82315826,127.0439453,-14.99683405
11/26/2024,3:18:49,-21.0130806,127.1225586,-14.99664504
11/27/2024,3:18:49,-21.19644547,127.2036133,-14.99659778
11/28/2024,3:18:49,-21.37316132,127.2880859,-14.99640877
11/29/2024,3:18:49,-21.54314041,127.3759766,-14.99631426
11/30/2024,3:18:49,-21.70629501,127.4658203,-14.99612525
12/01/2024,3:18:49,-21.8625412,127.5595703,-14.99603075
12/02/2024,3:18:49,-22.01180077,127.6552734,-14.99603075
12/03/2024,3:18:49,-22.15399551,127.7529297,-14.99593624
12/04/2024,3:18:49,-22.28904533,127.8535156,-14.99574723
12/05/2024,3:18:49,-22.41688156,127.9570313,-14.99565272
12/06/2024,3:18:49,-22.53743553,128.0625,-14.99565272
12/07/2024,3:18:49,-22.65063667,128.1699219,-14.99546371
12/08/2024,3:18:49,-22.75642967,128.2783203,-14.9953692
12/09/2024,3:18:49,-22.85475159,128.3896484,-14.9953692
12/10/2024,3:18:49,-22.94555664,128.5029297,-14.9952747
12/11/2024,3:18:49,-23.02879715,128.6171875,-14.99518019
12/12/2024,3:18:49,-23.10443306,128.7333984,-14.99508569
12/13/2024,3:18:49,-23.17243195,128.8505859,-14.99508569
12/14/2024,3:18:49,-23.23276329,128.96875,-14.99508569
12/15/2024,3:18:49,-23.28539848,129.088501,-14.99496165
12/16/2024,3:18:49,-23.33030891,129.2091827,-14.99495574
12/17/2024,3:18:49,-23.36746979,129.3307495,-14.99491439
12/18/2024,3:18:49,-23.3968544,129.453125,-14.99489077
12/19/2024,3:18:49,-23.41844177,129.5761719,-14.99486123
12/20/2024,3:18:49,-23.43220901,129.699707,-14.99484942
12/21/2024,3:18:49,-23.43814087,129.8236084,-14.99481398

