This routine takes the input coordinates and coordinate system of the map centre and converts them to the apparent coords at the time of the observation. In addition, the angle between the north direction in the input coordinate frame and that in the apparent frame is calculated (measured anti-clockwise from input north, in radians). See SCU/3.0/JFL/ 0393.

• [AZ] coords: Calculate the apparent RA and DEC at the LST when the routine is called by:-

  $$sin\left(dec\text{\_}app\right)=sin\left(lat\text{\_}obs\right)\ast sin\left(el\right)+cos\left(lat\text{\_}obs\right)\ast cos\left(el\right)\ast cos\left(az\right)$$

  (4)

  $$sin\left(H\text{\_}A\right)=-\frac{sin\left(az\right)\ast cos\left(el\right)}{cos\left(dec\text{\_}app\right)}$$

  (5)

  $$cos\left(H\text{\_}A\right)=\frac{sin\left(el\right)-sin\left(dec\text{\_}app\right)\ast sin\left(lat\text{\_}obs\right)}{cos\left(dec\text{\_}app\right)\ast cos\left(lat\text{\_}obs\right)}$$

  (6)

  $cos\left(dec\text{\_}app\right)$ is present in the denominator of both the $sin\left(H\text{\_}A\right)$ and $cos\left(H\text{\_}A\right)$ terms and it could cause both to blow up – so it’s left out as only the ratio is important

  $$RA\text{\_}app=LST-H\text{\_}A$$

  (7)

  $$sin\left(rotation\right)=\frac{sin\left(az\right)\ast cos\left(lat\text{\_}obs\right)}{cos\left(dec\text{\_}app\right)}$$

  (8)

  $$cos\left(rotation\right)=\frac{sin\left(lat\text{\_}obs\right)-sin\left(dec\text{\_}app\right)\ast sin\left(el\right)}{cos\left(dec\text{\_}app\right)\ast cos\left(el\right)}$$

  (9)

  Again, $cos\left(dec\text{\_}app\right)$ appears in the denominator of both $sin$ and $cos$ expressions and is left out of the calculation because on ly the ratio is important.

• [RB] coords: Use SLA_FK54Z to convert to RJ. Use SLA_MAP to convert to apparent, giving ra_app, dec_app. Use same method to calculate apparent position of RB N pole, giving ra_N_app, dec_N_app. Then calculate rotation from:-

  $$\mathrm{d}RA=ra\text{\_}app-ra\text{\_}N\text{\_}app$$

  (10)

  $$sin\left(rotation\right)=\frac{sin\left(\mathrm{d}RA\right)\ast cos\left(dec\text{\_}N\text{\_}app\right)}{cos\left(lat\right)}$$

  (11)

  $$cos\left(rotation\right)=\frac{sin\left(dec\text{\_}N\text{\_}app\right)-sin\left(dec\text{\_}app\right)\ast sin\left(lat\right)}{cos\left(dec\text{\_}app\right)\ast cos\left(lat\right)}$$

  (12)

  Since $cos\left(lat\right)$ is in the denominator for both $sin$ and $cos$ terms, is always $+$ve except for $\pm \pi /2$ where it goes to zero and blows up the equations, leave it out in the calculations. The ratio of sin and cos will be unaffected.

  If dec_app = $\pi /2$ (i.e. at N pole of apparent system) then

  $$rotation=\pi -\left(ra\text{\_}N\text{\_}app-ra\text{\_}app\right)$$

  (13)

• [RJ] coords: Use SLA_MAP to convert to apparent. Use same method to calculate apparent position of RB N pole. Derive rotation angle in the same way as for RB.

• [GA] coords: Use SLA_GALEQ to convert to RJ. Use SLA_MAP to convert to apparent, giving ra_app, dec_app. Use same method to calculate apparent position of GA N pole, giving ra_N_app, dec_N_app. Derive rotation angle in the same way as for RB.

• [EQ] coords: Use SLA_ECLEQ to convert to RJ. Use SLA_MAP to convert to apparent, giving ra_app, dec_app. Use same method to calculate apparent position of EQ N pole, giving ra_N_app, dec_N_app. Derive rotation angle in the same way as for RB.

• [HA] coords: Apparent RA = LST - LONG

  Apparent Dec = LAT

  Rotation = 0.0D0

• [RD] coords: Apparent RA, Dec set to input values. Rotation = 0.0.

• [PLANET] coords: If MJD1 = MJD2 then apparent RA, Dec set to input LONG, LAT. Rotation = 0.0. Otherwise apparent RA, Dec interpolated (or extrapolated) between LONG, LAT, MJD1 and LONG2, LAT2, MJD2 according to MJD. Rotation = 0.

CALL SCULIB_CALC_APPARENT (LAT_OBS, LONG, LAT, LONG2, LAT2, MAP_X, MAP_Y, COORD_TYPE, LST, MJD, MJD1, MJD2, RA_APP, DEC_APP, ROTATION, STATUS)

LAT_OBS = DOUBLE PRECISION (Given)

LONG = DOUBLE PRECISION (Given)

LAT = DOUBLE PRECISION (Given)

LONG2 = DOUBLE PRECISION (Given)

LAT2 = DOUBLE PRECISION (Given)

MAP_X = DOUBLE PRECISION (Given)

MAP_Y = DOUBLE PRECISION (Given)

COORD_TYPE = CHARACTER$\ast$($\ast$) (Given)

LST = DOUBLE PRECISION (Given)

MJD = DOUBLE PRECISION (Given)

MJD1 = DOUBLE PRECISION (Given)

MJD2 = DOUBLE PRECISION (Given)

RA_APP = DOUBLE PRECISION (Returned)

DEC_APP = DOUBLE PRECISION (Returned)

ROTATION = DOUBLE PRECISION (Returned)

STATUS = INTEGER (Given and returned)

Does not handle LOCAL_COORDS for MAP_X and MAP_Y (see SCULIB_APARRENT_2_MP for information on how to do this)

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