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?
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).
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
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
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
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.
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.
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.
