Check your sources/data for Antares. According to
SIMBAD, the Antares star system is approximately 170pc from Terra, and is located at a bearing from Terra of 351.9° Galactic Longitude
* and +15.1° North Galactic Latitude. This places it slightly trailing of coreward, and at a moderate northern inclination from the galactic plane.
My source for Antares data is the ICRS equatorial coördinates on SIMBAD, with
α (right ascension) = 16
h 29
m 24.45970
s,
δ (declination) = -26° 25′ 55.2094″, and
π (parallax) = 5.89 ± 1.00 mas. Using the
iauIcrs2g() function in the SOFA astronomy library, those equatorial coördinates resulted in galactic coördinates
l (galactic longitude) = 351.947131313457°,
b (galactic latitude) of +15.064324703365°, and
r (radius = distance from Terra) of 169.779286926995 pc.
I’d converted
l,
b,
r (galactic spherical coördinates) to
U,
V,
W (galactic Cartesian coördinates) using
r cos
b cos
l,
r cos
b sin
l, and
r sin
b respectively = 162.328139855781 pc, -22.966496121611 pc, and 44.126197845463 pc from Terra respectively.
If that conversion was mistaken, and
r sin
b cos
l,
r sin
b sin
l, and
r cos
b respectively should have been used instead, then
U,
V, W results in 43.691079452543 pc, -6.181497599168 pc, and 163.944761835022 pc from Terra respectively. However, a W of almost 164 pc doesn’t reflect a moderate “northern” inclination from the galactic plane, so I think that the original trigonometric conversion was correct.
If the original trigonometric conversion to Cartesian was correct, then I must have misinterpreted
U and
V regarding Antares. If
U is positive corewards and negative rimwards,
V is positive spinwards and negative trailing, and
W is positive upwards and negative downwards (i.e. a “right-hand” rule), then that would match a position that is slightly trailing of coreward with an upward inclination from the galactic plane. If you found that my description of the actual position of Deneb was on target, then that would suggest that Antares is really 162 pc coreward, 23 pc trailing, and 44 pc upward of Sol, which puts Antares 119 pc coreward, 453 pc trailing, and 29 pc upward of Deneb, which is still quite different to their positions in the canonical
Traveller sector arrangement.