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I've built some open source software that calculates Ephemeris from JPL osculating elements to simplify imaging and tracking of Comets, Asteroids, and Near-Earth bodies. This works very accurately a vast majority of the time, but one recent case for the comet "62P/Tsuchinshan 1" is so far off, I think I'm missing something fundamental.

Here are the orbital elements provided by JPL:

IAU76/J2000 helio. ecliptic osc. elements (au, days, deg., period=Julian yrs):
 
  EPOCH=  2456747.5 ! 2014-Mar-31.0000000 (TDB)    RMSW= n.a.
   EC= .5979618781895422   QR= 1.382607510700522   TP= 2455743.3820518344
   OM= 90.29719656740598   W= 30.26606286639662    IN= 9.714058444838786
   A= 3.438996044639659    MA= 155.1819802019812   ADIST= 5.495384578578796
   PER= 6.3775770874135    N= .15454557            ANGMOM= .025569021
   DAN= 1.45692            DDN= 4.56909            L= 120.2043443
   B= 4.8785127            MOID= .40888399         TP= 2011-Jun-30.8820518344

and the upcoming ephemeris.

2460302.500000000 = A.D. 2023-Dec-24 00:00:00.0000 TDB 
 EC= 6.245127137515316E-01 QR= 1.892313964563497E+08 IN= 4.737627331312055E+00
 OM= 6.866852445432606E+01 W = 4.729722200318292E+01 Tp=  2460303.610740428325
 N = 1.844936882516244E-06 MA= 3.598229451470649E+02 TA= 3.590192456781422E+02
 A = 5.039621936257275E+08 AD= 8.186929907951052E+08 PR= 1.951286265733974E+08

All of my calculations match up except one - the mean anomaly. This ephemeris reveals it is 359.8 degrees, which I am interpreting as just about at perihelion. However, if I combine the periapsis date (2455743.3820518344) and the orbital period (6.3775770874135 Julian years), then I believe I should expect the next perihelion to be at 2455743.38 + 2 * 6.38 Julian Years = ~April 1, 2024. My ephemeris calculations line up with the expectation, so I think this is the part I am missing.

What would be the correct way to calculate the mean anomaly given these elements? Is this comet's mean velocity increasing over time?

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1 Answer 1

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In the osculating elements for 2023-12-24, the period of 1.9513×108 seconds is 6.183 years, or 71 days shorter than the 6.378 year period in the elements for 2014-03-31. An encounter with Jupiter, 0.27 au on 2020-04-22, appears to have altered the comet's orbit. The HORIZONS-generated elements in this table show a distinct "before" and "after."

JD Date e q (au) i (°) Ω (°) ω (°) tp (JD) n (°/d) a (au) Q (au) Per (d)
2457000.5 2014-12-09 0.59795 1.3827 9.7122 90.291 30.286 2458073.1 0.15454 3.4390 5.4954 2329.5
2458000.5 2017-09-04 0.59750 1.3838 9.7078 90.244 30.348 2458073.6 0.15461 3.4381 5.4923 2328.5
2459000.5 2020-05-31 0.65292 1.1508 6.4524 81.857 35.662 2458102.1 0.16326 3.3155 5.4803 2205.1
2460000.5 2023-02-25 0.62498 1.2638 4.7365 68.696 47.311 2460303.6 0.15933 3.3698 5.4759 2259.5
2461000.5 2025-11-21 0.62469 1.2651 4.7366 68.662 47.338 2460303.8 0.15926 3.3708 5.4765 2260.5

You don't need to do anything unusual as long as the elements are valid at the time of interest. The comet's trajectory was not Keplerian during the Jupiter encounter, so elements for an epoch before that cannot yield accurate predictions for times after that. The Minor Planet Center currently has elements for an epoch of 2023-09-13.

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