solar_transit_times.csv

Date,Transit Time,Latitude
12/20/2023,03:17:50,-23.42260551
12/21/2023,03:18:19,-23.43438224
12/22/2023,03:18:49,-23.43830681
12/23/2023,03:19:19,-23.43437958
12/24/2023,03:19:49,-23.42260641
12/25/2023,03:20:18,-23.40299606
12/26/2023,03:20:48,-23.37556076
12/27/2023,03:21:18,-23.34031283
12/28/2023,03:21:47,-23.29726982
12/29/2023,03:22:16,-23.2464467
12/30/2023,03:22:45,-23.18786834
12/31/2023,03:23:14,-23.12155467
1/1/2024,03:23:43,-23.04753766
1/2/2024,03:24:11,-22.96584454
1/3/2024,03:24:39,-22.87651311
1/4/2024,03:25:07,-22.77958091
1/5/2024,03:25:34,-22.67509412
1/6/2024,03:26:01,-22.56309953
1/7/2024,03:26:27,-22.44365066
1/8/2024,03:26:53,-22.31680435
1/9/2024,03:27:19,-22.18262335
1/10/2024,03:27:44,-22.04117745
1/11/2024,03:28:08,-21.89253574
1/12/2024,03:28:32,-21.73677426
1/13/2024,03:28:55,-21.57396817
1/14/2024,03:29:18,-21.40419957
1/15/2024,03:29:40,-21.22754991
1/16/2024,03:30:01,-21.0441022
1/17/2024,03:30:22,-20.85394682
1/18/2024,03:30:42,-20.65717514
1/19/2024,03:31:01,-20.45388578
1/20/2024,03:31:19,-20.24417436
1/21/2024,03:31:37,-20.02813922
1/22/2024,03:31:54,-19.80588298
1/23/2024,03:32:10,-19.57750435
1/24/2024,03:32:25,-19.34310275
1/25/2024,03:32:40,-19.1027782
1/26/2024,03:32:54,-18.85663067
1/27/2024,03:33:07,-18.60476073
1/28/2024,03:33:19,-18.34726631
1/29/2024,03:33:30,-18.08425049
1/30/2024,03:33:41,-17.81581623
1/31/2024,03:33:50,-17.54206483
2/1/2024,03:33:59,-17.2631027
2/2/2024,03:34:08,-16.9790359
2/3/2024,03:34:15,-16.68997424
2/4/2024,03:34:22,-16.39602751
2/5/2024,03:34:27,-16.097308
2/6/2024,03:34:32,-15.79392895
2/7/2024,03:34:36,-15.4860112
2/8/2024,03:34:40,-15.17367332
2/9/2024,03:34:42,-14.85703768
2/10/2024,03:34:44,-14.53622651
2/11/2024,03:34:45,-14.21136153
2/12/2024,03:34:46,-13.88256412
2/13/2024,03:34:45,-13.54995592
2/14/2024,03:34:44,-13.21365801
2/15/2024,03:34:42,-12.87379245
2/16/2024,03:34:39,-12.53048191
2/17/2024,03:34:36,-12.18384651
2/18/2024,03:34:31,-11.83400542
2/19/2024,03:34:26,-11.48107506
2/20/2024,03:34:21,-11.12517144
2/21/2024,03:34:15,-10.76739373
2/22/2024,03:34:07,-10.40489014
2/23/2024,03:34:00,-10.04073182
2/24/2024,03:33:52,-9.674038387
2/25/2024,03:33:43,-9.304915245
2/26/2024,03:33:33,-8.933466662
2/27/2024,03:33:23,-8.559797514
2/28/2024,03:33:13,-8.184010176
2/29/2024,03:33:02,-7.806208783
3/1/2024,03:32:50,-7.426496729
3/2/2024,03:32:38,-7.044978673
3/3/2024,03:32:25,-6.66175965
3/4/2024,03:32:13,-6.27694617
3/5/2024,03:31:59,-5.890645996
3/6/2024,03:31:45,-5.502968819
3/7/2024,03:31:31,-5.114026939
3/8/2024,03:31:17,-4.723933491
3/9/2024,03:31:02,-4.332803118
3/10/2024,03:30:46,-3.940749357
3/11/2024,03:30:31,-3.547885827
3/12/2024,03:30:15,-3.154324922
3/13/2024,03:29:59,-2.760178783
3/14/2024,03:29:42,-2.365559532
3/15/2024,03:29:26,-1.970578135
3/16/2024,03:29:09,-1.575344198
3/17/2024,03:28:51,-1.179965202
3/18/2024,03:28:34,-0.784545761
