3
$\begingroup$

In the game i'm working on a particular event happens during a solar eclipse while the Earth and Ceres are in line, or a few days before. I'm looking for dates between 2100 and 2300.

Anyone know a way to calculate when or even if that will happen in that time frame?

$\endgroup$
3
  • 1
    $\begingroup$ @PrincePugs JPL disagrees. Please see ssd.jpl.nasa.gov/horizons/time_spans.html & ssd.jpl.nasa.gov/horizons/manual.html#longterm $\endgroup$
    – PM 2Ring
    Nov 10, 2022 at 5:13
  • 1
    $\begingroup$ @PM2Ring i'll have to wait til tomorrow to pull that up on my computer, but from what a can see on my phone that is exactly what i need to find my answer. Thank you. $\endgroup$
    – Rasip
    Nov 10, 2022 at 5:53
  • 1
    $\begingroup$ Are you looking for an eclipse (or transit, rather) of the sun by Earth, as seen from Ceres? Considering that the orbit of Ceres has a fairly high inclination, that's only possible at two points in its orbit, which will make it quite rare. $\endgroup$ Nov 15, 2022 at 14:42

1 Answer 1

4
$\begingroup$

According to Fred Espenak, aka Mr Eclipse, there's a total solar eclipse on 2117-Sep-26 00:55:42 TD (00:53:15 UT1). 

Total solar eclipse, 2117-Sep-26

Less than two days later, at 2117-Sep-27 22:07:25 UTC, Ceres is opposite the Sun, in terms of ecliptic longitude. The orbit of Ceres is moderately inclined to the ecliptic, and at that time its ecliptic latitude is around 15° south of the ecliptic.

Here's some relevant data from Horizons

The Sun

 Date__(UT)__HR:MN        ObsEcLon    ObsEcLat
 2117-Sep-26 00:00     182.9044612   0.0000363
 2117-Sep-26 01:00     182.9452781   0.0000347
 2117-Sep-26 02:00     182.9860960   0.0000330
 2117-Sep-26 03:00     183.0269149   0.0000313
 2117-Sep-26 04:00     183.0677347   0.0000296
 2117-Sep-26 05:00     183.1085555   0.0000279
 2117-Sep-26 06:00     183.1493772   0.0000263
 2117-Sep-26 07:00     183.1901998   0.0000246
 2117-Sep-26 08:00     183.2310234   0.0000229
 2117-Sep-26 09:00     183.2718480   0.0000212
 2117-Sep-26 10:00     183.3126735   0.0000195
 2117-Sep-26 11:00     183.3535000   0.0000178
 2117-Sep-26 12:00     183.3943274   0.0000162
 2117-Sep-26 13:00     183.4351557   0.0000145
 2117-Sep-26 14:00     183.4759850   0.0000128
 2117-Sep-26 15:00     183.5168152   0.0000111
 2117-Sep-26 16:00     183.5576464   0.0000095
 2117-Sep-26 17:00     183.5984785   0.0000078
 2117-Sep-26 18:00     183.6393116   0.0000061
 2117-Sep-26 19:00     183.6801456   0.0000044
 2117-Sep-26 20:00     183.7209805   0.0000028
 2117-Sep-26 21:00     183.7618164   0.0000011
 2117-Sep-26 22:00     183.8026532  -0.0000006
 2117-Sep-26 23:00     183.8434910  -0.0000022
 2117-Sep-27 00:00     183.8843297  -0.0000039
 2117-Sep-27 01:00     183.9251693  -0.0000056
 2117-Sep-27 02:00     183.9660099  -0.0000072
 2117-Sep-27 03:00     184.0068514  -0.0000089
 2117-Sep-27 04:00     184.0476938  -0.0000105
 2117-Sep-27 05:00     184.0885372  -0.0000122
 2117-Sep-27 06:00     184.1293815  -0.0000138
 2117-Sep-27 07:00     184.1702267  -0.0000154
 2117-Sep-27 08:00     184.2110728  -0.0000171
 2117-Sep-27 09:00     184.2519199  -0.0000187
 2117-Sep-27 10:00     184.2927680  -0.0000203
 2117-Sep-27 11:00     184.3336169  -0.0000219
 2117-Sep-27 12:00     184.3744668  -0.0000236
 2117-Sep-27 13:00     184.4153176  -0.0000252
 2117-Sep-27 14:00     184.4561693  -0.0000268
 2117-Sep-27 15:00     184.4970220  -0.0000284
 2117-Sep-27 16:00     184.5378755  -0.0000300
 2117-Sep-27 17:00     184.5787300  -0.0000316
 2117-Sep-27 18:00     184.6195854  -0.0000331
 2117-Sep-27 19:00     184.6604418  -0.0000347
 2117-Sep-27 20:00     184.7012990  -0.0000363
 2117-Sep-27 21:00     184.7421572  -0.0000378
 2117-Sep-27 22:00     184.7830163  -0.0000394
 2117-Sep-27 23:00     184.8238763  -0.0000409
 2117-Sep-28 00:00     184.8647372  -0.0000425

