Falcon Heavy booster & Tesla ephems

From: Bill Gray via Seesat-l <seesat-l_at_satobs.org>
Date: Wed, 7 Feb 2018 12:29:06 -0500
Hello all,

    Well,  I've got some info for computing an orbit,  and
therefore ephemerides.  Unfortunately,  the info in question
is somewhat contradictory.

    Musk's Twitter image tells us that the Tesla ended up
with q=0.98 AU,  Q=2.61 AU,  C3=12.0 km^2/s^2,  which means
that it'll be leaving us at roughly sqrt(12)=3.46 km/s once
it's most of the way out of our gravity field.  That C3
is not enough to get you out to Ceres;  it leads,  at best,
to an a=1.325 AU orbit,  i.e.,  something pretty close to
the intended Mars transfer orbit.  I'm going to guess that
the C3 is right and the Q is wrong;  the object is _not_
going out toward Ceres,  and is instead closer to the
originally planned orbit.  Since this is a guess, the following
should be taken with a large dose of salt.

    The all-sky image from MMT looks as if it was roughly
where the TLEs would have expected,  with the middle of the
burn somewhere around 02:30 UTC on 7 Feb,  plus or minus a
minute or so.

    I ran an orbit based on "here's a state vector from
the TLE for 02:30 UTC,  with the velocity increased so
that its total energy gets it to leave us at 3.46 km/s."
That gets me the following orbital elements (geocentric
not long after the burn,  and heliocentric once it basically
"clears" the earth/moon system) :

Orbital elements:  2018-017X
    Perigee 2018 Feb 7.108542 +/- 0.000217 TT =  2:36:18 (JD 2458156.608542)
Epoch 2018 Feb  8.0 TT = JDT 2458157.5                        Gray
q  7131.80034 +/- 1.97              (J2000 equator)
                                     Peri.  152.15202 +/- 0.024
                                     Node   285.31375 +/- 0.0012
e   1.2024743 +/- 0.000383          Incl.   29.21177 +/- 0.0018

Orbital elements:  2018-017X
    Perihelion 2018 Feb 6.490939 TT = 11:46:57 (JD 2458155.990939)
Epoch 2018 Feb 10.0 TT = JDT 2458159.5   Earth MOID: 0.0002   Ma: 0.0114
M   2.25389                         (J2000 ecliptic)
n   0.64230639     Peri.  180.09192
a   1.33037645     Node   317.25015
e   0.2585965      Incl.    0.74743
P   1.53/560.47d    q 0.98634572  Q 1.67440719

    ("2018-017X" = "orbit could be for the booster,  could be for
the Tesla."  We are not at a level of accuracy where I can give
separate orbits for them!)

    I've created "fake" observations in the MPC format below.  I'm
afraid this won't help out the SeeSat-L crowd much,  but the
minor planet folks should be able to cut and paste these observations
into Find_Orb,  either on-line or the version installed to your
machine,  and it'll generate the correct orbit,  and you can then
compute topocentric ephemerides.  And with luck,  somebody will
recover this object and we'll compute orbits based on for-real data
instead of orbits based on tweets.  (Not that I can really blame
Mr. Musk.  I should have asked for elements months ago.  I do have
an inquiry into their media address,  but I expect all their PR
folks are currently busy serving other customers.)

    It's also possible that ephemerides will be available through
the Minor Planet Center's DASO service :

https://www.minorplanetcenter.net/iau/artsats/artsats.html

    I've sent them ephems based on the above orbit,  and they may
(or may not) put 'em up.

-- Bill

2018-017X     C2018 02 07.53000 14 45 15.544-25 51 29.12                     E12
2018-017X     C2018 02 07.54000 14 45 46.415-25 54 12.17                     E12
2018-017X     C2018 02 07.55000 14 46 14.419-25 56 50.89                     E12
2018-017X     C2018 02 07.56000 14 46 39.687-25 59 24.94                     E12
2018-017X     C2018 02 07.57000 14 47 02.346-26 01 53.99                     E12
2018-017X     C2018 02 07.58000 14 47 22.520-26 04 17.74                     E12
2018-017X     C2018 02 07.59000 14 47 40.332-26 06 35.86                     E12
2018-017X     C2018 02 07.60000 14 47 55.902-26 08 48.05                     E12
2018-017X     C2018 02 07.61000 14 48 09.348-26 10 54.02                     E12
2018-017X     C2018 02 07.62000 14 48 20.790-26 12 53.48                     E12
2018-017X     C2018 02 07.63000 14 48 30.342-26 14 46.18                     E12
2018-017X     C2018 02 07.64000 14 48 38.122-26 16 31.86                     E12
2018-017X     C2018 02 07.65000 14 48 44.243-26 18 10.31                     E12
2018-017X     C2018 02 07.66000 14 48 48.819-26 19 41.33                     E12
2018-017X     C2018 02 07.67000 14 48 51.964-26 21 04.73                     E12
2018-017X     C2018 02 07.68000 14 48 53.790-26 22 20.37                     E12
2018-017X     C2018 02 07.69000 14 48 54.407-26 23 28.12                     E12
2018-017X     C2018 02 07.70000 14 48 53.926-26 24 27.87                     E12
2018-017X     C2018 02 07.71000 14 48 52.455-26 25 19.56                     E12
2018-017X     C2018 02 07.72000 14 48 50.102-26 26 03.14                     E12
2018-017X     C2018 02 07.73000 14 48 46.972-26 26 38.59                     E12
2018-017X     C2018 02 07.74000 14 48 43.169-26 27 05.93                     E12
2018-017X     C2018 02 07.75000 14 48 38.794-26 27 25.21                     E12
2018-017X     C2018 02 07.76000 14 48 33.947-26 27 36.48                     E12
2018-017X     C2018 02 07.77000 14 48 28.724-26 27 39.86                     E12
2018-017X     C2018 02 07.78000 14 48 23.221-26 27 35.46                     E12
2018-017X     C2018 02 07.79000 14 48 17.528-26 27 23.43                     E12
2018-017X     C2018 02 07.80000 14 48 11.733-26 27 03.96                     E12
2018-017X     C2018 02 07.81000 14 48 05.922-26 26 37.24                     E12
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Received on Wed Feb 07 2018 - 11:30:01 UTC

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