3/19/2024,03:28:17,-0.389188148
3/20/2024,03:27:59,0.006007845
3/21/2024,03:27:41,0.400944464
3/22/2024,03:27:23,0.795525856
3/23/2024,03:27:05,1.189657949
3/24/2024,03:26:47,1.583248179
3/25/2024,03:26:29,1.976205102
3/26/2024,03:26:10,2.368438346
3/27/2024,03:25:52,2.759857846
3/28/2024,03:25:34,3.150374136
3/29/2024,03:25:16,3.5398974
3/30/2024,03:24:58,3.928336975
3/31/2024,03:24:40,4.315600878
4/1/2024,03:24:22,4.701596294
4/2/2024,03:24:04,5.086227738
4/3/2024,03:23:47,5.469398892
4/4/2024,03:23:29,5.851010442
4/5/2024,03:23:12,6.230960806
4/6/2024,03:22:55,6.60914783
4/7/2024,03:22:39,6.985469189
4/8/2024,03:22:22,7.359821734
4/9/2024,03:22:06,7.732103487
4/10/2024,03:21:50,8.102212732
4/11/2024,03:21:34,8.470046854
4/12/2024,03:21:18,8.835502924
4/13/2024,03:21:03,9.198480214
4/14/2024,03:20:48,9.558878702
4/15/2024,03:20:34,9.91659998
4/16/2024,03:20:20,10.27154969
4/17/2024,03:20:06,10.62363395
4/18/2024,03:19:52,10.9727618
4/19/2024,03:19:39,11.3188443
4/20/2024,03:19:27,11.66179258
4/21/2024,03:19:14,12.00152095
4/22/2024,03:19:03,12.33794415
4/23/2024,03:18:51,12.67097769
4/24/2024,03:18:40,13.00053928
4/25/2024,03:18:30,13.32654549
4/26/2024,03:18:20,13.64891502
4/27/2024,03:18:11,13.96756394
4/28/2024,03:18:02,14.2824073
4/29/2024,03:17:53,14.59336153
4/30/2024,03:17:45,14.90033782
5/1/2024,03:17:38,15.20324815
5/2/2024,03:17:31,15.50200139
5/3/2024,03:17:25,15.79650497
5/4/2024,03:17:20,16.08666737
5/5/2024,03:17:15,16.37239674
5/6/2024,03:17:10,16.65360142
5/7/2024,03:17:06,16.9301922
5/8/2024,03:17:03,17.20207826
5/9/2024,03:17:00,17.46917241
5/10/2024,03:16:58,17.73138665
5/11/2024,03:16:56,17.98863109
5/12/2024,03:16:55,18.24081969
5/13/2024,03:16:55,18.48786849
5/14/2024,03:16:55,18.7296957
5/15/2024,03:16:56,18.966222
5/16/2024,03:16:57,19.19737131
5/17/2024,03:16:59,19.42307009
5/18/2024,03:17:01,19.64324524
5/19/2024,03:17:04,19.85782908
5/20/2024,03:17:07,20.06675518
5/21/2024,03:17:11,20.26995904
5/22/2024,03:17:15,20.46737683
5/23/2024,03:17:20,20.65895008
5/24/2024,03:17:25,20.84461847
5/25/2024,03:17:31,21.02432366
5/26/2024,03:17:38,21.19800872
5/27/2024,03:17:44,21.36561482
5/28/2024,03:17:52,21.52708209
5/29/2024,03:18:00,21.68235326
5/30/2024,03:18:08,21.8313673
5/31/2024,03:18:17,21.974067
6/1/2024,03:18:26,22.11039496
6/2/2024,03:18:35,22.24029981
6/3/2024,03:18:45,22.3637311
6/4/2024,03:18:56,22.48064158
6/5/2024,03:19:06,22.59098677
6/6/2024,03:19:17,22.69472746
6/7/2024,03:19:29,22.79182341
6/8/2024,03:19:40,22.88223694
6/9/2024,03:19:52,22.96593221
6/10/2024,03:20:04,23.0428766
6/11/2024,03:20:16,23.1130425
6/12/2024,03:20:29,23.17640323
6/13/2024,03:20:41,23.23293677
6/14/2024,03:20:54,23.28262456
6/15/2024,03:21:07,23.3254528
6/16/2024,03:21:20,23.36141014
6/17/2024,03:21:33,23.39048759
6/18/2024,03:21:46,23.41268349
6/19/2024,03:21:59,23.42799377
6/20/2024,03:22:12,23.43642044
6/21/2024,03:22:25,23.43796921
6/22/2024,03:22:38,23.43264389