The Moon

 Date__(UT)__HR:MN        ObsEcLon    ObsEcLat
 2117-Sep-26 00:00     182.4109811   0.5038937
 2117-Sep-26 01:00     183.0436204   0.4455069
 2117-Sep-26 02:00     183.6763551   0.3870554
 2117-Sep-26 03:00     184.3091737   0.3285475
 2117-Sep-26 04:00     184.9420644   0.2699914
 2117-Sep-26 05:00     185.5750156   0.2113955
 2117-Sep-26 06:00     186.2080157   0.1527682
 2117-Sep-26 07:00     186.8410529   0.0941179
 2117-Sep-26 08:00     187.4741156   0.0354528
 2117-Sep-26 09:00     188.1071922  -0.0232187
 2117-Sep-26 10:00     188.7402708  -0.0818880
 2117-Sep-26 11:00     189.3733400  -0.1405470
 2117-Sep-26 12:00     190.0063880  -0.1991872
 2117-Sep-26 13:00     190.6394033  -0.2578003
 2117-Sep-26 14:00     191.2723741  -0.3163778
 2117-Sep-26 15:00     191.9052889  -0.3749115
 2117-Sep-26 16:00     192.5381361  -0.4333931
 2117-Sep-26 17:00     193.1709042  -0.4918142
 2117-Sep-26 18:00     193.8035817  -0.5501665
 2117-Sep-26 19:00     194.4361571  -0.6084418
 2117-Sep-26 20:00     195.0686189  -0.6666318
 2117-Sep-26 21:00     195.7009557  -0.7247284
 2117-Sep-26 22:00     196.3331561  -0.7827232
 2117-Sep-26 23:00     196.9652089  -0.8406082
 2117-Sep-27 00:00     197.5971028  -0.8983752
 2117-Sep-27 01:00     198.2288265  -0.9560162
 2117-Sep-27 02:00     198.8603688  -1.0135232
 2117-Sep-27 03:00     199.4917187  -1.0708880
 2117-Sep-27 04:00     200.1228651  -1.1281028
 2117-Sep-27 05:00     200.7537970  -1.1851596
 2117-Sep-27 06:00     201.3845034  -1.2420507
 2117-Sep-27 07:00     202.0149736  -1.2987681
 2117-Sep-27 08:00     202.6451966  -1.3553041
 2117-Sep-27 09:00     203.2751619  -1.4116511
 2117-Sep-27 10:00     203.9048587  -1.4678013
 2117-Sep-27 11:00     204.5342764  -1.5237472
 2117-Sep-27 12:00     205.1634047  -1.5794813
 2117-Sep-27 13:00     205.7922330  -1.6349961
 2117-Sep-27 14:00     206.4207511  -1.6902842
 2117-Sep-27 15:00     207.0489487  -1.7453383
 2117-Sep-27 16:00     207.6768157  -1.8001511
 2117-Sep-27 17:00     208.3043420  -1.8547155
 2117-Sep-27 18:00     208.9315177  -1.9090244
 2117-Sep-27 19:00     209.5583329  -1.9630707
 2117-Sep-27 20:00     210.1847778  -2.0168474
 2117-Sep-27 21:00     210.8108428  -2.0703477
 2117-Sep-27 22:00     211.4365182  -2.1235647
 2117-Sep-27 23:00     212.0617948  -2.1764919
 2117-Sep-28 00:00     212.6866630  -2.2291224

