|
| 1 | +/* Handling of (conventional) proper motions. |
| 2 | +
|
| 3 | +This code is largely based on a FORTRAN function written by Lennart Lindegren |
| 4 | +(Lund Obs) in 1995 that implements the procedure described in The Hipparcos |
| 5 | +and Tycho Catalogues (ESA SP-1200), Volume 1, Section 1.5.5, 'Epoch |
| 6 | +Transformation: Rigorous Treatment'; cf. |
| 7 | +<https://www.cosmos.esa.int/documents/532822/552851/vol1_all.pdf/99adf6e3-6893-4824-8fc2-8d3c9cbba2b5>. |
| 8 | +*/ |
| 9 | + |
| 10 | +#include<math.h> |
| 11 | +#include<pgs_util.h> |
| 12 | + |
| 13 | +#include"point.h" |
| 14 | +#include"epochprop.h" |
| 15 | +#include"vector3d.h" |
| 16 | + |
| 17 | +PG_FUNCTION_INFO_V1(epoch_prop); |
| 18 | + |
| 19 | +/* Astronomical unit in kilometers */ |
| 20 | +#defineAU 1.495978701e8 |
| 21 | + |
| 22 | +/* Julian year in seconds */ |
| 23 | +#defineJ_YEAR (365.25*86400) |
| 24 | + |
| 25 | +/* A_nu as per ESA/SP-1200 */ |
| 26 | +#defineA_NU (AU/(J_YEAR)) |
| 27 | + |
| 28 | +/* Following SOFA, we use 1e-7 arcsec as minimal parallax |
| 29 | +("celestial sphere"); parallax=0 exactly means "infinite distance", which |
| 30 | +leads to all sorts for problems; our parallaxes come in in mas, so: */ |
| 31 | +#definePX_MIN 1e-7*1000 |
| 32 | + |
| 33 | +/* propagate an object at a phase vector over a time difference of delta_t, |
| 34 | +stuffing an updated phase vector in result. |
| 35 | +
|
| 36 | +This does not propagate errors. |
| 37 | +*/ |
| 38 | +staticvoidpropagate_phasevec( |
| 39 | +constphasevec*pv, |
| 40 | +constdoubledelta_t, |
| 41 | +phasevec*result) { |
| 42 | + |
| 43 | +doubledistance_factor,mu0abs,zeta0,parallax; |
| 44 | + |
| 45 | +Vector3Dp0,r0,q0; |
| 46 | +Vector3Dmu0,pprime,qprime,mu,muprime,u,uprime; |
| 47 | + |
| 48 | +/* for very small or null parallaxes, our algorithm breaks; avoid that |
| 49 | +and, if we did emergency measures, do not talk about parallax and |
| 50 | +radial velocity in the output */ |
| 51 | +if (pv->parallax_valid) { |
| 52 | +parallax=pv->parallax; |
| 53 | +}else { |
| 54 | +parallax=PX_MIN; |
| 55 | +} |
| 56 | +result->parallax_valid=pv->parallax_valid; |
| 57 | + |
| 58 | +/* compute the normal triad as Vector3D-s, eq. (1.2.15)*/ |
| 59 | +spoint_vector3d(&r0,&(pv->pos)); |
| 60 | + |
| 61 | +p0.x=-sin(pv->pos.lng); |
| 62 | +p0.y=cos(pv->pos.lng); |
| 63 | +p0.z=0; |
| 64 | + |
| 65 | +q0.x=-sin(pv->pos.lat)*cos(pv->pos.lng); |
| 66 | +q0.y=-sin(pv->pos.lat)*sin(pv->pos.lng); |
| 67 | +q0.z=cos(pv->pos.lat); |
| 68 | + |
| 69 | +/* the original proper motion vector */ |
| 70 | +mu0.x=mu0.y=mu0.z=0; |
| 71 | +vector3d_addwithscalar(&mu0,pv->pm[0],&p0); |
| 72 | +vector3d_addwithscalar(&mu0,pv->pm[1],&q0); |
| 73 | +mu0abs=vector3d_length(&mu0); |
| 74 | + |
| 75 | +/* radial velocity in mas/yr ("change of parallax per year"). eq. (1.5.24) |
| 76 | +We're transforming this to rad/yr so the units work out below */ |
| 77 | +zeta0= (pv->rv*parallax /A_NU) /3.6e6 /RADIANS; |
| 78 | +/* distance factor eq. (1.5.25) */ |
| 79 | +distance_factor=1/sqrt(1 |
| 80 | ++2*zeta0*delta_t |
| 81 | ++ (mu0abs*mu0abs+zeta0*zeta0)*delta_t*delta_t); |
| 82 | + |
| 83 | +/* the propagated proper motion vector, eq. (1.5.28) */ |
| 84 | +muprime.x=muprime.y=muprime.z=0; |
| 85 | +vector3d_addwithscalar(&muprime, (1+zeta0*delta_t),&mu0); |
| 86 | +vector3d_addwithscalar(&muprime,-mu0abs*mu0abs*delta_t,&r0); |
| 87 | +mu.x=mu.y=mu.z=0; |
| 88 | +vector3d_addwithscalar(&mu,pow(distance_factor,3),&muprime); |
| 89 | + |
| 90 | +/* parallax, eq. (1.5.27) */ |
| 91 | +result->parallax=distance_factor*parallax; |
| 92 | +/* zeta/rv, eq. (1.5.29); go back from rad to mas, too */ |
| 93 | +result->rv= (zeta0+ (mu0abs*mu0abs+zeta0*zeta0)*delta_t) |
| 94 | +*distance_factor*distance_factor |
| 95 | +*3.6e6*RADIANS |
| 96 | +*A_NU /result->parallax; |
