/[PAMELA software]/YodaProfiler/inc/sgp4.h
ViewVC logotype

Contents of /YodaProfiler/inc/sgp4.h

Parent Directory Parent Directory | Revision Log Revision Log


Revision 1.3 - (show annotations) (download)
Tue Jan 23 17:04:09 2007 UTC (17 years, 10 months ago) by mocchiut
Branch: MAIN
CVS Tags: v3r00
Changes since 1.2: +236 -0 lines
File MIME type: text/plain
Updated GL_TLE class

1 //
2 // stdafx.h
3 //
4 #ifndef sgp4_h
5 #define sgp4_h
6
7 //#define WIN32_LEAN_AND_MEAN // Exclude rarely-used stuff from Windows headers
8 #include <stdio.h>
9 //#include <tchar.h>
10 #include <ctype.h>
11 #include <string>
12 #include <map>
13 #include <vector>
14 #include <algorithm>
15 #include <assert.h>
16 #include <time.h>
17 #include <math.h>
18
19 using namespace std;
20 //
21 // globals.h
22 //
23
24 const double PI = 3.141592653589793;
25 const double TWOPI = 2.0 * PI;
26 const double RADS_PER_DEG = PI / 180.0;
27
28 const double GM = 398601.2; // Earth gravitational constant, km^3/sec^2
29 const double GEOSYNC_ALT = 42241.892; // km
30 const double EARTH_DIA = 12800.0; // km
31 const double DAY_SIDERAL = (23 * 3600) + (56 * 60) + 4.09; // sec
32 const double DAY_24HR = (24 * 3600); // sec
33
34 const double AE = 1.0;
35 const double AU = 149597870.0; // Astronomical unit (km) (IAU 76)
36 const double SR = 696000.0; // Solar radius (km) (IAU 76)
37 const double TWOTHRD = 2.0 / 3.0;
38 const double XKMPER_WGS72 = 6378.135; // Earth equatorial radius - km (WGS '72)
39 const double F = 1.0 / 298.26; // Earth flattening (WGS '72)
40 const double GE = 398600.8; // Earth gravitational constant (WGS '72)
41 const double J2 = 1.0826158E-3; // J2 harmonic (WGS '72)
42 const double J3 = -2.53881E-6; // J3 harmonic (WGS '72)
43 const double J4 = -1.65597E-6; // J4 harmonic (WGS '72)
44 const double CK2 = J2 / 2.0;
45 const double CK4 = -3.0 * J4 / 8.0;
46 const double XJ3 = J3;
47 const double E6A = 1.0e-06;
48 const double QO = AE + 120.0 / XKMPER_WGS72;
49 const double S = AE + 78.0 / XKMPER_WGS72;
50 const double HR_PER_DAY = 24.0; // Hours per day (solar)
51 const double MIN_PER_DAY = 1440.0; // Minutes per day (solar)
52 const double SEC_PER_DAY = 86400.0; // Seconds per day (solar)
53 const double OMEGA_E = 1.00273790934; // earth rotation per sideral day
54 const double XKE = sqrt(3600.0 * GE / //sqrt(ge) ER^3/min^2
55 (XKMPER_WGS72 * XKMPER_WGS72 * XKMPER_WGS72));
56 const double QOMS2T = pow((QO - S), 4); //(QO - S)^4 ER^4
57
58 // Utility functions
59 double sqr (const double x);
60 double Fmod2p(const double arg);
61 double AcTan (const double sinx, double cosx);
62
63 double rad2deg(const double);
64 double deg2rad(const double);
65 //
66 // coord.h
67 //
68 // Copyright 2002-2003 Michael F. Henry
69 //
70 //////////////////////////////////////////////////////////////////////
71 // Geocentric coordinates.
72 class cCoordGeo
73 {
74 public:
75 cCoordGeo();
76 cCoordGeo(double lat, double lon, double alt) :
77 m_Lat(lat), m_Lon(lon), m_Alt(alt) {}
78 virtual ~cCoordGeo() {};
79
80 double m_Lat; // Latitude, radians (negative south)
81 double m_Lon; // Longitude, radians (negative west)
82 double m_Alt; // Altitude, km (above mean sea level)
83 };
84
85 //////////////////////////////////////////////////////////////////////
86 // Topocentric-Horizon coordinates.
