# StarData: proper motion of a star in HelioCoordinates

I am not an astronomer, but am trying to calculate the trajectory of an interstellar space probe, for example to Proxima Centauri. The HelioCoordinates seem appropriate, as typically used within the solar system. (I am assuming HelioCoordinates is an ecliptic Cartesian coordinate system centered on the Sun. Unfortunately StarData "Definition" is missing for "HelioCoordinates" and all the other properties I have checked.) But I am having difficulty with characterizing the proper motion of Proxima in these coordinates. As a check, I used a nearby star Hadar for comparison -- since it is much farther away, its proper motion is small. This is confirmed:

In[168]:= {StarData["ProximaCentauri", "ProperMotion"],
Out[168]= {Quantity[1895.42, ("MilliarcSeconds")/("Years")],
Quantity[30.16, ("MilliarcSeconds")/("Years")]}


Now I try to calculate the same motion in heliocoordinates. The results don't agree with the reported proper motion, and further are almost identical for the two stars:

In[169]:= motionInOneYear[star_] := Module[{p1, p2},
p1 = StarData[star,
Dated["HelioCoordinates", DateObject[{2020, 1, 1}]]]/
Quantity["ly"];
p1 = p1/Norm[p1]; (* normalize so the point is on a unit sphere *);
(* one year later *)
p2 = StarData[star,
Dated["HelioCoordinates", DateObject[{2021, 1, 1}]]]/
Quantity["ly"];
p2 = p2/Norm[p2];
(* distance between points on unit sphere is angular change in \
]

Out[170]= {435.456, 424.801}


I conclude that there are two things going on: (a) StarData in HelioCoordates does not take into account the proper motion of the star (it just uses data from an epoch, even though it seems to accept a date) and (b) what I am seeing is a change in star position due to the rotational motion of the solar system. Or in other words, in HelioCoordinates the far star field is moving slowly due to a rotational motion of the solar system ecliptic plane. Is my interpretation correct? If so, what is the best way to characterize the position of Proxima Centauri in HelioCoordinates that does take the star's proper motion into account? Or perhaps I should be using a different coordinate system from the get-go?

Addition: After further investigation it seems clear that the variation in star positions I am seeing is not due to proper motion but rather due to the precession/nutation of the heliocentric coordinate system in question. I have therefore decided to do all my space probe trajectory calculations in the heliocentric coordinates, so at least they are consistent. Then I will have to characterize the star proper motion separately from that. I would criticize Wolfram for not properly documenting what database they are using or its limitations. No wonder nobody has answered my question.

• Let me welcome you to mathematica.stackexchange and thank you for asking such a well-written and detailed question as your first post. Apr 18, 2019 at 18:57
• Thanks for the compliment from @halirutan. I am a long-time user of Mathematica, but new to the astronomy aspects. I tend to avoid the more obscure features to avoid getting into deep issues. Apr 20, 2019 at 22:51
• I would love to see you answer your own question, if you have the time and a suitable solution or workaround. It seems an extremely interesting area and I'd be very curious to see how to solve your problem. Sorry I am unable to help, but this stuff is way out of my knowledgebase :) Apr 21, 2019 at 8:34