| 97 | + |
| 98 | +/* propagated position, eq. (1.5.26) */ |
| 99 | +uprime.x=uprime.y=uprime.z=0; |
| 100 | +vector3d_addwithscalar(&uprime, (1+zeta0*delta_t),&r0); |
| 101 | +vector3d_addwithscalar(&uprime,delta_t,&mu0); |
| 102 | +u.x=u.y=u.z=0; |
| 103 | +vector3d_addwithscalar(&u,distance_factor,&uprime); |
| 104 | +vector3d_spoint(&(result->pos),&u); |
| 105 | + |
| 106 | +/* compute a new triad for the propagated position, eq (1.5.15) */ |
| 107 | +pprime.x=-sin(result->pos.lng); |
| 108 | +pprime.y=cos(result->pos.lng); |
| 109 | +pprime.z=0; |
| 110 | +qprime.x=-sin(result->pos.lat)*cos(result->pos.lng); |
| 111 | +qprime.y=-sin(result->pos.lat)*sin(result->pos.lng); |
| 112 | +qprime.z=cos(result->pos.lat); |
| 113 | + |
| 114 | +/* use it to compute the proper motions, eq. (1.5.32) */ |
| 115 | +result->pm[0]=vector3d_scalar(&pprime,&mu); |
| 116 | +result->pm[1]=vector3d_scalar(&qprime,&mu); |
| 117 | +} |
| 118 | + |
| 119 | + |
| 120 | +/* |
| 121 | +Propagate a position with proper motions and optionally parallax |
| 122 | +and radial velocity. |
| 123 | +
|
| 124 | +Arguments: pos0 (spoint), pm_long, pm_lat (in rad/yr) |
| 125 | +par (parallax, mas), rv (in km/s), delta_t (in years) |
| 126 | +
|
| 127 | +This returns a 6-array of lat, long (in rad), parallax (in mas) |
| 128 | +pmlat, pmlong (in rad/yr), rv (in km/s). |
| 129 | +*/ |
| 130 | +Datum |
| 131 | +epoch_prop(PG_FUNCTION_ARGS) { |
| 132 | +doubledelta_t; |
| 133 | +phasevecinput,output; |
| 134 | +ArrayType*result; |
| 135 | +Datumretvals[6]; |
| 136 | + |
| 137 | +if (PG_ARGISNULL(0)) { |
| 138 | +ereport(ERROR, |
| 139 | +(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED), |
| 140 | +errmsg("NULL position not supported in epoch propagation"))); } |
| 141 | +memcpy(&(input.pos), (void*)PG_GETARG_POINTER(0),sizeof(SPoint)); |
| 142 | +if (PG_ARGISNULL(1)) { |
| 143 | +input.parallax=0; |
| 144 | +}else { |
| 145 | +input.parallax=PG_GETARG_FLOAT8(1); |
| 146 | +} |
| 147 | +input.parallax_valid=fabs(input.parallax)>PX_MIN; |
| 148 | + |
| 149 | +if (PG_ARGISNULL(2)) { |
| 150 | +input.pm[0]=0; |
| 151 | +}else { |
| 152 | +input.pm[0]=PG_GETARG_FLOAT8(2); |
| 153 | +} |
| 154 | + |
| 155 | +if (PG_ARGISNULL(3)) { |
| 156 | +input.pm[1]=0; |
| 157 | +}else { |
| 158 | +input.pm[1]=PG_GETARG_FLOAT8(3); |
| 159 | +} |
| 160 | + |
| 161 | +if (PG_ARGISNULL(4)) { |
| 162 | +input.rv=0; |
| 163 | +}else { |
| 164 | +input.rv=PG_GETARG_FLOAT8(4); |
| 165 | +} |
| 166 | + |
| 167 | +if (PG_ARGISNULL(5)) { |
| 168 | +ereport(ERROR, |
| 169 | +(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED), |
| 170 | +errmsg("NULL delta t not supported in epoch propagation"))); } |
| 171 | +delta_t=PG_GETARG_FLOAT8(5); |
| 172 | + |
| 173 | +propagate_phasevec(&input,delta_t,&output); |
| 174 | + |
| 175 | +/* change to internal units: rad, rad/yr, mas, and km/s */ |
| 176 | +retvals[0]=Float8GetDatum(output.pos.lng); |
| 177 | +retvals[1]=Float8GetDatum(output.pos.lat); |
| 178 | +retvals[2]=Float8GetDatum(output.parallax); |
| 179 | +retvals[3]=Float8GetDatum(output.pm[0]); |
| 180 | +retvals[4]=Float8GetDatum(output.pm[1]); |
| 181 | +retvals[5]=Float8GetDatum(output.rv); |
| 182 | + |
| 183 | +{ |
| 184 | +boolisnull[6]= {0,0,0,0,0,0}; |
| 185 | +intlower_bounds[1]= {1}; |
| 186 | +intdims[1]= {6}; |
| 187 | +#ifdefUSE_FLOAT8_BYVAL |
| 188 | +boolembyval= true; |
| 189 | +#else |
| 190 | +boolembyval= false; |
| 191 | +#endif |
| 192 | + |
| 193 | +if (!output.parallax_valid) { |
| 194 | +/* invalidate parallax and rv */ |
| 195 | +isnull[2]=1; |
| 196 | +isnull[5]=1; |
| 197 | +} |
| 198 | + |
| 199 | +result=construct_md_array(retvals,isnull,1,dims,lower_bounds, |
| 200 | +FLOAT8OID,sizeof(float8),embyval,'d'); |
| 201 | +} |
| 202 | +PG_RETURN_ARRAYTYPE_P(result); |
| 203 | +} |