87 class cCoordTopo
88 {
89 public:
90 cCoordTopo();
91 cCoordTopo(double az, double el, double rng, double rate) :
92 m_Az(az), m_El(el), m_Range(rng), m_RangeRate(rate) {}
93 virtual ~cCoordTopo() {};
94
95 double m_Az; // Azimuth, radians
96 double m_El; // Elevation, radians
97 double m_Range; // Range, kilometers
98 double m_RangeRate; // Range rate of change, km/sec
99 // Negative value means "towards observer"
100 };
101
102 // cVector.h: interface for the cVector class.
103 //
104 // Copyright 2003 (c) Michael F. Henry
105 //
106 //////////////////////////////////////////////////////////////////////
107
108 class cVector
109 {
110 public:
111 cVector(double x = 0.0, double y = 0.0, double z = 0.0, double w = 0.0) :
112 m_x(x), m_y(y), m_z(z), m_w(w) {}
113 virtual ~cVector() {};
114
115 void Sub(const cVector&); // subtraction
116 void Mul(double factor); // multiply each component by 'factor'
117
118 double Angle(const cVector&) const; // angle between two vectors
119 double Magnitude() const; // vector magnitude
120 double Dot(const cVector& vec) const; // dot product
121
122 // protected:
123 double m_x;
124 double m_y;
125 double m_z;
126 double m_w;
127 };
128 //
129 // cTle.h
130 //
131 // This class will accept a single set of two-line elements and then allow
132 // a client to request specific fields, such as epoch, mean motion,
133 // etc., from the set.
134 //
135 // Copyright 1996-2003 Michael F. Henry
136 //
137 /////////////////////////////////////////////////////////////////////////////
138 class cTle
139 {
140 public:
141 cTle(string&, string&, string&);
142 cTle(const cTle &tle);
143 ~cTle();
144
145 enum eTleLine
146 {
147 LINE_ZERO,
148 LINE_ONE,
149 LINE_TWO
150 };
151
152 enum eField
153 {
154 FLD_FIRST,
155 FLD_NORADNUM = FLD_FIRST,
156 FLD_INTLDESC,
157 FLD_SET, // TLE set number
158 FLD_EPOCHYEAR, // Epoch: Last two digits of year
159 FLD_EPOCHDAY, // Epoch: Fractional Julian Day of year
160 FLD_ORBITNUM, // Orbit at epoch
161 FLD_I, // Inclination
162 FLD_RAAN, // R.A. ascending node
163 FLD_E, // Eccentricity
164 FLD_ARGPER, // Argument of perigee
165 FLD_M, // Mean anomaly
166 FLD_MMOTION, // Mean motion
167 FLD_MMOTIONDT, // First time derivative of mean motion
168 FLD_MMOTIONDT2,// Second time derivative of mean motion
169 FLD_BSTAR, // BSTAR Drag
170 FLD_LAST // MUST be last
171 };
172
173 enum eUnits
174 {
175 U_FIRST,
176 U_RAD = U_FIRST, // radians
177 U_DEG, // degrees
178 U_NATIVE, // TLE format native units (no conversion)
179 U_LAST // MUST be last
180 };
181
182 void Initialize();
183
184 static int CheckSum(const string&);
185 static bool IsValidLine(string&, eTleLine);
186 static string ExpToDecimal(const string&);
187
188 static void TrimLeft(string&);
189 static void TrimRight(string&);
190
191 double getField(eField fld, // which field to retrieve
192 eUnits unit = U_NATIVE, // return units in rad, deg etc.
