Moon's position angle?

[CoolTowel]

I want to calculate the position angle like that in this NASA page. This position angle (I think) is the position angle of north pole with respect to the moon's location.

So I used the Astronomy_RotationAxis function to get the vector that pointing in the direction of the body's north pole in J2000 as described here. Then I scaled it to a reasonable length (the radius of moon in AU), and added it to the vector of moon's location in geocentric Cartesian coordinates (given by Astronomy_GeoVector). Then I think I got the vector moon's north pole location. Finally I converted both vector to ra dec, and used the iauPas function provided by SOFA to calculate the position angle.

But I can't get the correct value, I got the value varies between about +-1.5 degrees. But the correct value should varies between +-20 degrees (roughly the the angle between equator and moon's orbit plane)

I wrote above code in Swift (which can easily use C libraries).

var oneAstronomyTime = Astronomy_MakeTime(2023, 1, 1, 00, 00, 00.0)

let moonAxis = withUnsafeMutablePointer(to: &oneAstronomyTime) {timeptr in
    Astronomy_RotationAxis(BODY_MOON, timeptr) // moon axis info
}

let moonVector = Astronomy_GeoVector(BODY_MOON, oneAstronomyTime, NO_ABERRATION) // moon's location vector

var moonNorthVector: astro_vector_t! = astro_vector_t() // moon north pole location vector in geocentric coords
moonNorthVector.status = ASTRO_SUCCESS

var scale: Double = 0.0000116138 // moon radius in au
moonNorthVector.x = moonVector.x + moonAxis.north.x * scale
moonNorthVector.y = moonVector.y + moonAxis.north.y * scale
moonNorthVector.z = moonVector.z + moonAxis.north.z * scale // moon location vector add the north pole vector
moonNorthVector.t = moonVector.t // set the same time

var moonEQ = Astronomy_EquatorFromVector(moonVector) // moon location in ra dec
var moonNorthEQ = Astronomy_EquatorFromVector(moonNorthVector) // moon north pole location in ra dec

var psa = iauPas(degToRad(moonEQ.ra), degToRad(moonEQ.dec), degToRad(moonNorthEQ.ra), degToRad(moonNorthEQ.dec)) // iau standard function calculate the position angle in rad

return radToDeg(psa) // give the position angle in deg

[CoolTowel]

I just found that the value I got are smaller by a factor of 14.5 compared with the NASA value, that is weird...

[cosinekitty]

One thing that will affect your calculations is that right ascension (RA) is not measured in degrees, but sidereal hours. To convert RA to degrees, you need to multiply it by (360/24) = 15. Can you try making that correction and see how it affects your results?

[CoolTowel]

Yes that‘s the reason. Thank you very much! I didn't check the astro_equatorial_t structure carefully

[cosinekitty]

I'm glad that helped!