6/23/2024,03:22:50,23.42045206
6/24/2024,03:23:03,23.40140162
6/25/2024,03:23:16,23.37549955
6/26/2024,03:23:28,23.34275045
6/27/2024,03:23:41,23.30316714
6/28/2024,03:23:53,23.25675701
6/29/2024,03:24:05,23.20353809
6/30/2024,03:24:17,23.14352808
7/1/2024,03:24:29,23.07675237
7/2/2024,03:24:40,23.00323978
7/3/2024,03:24:51,22.9230223
7/4/2024,03:25:02,22.83613504
7/5/2024,03:25:13,22.74261717
7/6/2024,03:25:23,22.64250806
7/7/2024,03:25:33,22.53585009
7/8/2024,03:25:42,22.42268672
7/9/2024,03:25:51,22.30306562
7/10/2024,03:26:00,22.17703482
7/11/2024,03:26:08,22.04464393
7/12/2024,03:26:16,21.90594921
7/13/2024,03:26:23,21.76100565
7/14/2024,03:26:30,21.60987369
7/15/2024,03:26:36,21.4526125
7/16/2024,03:26:41,21.28928504
7/17/2024,03:26:46,21.11995619
7/18/2024,03:26:51,20.94469271
7/19/2024,03:26:55,20.7635592
7/20/2024,03:26:58,20.57662707
7/21/2024,03:27:01,20.38396034
7/22/2024,03:27:03,20.1856262
7/23/2024,03:27:05,19.98168457
7/24/2024,03:27:06,19.77219902
7/25/2024,03:27:07,19.55723188
7/26/2024,03:27:07,19.33684746
7/27/2024,03:27:06,19.11111047
7/28/2024,03:27:05,18.88009191
7/29/2024,03:27:03,18.64386911
7/30/2024,03:27:01,18.40252001
7/31/2024,03:26:58,18.15612475
8/1/2024,03:26:54,17.90476816
8/2/2024,03:26:50,17.64853444
8/3/2024,03:26:46,17.38750808
8/4/2024,03:26:40,17.12177647
8/5/2024,03:26:34,16.85142387
8/6/2024,03:26:28,16.57653931
8/7/2024,03:26:21,16.29720754
8/8/2024,03:26:13,16.0135182
8/9/2024,03:26:05,15.72555727
8/10/2024,03:25:56,15.43341612
8/11/2024,03:25:46,15.13718228
8/12/2024,03:25:36,14.83694673
8/13/2024,03:25:25,14.53279845
8/14/2024,03:25:14,14.22482877
8/15/2024,03:25:02,13.91312682
8/16/2024,03:24:50,13.59778231
8/17/2024,03:24:37,13.27888443
8/18/2024,03:24:24,12.95651736
8/19/2024,03:24:10,12.63076654
8/20/2024,03:23:55,12.30170929
8/21/2024,03:23:41,11.96942182
8/22/2024,03:23:25,11.63397845
8/23/2024,03:23:10,11.29545396
8/24/2024,03:22:53,10.95392515
8/25/2024,03:22:37,10.60947432
8/26/2024,03:22:20,10.26218684
8/27/2024,03:22:03,9.912152142
8/28/2024,03:21:45,9.559462249
8/29/2024,03:21:27,9.204208903
8/30/2024,03:21:09,8.846487659
8/31/2024,03:20:50,8.486391382
9/1/2024,03:20:31,8.12401488
9/2/2024,03:20:12,7.759453426
9/3/2024,03:19:53,7.39280066
9/4/2024,03:19:33,7.024152447
9/5/2024,03:19:13,6.653602689
9/6/2024,03:18:53,6.28124621
9/7/2024,03:18:32,5.907178606
9/8/2024,03:18:12,5.531494511
9/9/2024,03:17:51,5.15428947
9/10/2024,03:17:30,4.775658619
9/11/2024,03:17:09,4.395697524
9/12/2024,03:16:48,4.014500558
9/13/2024,03:16:26,3.632162746
9/14/2024,03:16:05,3.248777215
9/15/2024,03:15:43,2.864435472
9/16/2024,03:15:22,2.479225888
9/17/2024,03:15:00,2.093232864
9/18/2024,03:14:39,1.706536801
9/19/2024,03:14:17,1.319214956
9/20/2024,03:13:56,0.931344134
9/21/2024,03:13:34,0.543003902
9/22/2024,03:13:13,0.15427815
9/23/2024,03:12:52,-0.234744143
9/24/2024,03:12:31,-0.623969625
9/25/2024,03:12:10,-1.013301898
