In this page, I will post my best estimate of Starman’s whereabouts. I will update the page as I gain access to additional and more accurate information.
Space is big. It is also full of forces, big and small, acting over extended periods. Without access to the precise orbital estimates calculated by SpaceX, my results are bound to be extremely innacurate. How innacurate? Well, consider them useless for any purpose, except, perhaps, for entertainment.
You will notice that my calculations carry many decimals digits. This is intentional, and meant to make it easier for others to compare their calculations against mine. It should not be made to imply that my results carry that many significant figures.
In the following calculations, I take the Astronomical Unit as
the gravitational parameter of the Sun as provided in DE430, JPL’s latest Planetary Ephemerides,
and the known orbital parameters as provided in Elon Musk’s tweet (the tweet’s image is shown below)
When is Starman coming back?
From the information available as of this writing, we can readily approximate Starman’s heliocentric eccentricity
or \(268528177.9065\) km, and heliocentric orbital period,
equivalent to (878.40562107150913) days, or (2.4049435210718935) years (I take a year as (365.25) days).
Elon’s tweet was sent on February 06th, 2018 at 07:46:00 PM (PST). Adding the orbital period, we determine that Starman would reach periapsis on July 4th, 2020 at 05:30:05 AM (PST).
Before you prepare to celebrate Starman’s arrival, keep in mind that (1) the calculations are innacurate, (2) periapsis means the orbital point closest to the Sun, as opposed to Earth encounter. In fact, even if the calculations were perfect, Earth would not be at the orbital location of Starman’s periapsis on that date.
Can Starman Hit Us?
I have very limited data to perform reliable calculations, but my money is on Starman staying safely away from us for the foreseable future.
More Updates To Follow
Our previous entry is based on dubious data. Apparently, Elon’s tweet does not report the correct orbital parameters. You can see this by calculating the that corresponds to the reported periapsis and apoapsis radii, and verifying that the obtained is much, much higher.
JPL data from 2018-02-07
JPL reportedly received an orbit fix and performed a preliminary, low-fidelity propagation that leads to the following orbital elements (Geometric, Earth-Mean Equator and Equinox of J2000) at epoch 2018-Feb-09 23:45:01.0000 TDB:
JD = 2458159.489594907 Julian Day Number, TDB EC = 2.647486804652587E-01 Eccentricity QR = 9.860588520496463E-01 Periapsis distance, (AU) IN = 2.424872612161389E+01 Inclination (deg) OM = 3.582144541378262E+02 Longitude of Ascending Node (deg) W = 1.363703978776156E+02 Argument of Perifocus, w (deg) Tp = 2458153.692627305165 Time of periapsis (JD TDB) N = 6.346050715251113E-01 Mean motion, n (deg/day) MA = 3.678785039794062E+00 Mean anomaly, M (deg) TA = 6.556257062441905E+00 True anomaly, nu (deg) A = 1.341118099146852E+00 Semi-major axis, a (AU) AD = 1.696177346244057E+00 Apoapsis distance (AU) PR = 5.672819461319965E+02 Sidereal orbit period (day)
Now we have an apoapsis distance of about 1.70 AU (as opposed to the originally-reported 2.61 AU).