How can I track the Tesla Roadster in Pyephem?

Question

As you may be aware, SpaceX launched a Tesla Roadster into space, and it is now orbiting the sun.

https://en.wikipedia.org/wiki/Elon_Musk%27s_Tesla_Roadster

How can I track this in Pyephem? You can find some orbital elements on JPL's Horizons site https://ssd.jpl.nasa.gov/horizons.cgi?CGISESSID=c3cbd47fbf603007d1b627107c28962f&s_body=1#top, search for Tesla

and it looks like the relevant data is:

 EPOCH= 2458164.5
  EC= .2585469914787243  QR= .9860596231806226  TP= 2458153.620483722645
  OM= 317.3549094214575  W = 177.3203028023227  IN= 1.088451292866039
  A1= 2.960683526738534E-9  R0= 1.  ALN= 1.  NM= 2.  NK= 0.
  SRC= -2.057839421666802E-7  7.966781900129693E-9  -1.720426606925749E-9
       -4.722542923190676E-7  2.197679131968537E-9  -1.230413802372471E-6
       -2.500290306870021E-7 -3.361070889248183E-9  -1.765963020682463E-5
       -3.047907547965759E-7 -4.640202045440381E-7  -4.271481116360573E-9
        2.657789409005983E-5  1.726818074599357E-6  -1.359673746135991E-6
       -2.478836748687631E-5 -2.309863204867099E-8   -.0002351644867403515
       -1.875169281895894E-6 -2.063647245529267E-6  -1.670539551586607E-6
       -4.019207817588603E-6 -3.128134469402375E-9  -3.034540373576942E-5
        1.733661692209129E-7 -7.052327854535979E-7  -2.650181216776434E-7
       -1.310976135791957E-10
    H= 25.289 G= 0.15

How do I plug that into Pyephem? I've done plenty of tracking of geocentric orbiters, but nothing heliocentric.

Thanks!

James C · Answer 1 · 2018-08-07T22:22:36.980

Here's how it should work. Create a new EllipticalBody:

tesla=ephem.EllipticalBody()
tesla.name='Tesla Roadster'

then set the parameters (parameter definitions from here and here):

tesla._epoch=2458164.5         #julian date of osculating elements
tesla._e=0.2585469914787243    #eccentricity
tesla._Om='317.3549094214575'  #longitude of ascending node wrt ecliptic
tesla._om='177.3203028023227'  #argument of perihelion wrt ecliptic
tesla._inc='1.088451292866039' #inclination of orbit plane wrt ecliptic
tesla._H=25.289                #absolute magnitude parameter
tesla._G=0.15                  #magnitude slope parameter
tesla._epoch_M=???             #probably the same as tesla._epoch
tesla._M=???                   #unknown quantity, see below
tesla._a=???                   #unknown quantity, see below

It's possible the epoch is wrong, as J2000 is equivalent to 2451545.0, and in PyEphem it's 36525.0, in which case, by my reckoning, perhaps

tesla._epoch=43144.5

then run compute:

tesla.compute()

But even so, I don't know what M or a are supposed to be. HORIZONS should output these parameters as MA and A, respectively, but they aren't apparent from the data. Theoretically, these can be derived from TP (Perihelion Julian Date) and QR (Perihelion Distance), which are given (since HORIZONS computes those from MA and A internally per the user manual), but I'm not entirely sure how this is done.

Some possibilities: from XEphem documentation, I learned some basic formulae:

a=q/(1-e) (since q=QR from HORIZONS, a=1.3299017090067253)
M=n(E-T) (T is TP from HORIZONS)
n=0.9856076686/P
P=a**(3/2)
M=6.991725093611749

Thing is, while this looks all fine and dandy, when you put it in, the numbers are way off of what HORIZONS states.

How can I track the Tesla Roadster in Pyephem?

1 Answers1