9/26/2024,03:11:50,-1.402642393
9/27/2024,03:11:29,-1.791891492
9/28/2024,03:11:09,-2.180948245
9/29/2024,03:10:49,-2.569711256
9/30/2024,03:10:29,-2.958078256
10/1/2024,03:10:10,-3.345946826
10/2/2024,03:09:51,-3.733213722
10/3/2024,03:09:32,-4.119775463
10/4/2024,03:09:14,-4.505527552
10/5/2024,03:08:56,-4.890365788
10/6/2024,03:08:38,-5.274184361
10/7/2024,03:08:21,-5.656878049
10/8/2024,03:08:04,-6.038340289
10/9/2024,03:07:47,-6.418463832
10/10/2024,03:07:31,-6.797142134
10/11/2024,03:07:16,-7.174268707
10/12/2024,03:07:01,-7.549735925
10/13/2024,03:06:46,-7.923439587
10/14/2024,03:06:32,-8.29527548
10/15/2024,03:06:18,-8.66514416
10/16/2024,03:06:05,-9.032948981
10/17/2024,03:05:53,-9.398597718
10/18/2024,03:05:41,-9.761998674
10/19/2024,03:05:30,-10.12305973
10/20/2024,03:05:19,-10.4816851
10/21/2024,03:05:09,-10.83777209
10/22/2024,03:05:00,-11.19121549
10/23/2024,03:04:51,-11.54190548
10/24/2024,03:04:43,-11.88972871
10/25/2024,03:04:36,-12.23457262
10/26/2024,03:04:30,-12.57632225
10/27/2024,03:04:24,-12.91486183
10/28/2024,03:04:19,-13.25007599
10/29/2024,03:04:15,-13.58184843
10/30/2024,03:04:12,-13.91006285
10/31/2024,03:04:09,-14.23460195
11/1/2024,03:04:08,-14.55535038
11/2/2024,03:04:07,-14.8721893
11/3/2024,03:04:07,-15.18500269
11/4/2024,03:04:07,-15.49367308
11/5/2024,03:04:09,-15.79808349
11/6/2024,03:04:11,-16.09811631
11/7/2024,03:04:14,-16.39365369
11/8/2024,03:04:18,-16.68458177
11/9/2024,03:04:23,-16.97078163
11/10/2024,03:04:29,-17.25214169
11/11/2024,03:04:35,-17.52854985
11/12/2024,03:04:43,-17.79989781
11/13/2024,03:04:51,-18.06608303
11/14/2024,03:05:00,-18.32700646
11/15/2024,03:05:10,-18.58256943
11/16/2024,03:05:20,-18.83267806
11/17/2024,03:05:32,-19.07723683
11/18/2024,03:05:44,-19.31614457
11/19/2024,03:05:57,-19.54930127
11/20/2024,03:06:11,-19.77660189
11/21/2024,03:06:26,-19.99794264
11/22/2024,03:06:42,-20.21321915
11/23/2024,03:06:58,-20.4223289
11/24/2024,03:07:15,-20.62517235
11/25/2024,03:07:33,-20.82164819
11/26/2024,03:07:52,-21.0116616
11/27/2024,03:08:12,-21.19511742
11/28/2024,03:08:32,-21.37192532
11/29/2024,03:08:53,-21.54199212
11/30/2024,03:09:15,-21.70523384
12/1/2024,03:09:37,-21.86156709
12/2/2024,03:10:00,-22.01090995
12/3/2024,03:10:24,-22.15318403
12/4/2024,03:10:48,-22.28831427
12/5/2024,03:11:12,-22.41622632
12/6/2024,03:11:38,-22.53685115
12/7/2024,03:12:03,-22.65012359
12/8/2024,03:12:30,-22.75598071
12/9/2024,03:12:56,-22.8543662
12/10/2024,03:13:23,-22.94522857
12/11/2024,03:13:51,-23.02852302
12/12/2024,03:14:19,-23.10420917
12/13/2024,03:14:47,-23.17225316
12/14/2024,03:15:15,-23.23262388
12/15/2024,03:15:44,-23.28529331
12/16/2024,03:16:13,-23.33023516
12/17/2024,03:16:42,-23.36742206
12/18/2024,03:17:12,-23.39682579
12/19/2024,03:17:41,-23.41842651
12/20/2024,03:18:11,-23.43220329
12/21/2024,03:18:41,-23.43814087
12/22/2024,03:19:10,-23.4362278
12/23/2024,03:19:40,-23.42645836
12/24/2024,03:20:10,-23.40883255