193 string *pstr = NULL, // return ptr for str value
194 bool bStrUnits = false) // 'true': append units to str val
195 const;
196 string getName() const { return m_strName; }
197 string getLine1() const { return m_strLine1;}
198 string getLine2() const { return m_strLine2;}
199
200 protected:
201 static double ConvertUnits(double val, eField fld, eUnits units);
202
203 private:
204 string getUnits(eField) const;
205 double getFieldNumeric(eField) const;
206
207 // Satellite name and two data lines
208 string m_strName;
209 string m_strLine1;
210 string m_strLine2;
211
212 // Converted fields, in atof()-readable form
213 string m_Field[FLD_LAST];
214
215 // Cache of field values in "double" format
216 typedef int FldKey;
217 FldKey Key(eUnits u, eField f) const { return (u * 100) + f; }
218 mutable map<FldKey, double> m_mapCache;
219 };
220
221 ///////////////////////////////////////////////////////////////////////////
222 //
223 // TLE data format
224 //
225 // [Reference: T.S. Kelso]
226 //
227 // Two line element data consists of three lines in the following format:
228 //
229 // AAAAAAAAAAAAAAAAAAAAAA
230 // 1 NNNNNU NNNNNAAA NNNNN.NNNNNNNN +.NNNNNNNN +NNNNN-N +NNNNN-N N NNNNN
231 // 2 NNNNN NNN.NNNN NNN.NNNN NNNNNNN NNN.NNNN NNN.NNNN NN.NNNNNNNNNNNNNN
232 //
233 // Line 0 is a twenty-two-character name.
234 //
235 // Lines 1 and 2 are the standard Two-Line Orbital Element Set Format identical
236 // to that used by NORAD and NASA. The format description is:
237 //
238 // Line 1
239 // Column Description
240 // 01-01 Line Number of Element Data
241 // 03-07 Satellite Number
242 // 10-11 International Designator (Last two digits of launch year)
243 // 12-14 International Designator (Launch number of the year)
244 // 15-17 International Designator (Piece of launch)
245 // 19-20 Epoch Year (Last two digits of year)
246 // 21-32 Epoch (Julian Day and fractional portion of the day)
247 // 34-43 First Time Derivative of the Mean Motion
248 // or Ballistic Coefficient (Depending on ephemeris type)
249 // 45-52 Second Time Derivative of Mean Motion (decimal point assumed;
250 // blank if N/A)
251 // 54-61 BSTAR drag term if GP4 general perturbation theory was used.
252 // Otherwise, radiation pressure coefficient. (Decimal point assumed)
253 // 63-63 Ephemeris type
254 // 65-68 Element number
255 // 69-69 Check Sum (Modulo 10)
256 // (Letters, blanks, periods, plus signs = 0; minus signs = 1)
257 //
258 // Line 2
259 // Column Description
260 // 01-01 Line Number of Element Data
261 // 03-07 Satellite Number
262 // 09-16 Inclination [Degrees]
263 // 18-25 Right Ascension of the Ascending Node [Degrees]
264 // 27-33 Eccentricity (decimal point assumed)
265 // 35-42 Argument of Perigee [Degrees]
266 // 44-51 Mean Anomaly [Degrees]
267 // 53-63 Mean Motion [Revs per day]
268 // 64-68 Revolution number at epoch [Revs]
269 // 69-69 Check Sum (Modulo 10)
270 //
271 // All other columns are blank or fixed.
272 //
273 // Example:
274 //
275 // NOAA 6
276 // 1 11416U 86 50.28438588 0.00000140 67960-4 0 5293
277 // 2 11416 98.5105 69.3305 0012788 63.2828 296.9658 14.24899292346978
278
279 //
280 // cJulian.h
281 //
282 // Copyright (c) 2003 Michael F. Henry
283 //
284 //
285 // See note in cJulian.cpp for information on this class and the epoch dates
286 //
287 const double EPOCH_JAN1_00H_1900 = 2415019.5; // Jan 1.0 1900 = Jan 1 1900 00h UTC
288 const double EPOCH_JAN1_12H_1900 = 2415020.0; // Jan 1.5 1900 = Jan 1 1900 12h UTC
289 const double EPOCH_JAN1_12H_2000 = 2451545.0; // Jan 1.5 2000 = Jan 1 2000 12h UTC
290
291 //////////////////////////////////////////////////////////////////////////////
292 class cJulian
293 {
294 public:
295 cJulian() { Initialize(2000, 1); }
296 explicit cJulian(time_t t); // Create from time_t
297 explicit cJulian(int year, double day); // Create from year, day of year
298 explicit cJulian(int year, // i.e., 2004
299 int mon, // 1..12
300 int day, // 1..31
301 int hour, // 0..23
302 int min, // 0..59
303 double sec = 0.0); // 0..(59.999999...)
