Again on comet D/1770 L1 (Lexell)

Year 1757.

Three comets:

• D/1770 L1 (Lexell)
• P/2014 R5 (Lemmon-PANSTARRS)
• P/1999 RO28 (LONEOS)

Let's compare their nominal distance using JPL Horizons and Mercury6 software by John E. Chambers.

According to Mercury6 software, on 1757-Jul-1, the Lexell comet was at 0.33 (AU) from comet P/2014 R5 (Lemmon-PANSTARRS) and it was  at 0.16 (AU) from  comet P/1999 RO28 (LONEOS).

JPL Horizons models the Lexell comet in a different way.
According to JPL Horizons, the Lexell comet was at 1.53 (AU) from comet P/2014 R5 (Lemmon-PANSTARRS) and it was at 1.61 (AU) from  comet P/1999 RO28 (LONEOS).

Both JPL Horizons and Mercury agree and get the same result when looking  at the nominal distance between P/2014 R5 (Lemmon-PANSTARRS) and P/1999 RO28 (LONEOS).


Comet P/2014 R5 (Lemmon-PANSTARRS)

*******************************************************************************
JDCT 
   X     Y     Z
   VX    VY    VZ
   LT    RG    RR
*******************************************************************************
$$SOE
2362988.500000000 = A.D. 1757-Jul-17 00:00:00.0000 (CT)
  -5.257637317706235E+00  2.477814508385187E-01  6.790907841994050E-02
   1.426562748323473E-03 -5.796128684565190E-03  2.940516606550701E-05
   3.040181361915521E-02  5.263910851719347E+00 -1.697317088053800E-03
$$EOE
*******************************************************************************

Comet P/1999 RO28 (LONEOS)

*******************************************************************************
JDCT 
   X     Y     Z
   VX    VY    VZ
   LT    RG    RR
*******************************************************************************
$$SOE
2362988.500000000 = A.D. 1757-Jul-17 00:00:00.0000 (CT)
  -5.430809043797567E+00  3.084110607570195E-01 -7.118879844782251E-02
   2.327107819955809E-04 -4.558198020424996E-03  2.130564382053195E-03
   3.141896416246138E-02  5.440025008914496E+00 -5.186150467730436E-04
$$EOE
*******************************************************************************

Nominal distance (according to JPL Horizons): 0.23 (AU)
I get the same result using Mercury6 orbit simulator.

Given the orbit uncertainty that I am unable to evaluate, the idea that these comets are related is still a speculation.

I do not know if MPC should be involved in a case like this.

However, It would be nice to investigate this matter in a deeper way.


Kind Regards,
Alessandro Odasso

P/2014 R5 (Lemmon-PANSTARRS) vs D/1770 L1 (Lexell)

According to Horizons Web Interface, the nominal distance between the comet P/2014 R5 (Lemmon-PANSTARRS) and the Comet D/1770 L1 (Lexell) was 0.49 (AU) on 1772-Jun-25.

Symbol meaning [1 au=149597870.700 km, 1 day=86400.0 s]:

    JDCT     Epoch Julian Date, Coordinate Time
      X      x-component of position vector (AU)                               
      Y      y-component of position vector (AU)                               
      Z      z-component of position vector (AU)                               
      VX     x-component of velocity vector (AU/day)                           
      VY     y-component of velocity vector (AU/day)                           
      VZ     z-component of velocity vector (AU/day)                           
      LT     One-way down-leg Newtonian light-time (day)                       
      RG     Range; distance from coordinate center (AU)                       
      RR     Range-rate; radial velocity wrt coord. center (AU/day)

Comet      P/2014 R5 (Lemmon-PANSTARRS)

JDCT 
   X     Y     Z
   VX    VY    VZ
   LT    RG    RR
*******************************************************************************
$$SOE
2368445.500000000 = A.D. 1772-Jun-25 00:00:00.0000 (CT)
  -5.350772153692991E+00  7.519737209984863E-01  6.507105626789669E-02
   5.429545955058305E-04 -5.709574426723797E-03  4.064357076622107E-05
   3.120942901941327E-02  5.403745123539087E+00 -1.331674861182269E-03
$$EOE
******************************************************************************* 

Comet      D/1770 L1 (Lexell)

JDCT 
   X     Y     Z
   VX    VY    VZ
   LT    RG    RR
*******************************************************************************
$$SOE
2368445.500000000 = A.D. 1772-Jun-25 00:00:00.0000 (CT)
  -5.065183309814054E+00  1.154049192420066E+00  7.604951982430537E-02
  -3.367607369438152E-03 -2.956615617800361E-03  1.213072905725020E-04
   3.000696938171253E-02  5.195545691263794E+00  2.628153989642551E-03
$$EOE
******************************************************************************* 

Nominal distance: 0.49 (AU), Uncertainty: uknown

The same nominal result is obtained using the Mercury Integrator by John E. Chambers.

Before that date, the JPL Horizons and the Mercury results are no longer similar.

I suspect this is due to the different way used to model the close approaches with Jupiter but I am not sure.
In fact, as already known, comet Lexell went very near to Jupiter:

• 1779-07-27 - close approach at about 0.0015 (AU)
• 1767-03-28 - close approach at about 0.022 (AU)

Strange: the 1779 close approach was very low and yet JPL Horizons and Mercury go back to 1772 consistently.

However, the 1767 close approach is managed differently: before that date the results of JPL Horizons and Mercury are very different for comet Lexell (but still consistent for the other comet). Thus, the calculated distance between the two comets is very different.
To give an idea:

• according to Mercury software, in 1757-05-21 (ten years before the first close approach between Lexell and Jupiter)  the nominal distance between the two comets was as low as 0.14 (AU)

• according to JPL Horizons, on the same date, the distance was quite different: 1.68 (AU)

Conclusion

It would be nice to be able to male a statistical analysis (Montecarlo simulation?) to see if is possible to evaluate the uncertainty of the 1772 result and (if it holds up) the uncertainty of the 1757 result.

This analysis could confirm or reject what in this moment is only a speculation: these two comets might be related.

Kind Regards,
Alessandro Odasso