Stellarium Script

For the curious, here is the Stellarium script I used to find lat/long coordinates of where the sun is at a given time. Press F12 to open the script editor in Stellarium. Edit the first couple lines to configure it to what you want.

The output csv gets written to the User Data Directory. It won’t write anything until the simulation has finished.

Output includes the altitude measurement (in degrees), which should be close to 90 to be at the zenith. If it is way off then that means the script failed to converge and the data is bad. Try restarting Stellarium in that case; it seems to have issues when running too long.

Stellarium Script: find_obj_zenith.ssc

// plots position of planets/sun/moon

// Configuration Settings
var TARGET_NAME = "Sun" //name of object to track
var START_DATE = "2023-12-22T03:18:49" //time in UTC
var SKIP = false //how far to skip ahead past START_DATE before running (e.g. "+100day"); set to false to ignore
var STEP = "+1day" //how much time to step between measurements
var NUM_STEPS = 3 //total number measurements to make


//init output file
core.resetOutput()
var lines = ["Date, Time, Latitude, Longitude, Altitude"] //each line of output to write; start with header

function modulus(n, d)
{ return ((n % d) + d) % d }

// Moves location so that the specified object is directly overhead
function find_zenith_pos(obj_name)
{
	//initially set lat to obj dec
	var loc_info = core.getObserverLocationInfo()
	var obj_info = core.getObjectInfo(obj_name)
	core.setObserverLocation(loc_info.longitude, obj_info.dec, 0, 0)
	core.wait(0.05)
	
	var i = 0
	var old_alt = 9999 // start with any number that is not valid (i.e. not in range -90 to 90)
	while (i<30) //up to 30 attempts to converge on location
	{
		loc_info = core.getObserverLocationInfo()
		obj_info = core.getObjectInfo(obj_name)
		var alt = obj_info.altitude
		if(old_alt==alt) {return}
		old_alt = alt
		var az = obj_info.azimuth
		if (alt > 89.999999) {return}
		var ra = obj_info.ra
		var pol = 1 - 2*Math.round(az / 360) // if target is in East then add to longitude, else subtract
		var new_long = loc_info.longitude + pol*(90-alt)
		core.setObserverLocation(new_long, obj_info.dec, 0, 0)
		core.wait(0.08)
		i += 1
	}
}

// Repeats multiple measurements at a fixed step interval
function run_loop(target_name, step, count)
{
	for (i=0; i<count; i++)
	{
		find_zenith_pos(target_name)
		var loc_info = core.getObserverLocationInfo()
		var obj_info = core.getObjectInfo(target_name)
		var date = core.getDate("utc").replace("T", ", ")
		// convert to range -180 to +180 degrees
		var lat = modulus(loc_info.latitude + 180, 360) - 180
		var lon = modulus(loc_info.longitude + 180, 360) - 180
		
		lines.push(`${date}, ${lat}, ${lon}, ${obj_info.altitude}`)
	
		core.setDate(step)
		core.wait(0.02)
	}
}


// Execute //

//set start date
core.setTimeRate(0) //ensure simulation paused
core.setDate(START_DATE, "utc");
core.wait(0.02)

//skip ahead if defined
if (SKIP)
{
	core.setDate(SKIP)
	core.wait(0.02)
}

//perform measurements
run_loop(TARGET_NAME, STEP, NUM_STEPS)

//write output csv
core.output(lines.join('\n'))
core.saveOutputAs(TARGET_NAME+".csv")