304 ~cJulian() {};
305
306 double toGMST() const; // Greenwich Mean Sidereal Time
307 double toLMST(double lon) const; // Local Mean Sideral Time
308 time_t toTime() const; // To time_t type - avoid using
309
310 double FromJan1_00h_1900() const { return m_Date - EPOCH_JAN1_00H_1900; }
311 double FromJan1_12h_1900() const { return m_Date - EPOCH_JAN1_12H_1900; }
312 double FromJan1_12h_2000() const { return m_Date - EPOCH_JAN1_12H_2000; }
313
314 void getComponent(int *pYear, int *pMon = NULL, double *pDOM = NULL) const;
315 double getDate() const { return m_Date; }
316
317 void addDay (double day) { m_Date += day; }
318 void addHour(double hr ) { m_Date += (hr / HR_PER_DAY ); }
319 void addMin (double min) { m_Date += (min / MIN_PER_DAY); }
320 void addSec (double sec) { m_Date += (sec / SEC_PER_DAY); }
321
322 double spanDay (const cJulian& b) const { return m_Date - b.m_Date; }
323 double spanHour(const cJulian& b) const { return spanDay(b) * HR_PER_DAY; }
324 double spanMin (const cJulian& b) const { return spanDay(b) * MIN_PER_DAY; }
325 double spanSec (const cJulian& b) const { return spanDay(b) * SEC_PER_DAY; }
326
327 static bool IsLeapYear(int y)
328 { return (y % 4 == 0 && y % 100 != 0) || (y % 400 == 0); }
329
330 protected:
331 void Initialize(int year, double day);
332
333 double m_Date; // Julian date
334 };
335 //
336 // cEci.h
337 //
338 // Copyright (c) 2003 Michael F. Henry
339 //
340 //////////////////////////////////////////////////////////////////////
341 // class cEci
342 // Encapsulates an Earth-Centered Inertial position, velocity, and time.
343 class cEci
344 {
345 public:
346 cEci() { m_VecUnits = UNITS_NONE; }
347 cEci(const cCoordGeo &geo, const cJulian &cJulian);
348 cEci(const cVector &pos, const cVector &vel,
349 const cJulian &date, bool IsAeUnits = true);
350 virtual ~cEci() {};
351
352 cCoordGeo toGeo();
353
354 cVector getPos() const { return m_pos; }
355 cVector getVel() const { return m_vel; }
356 cJulian getDate() const { return m_date; }
357
358 void setUnitsAe() { m_VecUnits = UNITS_AE; }
359 void setUnitsKm() { m_VecUnits = UNITS_KM; }
360 bool UnitsAreAe() const { return m_VecUnits == UNITS_AE; }
361 bool UnitsAreKm() const { return m_VecUnits == UNITS_KM; }
362 void ae2km(); // Convert position, velocity vector units from AE to km
363
364 protected:
365 void MulPos(double factor) { m_pos.Mul(factor); }
366 void MulVel(double factor) { m_vel.Mul(factor); }
367
368 enum VecUnits
369 {
370 UNITS_NONE, // not initialized
371 UNITS_AE,
372 UNITS_KM,
373 };
374
375 cVector m_pos;
376 cVector m_vel;
377 cJulian m_date;
378 VecUnits m_VecUnits;
379 };
380 //
381 // cNoradBase.h
382 //
383 // This class provides a base class for the NORAD SGP4/SDP4
384 // orbit models.
385 //
386 // Copyright (c) 2003 Michael F. Henry
387 //
388 #pragma once
389
390 //////////////////////////////////////////////////////////////////////////////
391
392 class cEci;
393 class cOrbit;
394
395 //////////////////////////////////////////////////////////////////////////////
396
397 class cNoradBase
398 {
399 public:
400 cNoradBase(const cOrbit&);
401 virtual ~cNoradBase() {};
402
403 virtual bool getPosition(double tsince, cEci &eci) = 0;
404
405 protected:
406 cNoradBase& operator=(const cNoradBase&);
407
408 void Initialize();
409 bool FinalPosition(double incl, double omega, double e,
410 double a, double xl, double xnode,
411 double xn, double tsince, cEci &eci);
412
413 const cOrbit &m_Orbit;
414
415 // Orbital parameter variables which need only be calculated one
416 // time for a given orbit (ECI position time-independent).
417 double m_satInc; // inclination
418 double m_satEcc; // eccentricity
419
420 double m_cosio; double m_theta2; double m_x3thm1; double m_eosq;
421 double m_betao2; double m_betao; double m_aodp; double m_xnodp;
422 double m_s4; double m_qoms24; double m_perigee; double m_tsi;
423 double m_eta; double m_etasq; double m_eeta; double m_coef;
424 double m_coef1; double m_c1; double m_c2; double m_c3;
425 double m_c4; double m_sinio; double m_a3ovk2; double m_x1mth2;
426 double m_xmdot; double m_omgdot; double m_xhdot1; double m_xnodot;
427 double m_xnodcf; double m_t2cof; double m_xlcof; double m_aycof;
428 double m_x7thm1;
429 };
430 //
431 // cOrbit.h
432 //
433 // This is the header file for the class cOrbit. This class accepts a
434 // single satellite's NORAD two-line element set and provides information
435 // regarding the satellite's orbit such as period, axis length,
436 // ECI coordinates/velocity, etc., using the SGP4/SDP4 orbital models.
437 //
438 // Copyright (c) 2002-2003 Michael F. Henry
439 //
440 #pragma once
441
442 #include "math.h"
443
444 using namespace std;
445 //////////////////////////////////////////////////////////////////////////////
446
447 class cVector;
448 class cGeoCoord;
449 class cEci;
450
451 //////////////////////////////////////////////////////////////////////////////
452 class cOrbit
453 {
454 public:
455 cOrbit(const cTle &tle);
456 virtual ~cOrbit();
457
458 // Return satellite ECI data at given minutes since element's epoch.
459 bool getPosition(double tsince, cEci *pEci) const;
460
461 double Inclination() const { return radGet(cTle::FLD_I); }
462 double Eccentricity() const { return m_tle.getField(cTle::FLD_E); }
463 double RAAN() const { return radGet(cTle::FLD_RAAN); }
464 double ArgPerigee() const { return radGet(cTle::FLD_ARGPER); }
465 double BStar() const { return m_tle.getField(cTle::FLD_BSTAR) / AE;}
466 double Drag() const { return m_tle.getField(cTle::FLD_MMOTIONDT); }
467 double mnMotion() const { return m_tle.getField(cTle::FLD_MMOTION); }
468 double mnAnomaly() const { return radGet(cTle::FLD_M); }
469 double mnAnomaly(cJulian t) const; // mean anomaly (in radians) at time t
470
471 cJulian Epoch() const { return m_jdEpoch; }
472
473 double TPlusEpoch(const cJulian &t) const; // time span [t - epoch] in secs
474
475 string SatName(bool fAppendId = false) const;
476
477 // "Recovered" from the input elements
478 double SemiMajor() const { return m_aeAxisSemiMajorRec; }
479 double SemiMinor() const { return m_aeAxisSemiMinorRec; }
480 double mnMotionRec() const { return m_mnMotionRec; } // mn motion, rads/min
481 double Major() const { return 2.0 * SemiMajor(); } // major axis in AE
482 double Minor() const { return 2.0 * SemiMinor(); } // minor axis in AE
483 double Perigee() const { return m_kmPerigeeRec; } // perigee in km
484 double Apogee() const { return m_kmApogeeRec; } // apogee in km
485 double Period() const; // period in seconds
486
487 protected:
488 double radGet(cTle::eField fld) const
489 { return m_tle.getField(fld, cTle::U_RAD); }
490
491 double degGet(cTle::eField fld) const
492 { return m_tle.getField(fld, cTle::U_DEG); }
493
494 private:
495 cTle m_tle;
496 cJulian m_jdEpoch;
497 cNoradBase *m_pNoradModel;
498
499 // Caching variables; note units are not necessarily the same as tle units
500 mutable double m_secPeriod;
501
502 // Caching variables recovered from the input TLE elements
503 double m_aeAxisSemiMinorRec; // semi-minor axis, in AE units
504 double m_aeAxisSemiMajorRec; // semi-major axis, in AE units
505 double m_mnMotionRec; // radians per minute
506 double m_kmPerigeeRec; // perigee, in km
507 double m_kmApogeeRec; // apogee, in km
508 };
509
510 //
511 // cNoradSGP4.h
512 //
513 // This class implements the NORAD Simple General Perturbation 4 orbit
514 // model. This model provides the ECI coordiantes/velocity of satellites
515 // with orbit periods less than 225 minutes.
516 //
517 // Copyright (c) 2003 Michael F. Henry
518 //
519 #pragma once
520
521 class cOrbit;
522
523 //////////////////////////////////////////////////////////////////////////////
524 class cNoradSGP4 : public cNoradBase
525 {
526 public:
527 cNoradSGP4(const cOrbit &orbit);
528 virtual ~cNoradSGP4() {};
529
530 virtual bool getPosition(double tsince, cEci &eci);
531
532 protected:
533 double m_c5;
534 double m_omgcof;
535 double m_xmcof;
536 double m_delmo;
537 double m_sinmo;
538 };
539
540 //
541 // cNoradSDP4.h
542 //
543 // This class implements the NORAD Simple Deep Perturbation 4 orbit
544 // model. This model provides the ECI coordinates/velocity of satellites
545 // with periods >= 225 minutes.
546 //
547 // Copyright (c) 2003 Michael F. Henry
548 //
549 #pragma once
550
551 class cOrbit;
552
553 //////////////////////////////////////////////////////////////////////////////
554 class cNoradSDP4 : public cNoradBase
555 {
556 public:
557 cNoradSDP4(const cOrbit &orbit);
558 virtual ~cNoradSDP4() {};
559
560 virtual bool getPosition(double tsince, cEci &eci);
561
562 protected:
563 bool DeepInit(double *eosq, double *sinio, double *cosio, double *m_betao,
564 double *m_aodp, double *m_theta2, double *m_sing, double *m_cosg,
565 double *m_betao2,double *xmdot, double *omgdot, double *xnodott);
566
567 bool DeepSecular(double *xmdf, double *omgadf,double *xnode, double *emm,
568 double *xincc, double *xnn, double *tsince);
569 bool DeepCalcDotTerms (double *pxndot, double *pxnddt, double *pxldot);
570 void DeepCalcIntegrator(double *pxndot, double *pxnddt, double *pxldot,
571 const double &delt);
572 bool DeepPeriodics(double *e, double *xincc, double *omgadf,
573 double *xnode, double *xmam);
574 double m_sing;
575 double m_cosg;
576
577 // Deep Initialization
578 double eqsq; double siniq; double cosiq; double rteqsq; double ao;
579 double cosq2; double sinomo; double cosomo; double bsq; double xlldot;
580 double omgdt; double xnodot;
581
582 // Deep Secular, Periodic
583 double xll; double omgasm; double xnodes; double _em;
584 double xinc; double xn; double t;
585
586 // Variables shared by "Deep" routines
587 double dp_e3; double dp_ee2; double dp_savtsn; double dp_se2;
588 double dp_se3; double dp_sgh2; double dp_sgh3; double dp_sgh4;
589 double dp_sghs; double dp_sh2; double dp_sh3; double dp_si2;
590 double dp_si3; double dp_sl2; double dp_sl3; double dp_sl4;
591 double dp_xgh2; double dp_xgh3; double dp_xgh4; double dp_xh2;
592 double dp_xh3; double dp_xi2; double dp_xi3; double dp_xl2;
593 double dp_xl3; double dp_xl4; double dp_xqncl; double dp_zmol;
594 double dp_zmos;
595
596 double dp_atime; double dp_d2201; double dp_d2211; double dp_d3210;
597 double dp_d3222; double dp_d4410; double dp_d4422; double dp_d5220;
598 double dp_d5232; double dp_d5421; double dp_d5433; double dp_del1;
599 double dp_del2; double dp_del3; double dp_fasx2; double dp_fasx4;
600 double dp_fasx6; double dp_omegaq; double dp_sse; double dp_ssg;
601 double dp_ssh; double dp_ssi; double dp_ssl; double dp_step2;
602 double dp_stepn; double dp_stepp; double dp_thgr; double dp_xfact;
603 double dp_xlamo; double dp_xli; double dp_xni;
604
605 bool dp_iresfl;
606 bool dp_isynfl;
607
608 // DeepInit vars that change with epoch
609 double dpi_c; double dpi_ctem; double dpi_day; double dpi_gam;
610 double dpi_stem; double dpi_xnodce; double dpi_zcosgl; double dpi_zcoshl;
611 double dpi_zcosil; double dpi_zsingl; double dpi_zsinhl; double dpi_zsinil;
612 double dpi_zx; double dpi_zy;
613
614 };
615
616 #endif

  ViewVC Help
Powered by ViewVC 1.1.23