Ceres

 Date__(UT)__HR:MN        ObsEcLon    ObsEcLat
 2117-Sep-26 00:00       5.2214550 -15.4458935
 2117-Sep-26 01:00       5.2120622 -15.4455038
 2117-Sep-26 02:00       5.2026686 -15.4451098
 2117-Sep-26 03:00       5.1932742 -15.4447116
 2117-Sep-26 04:00       5.1838790 -15.4443092
 2117-Sep-26 05:00       5.1744831 -15.4439025
 2117-Sep-26 06:00       5.1650864 -15.4434917
 2117-Sep-26 07:00       5.1556890 -15.4430766
 2117-Sep-26 08:00       5.1462909 -15.4426573
 2117-Sep-26 09:00       5.1368921 -15.4422337
 2117-Sep-26 10:00       5.1274927 -15.4418060
 2117-Sep-26 11:00       5.1180927 -15.4413740
 2117-Sep-26 12:00       5.1086920 -15.4409378
 2117-Sep-26 13:00       5.0992908 -15.4404974
 2117-Sep-26 14:00       5.0898889 -15.4400527
 2117-Sep-26 15:00       5.0804865 -15.4396039
 2117-Sep-26 16:00       5.0710836 -15.4391508
 2117-Sep-26 17:00       5.0616801 -15.4386935
 2117-Sep-26 18:00       5.0522762 -15.4382319
 2117-Sep-26 19:00       5.0428718 -15.4377662
 2117-Sep-26 20:00       5.0334669 -15.4372962
 2117-Sep-26 21:00       5.0240616 -15.4368220
 2117-Sep-26 22:00       5.0146559 -15.4363435
 2117-Sep-26 23:00       5.0052498 -15.4358609
 2117-Sep-27 00:00       4.9958433 -15.4353740
 2117-Sep-27 01:00       4.9864364 -15.4348829
 2117-Sep-27 02:00       4.9770292 -15.4343876
 2117-Sep-27 03:00       4.9676217 -15.4338880
 2117-Sep-27 04:00       4.9582139 -15.4333843
 2117-Sep-27 05:00       4.9488058 -15.4328763
 2117-Sep-27 06:00       4.9393975 -15.4323641
 2117-Sep-27 07:00       4.9299889 -15.4318476
 2117-Sep-27 08:00       4.9205801 -15.4313270
 2117-Sep-27 09:00       4.9111711 -15.4308021
 2117-Sep-27 10:00       4.9017619 -15.4302730
 2117-Sep-27 11:00       4.8923526 -15.4297396
 2117-Sep-27 12:00       4.8829431 -15.4292021
 2117-Sep-27 13:00       4.8735335 -15.4286603
 2117-Sep-27 14:00       4.8641238 -15.4281143
 2117-Sep-27 15:00       4.8547140 -15.4275641
 2117-Sep-27 16:00       4.8453041 -15.4270097
 2117-Sep-27 17:00       4.8358942 -15.4264510
 2117-Sep-27 18:00       4.8264843 -15.4258881
 2117-Sep-27 19:00       4.8170744 -15.4253211
 2117-Sep-27 20:00       4.8076644 -15.4247497
 2117-Sep-27 21:00       4.7982546 -15.4241742
 2117-Sep-27 22:00       4.7888447 -15.4235944
 2117-Sep-27 23:00       4.7794350 -15.4230105
 2117-Sep-28 00:00       4.7700253 -15.4224223

I made a simple program to search for when Ceres is opposite the Sun, but I might have missed some because my algorithm doesn't take retrograde motion into account. Ceres has a synodic period of ~466.7 days, but its eccentricity is ~0.076875, so the period between oppositions ranges between 454 and 484 days.

Here's a plot of the motion of Ceres (red) relative to Earth (blue) from 2000-Jan-1 to 2009-Jan-1, with a 30 day step size.

Ceres geocentric trajectory

I created that plot using my script linked at the end of this answer, which can plot orbits of multiple bodies in 3D.


That's the only total solar eclipse close to a Sun-Ceres opposition for that century. There are a few others where the eclipse occurs near the opposition, but the time interval is a week or so.


Perhaps a better indicator of alignment is the angle from the Sun through the Earth to Ceres. From the Horizons manual:

23. Sun-Observer-Target (apparent solar elongation) angle

Sun-Observer-Target apparent SOLAR ELONGATION ANGLE seen from the observers' location at print-time.

The S-O-T solar elongation angle is numerically the minimum separation angle of the Sun and target in the sky in any direction. It does NOT indicate the amount of separation in the leading or trailing directions, which would be defined along the equator of a spherical coordinate system.

I grabbed the dates & times of all the total solar eclipses from 2100 to 2300 from the ASCII version of Fred Espenak's catalog and fed them to Horizons, looking for eclipses where the Sun-Earth-Ceres angle is greater than 160°. Here are the results.

Eclipse date Angle
2108 Oct 05 01:01:20 161.1742
2117 Sep 26 00:55:42 164.3924
2154 Oct 07 08:03:50 164.1278
2184 Mar 12 14:22:32 160.7959
2233 Dec 31 21:07:37 168.2191
2263 Jun 06 22:58:57 172.5126
2271 Jan 12 06:28:08 171.2051
2280 Jan 03 05:28:11 162.2298

The eclipse catalog uses Terrestrial Time, also known as Terrestrial Dynamical Time.

Eclipse Predictions by Fred Espenak, www.EclipseWise.com


Here's a plot of the Sun-Earth-Ceres angle for 23 years, with a time step of 5 days. 23 years is slightly under 5 times the orbital period of Ceres (1683.2583 days), and slightly more than 18 times its synodic period.

S-O-T plot

As you can see, the maximum angle only rarely reaches 170° near opposition.

Here's the Sage / Python plotting script. The valid time span for all small bodies in Horizons is 1599-12-10 23:59 to 2500-12-31 23:58. The target can be any body that Horizons has data for, but (usually) only major bodies can be used as the observer center. However, Horizons has special data for a few asteroids which allows them to be used as centers. The special ID for Ceres is 2000001.

$\endgroup$
1
  • 1
    $\begingroup$ I feel really bad because i just realized i conjunction is the wrong word for what i wanted. I thing i was looking for was a straight line running from the sun through the moon and Earth and on to Ceres. $\endgroup$
    – Rasip
    Nov 10, 2022 at 20:01

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .