Hypothetische Planeten

The Positions of the WvA Hypothetical Planets

The WvA hypothetical planets were postulated by Th.J.J. Ram and others. They have been applied within the WvA since the 1950-ies.

My article on the WvA hypothetical planets

C-code

/* HYPOPLAN.C calculation of an ephemeris of the three hypothetical planets as in use by the Ram school, calculated according to Erlewine, written in Microsoft C by Ingmar de Boer (c) 1996, 2000 This version: orbits according to Ram/Tollenaar. Checked: 27 september 2001 */ #include <stdio.h> #include <math.h> #define EARTH 0 #define PERSEFONE 1 #define HERMES 2 #define DEMETER 3 /* global structures */ typedef struct threeterms {double term1,term2,term3;} ThreeTerms; typedef struct position {double longitude,latitude,distance;} Position; typedef struct vector {double x,y,z;} Vector; typedef struct polar {double phi,theta,r;} Polar; typedef struct orbit { ThreeTerms M,e; double a; ThreeTerms PA,node,incl; } Orbit; /* array of orbits of planets according to Ram/Tollenaar a.o. */ Orbit orbits[4] = { {{358.47584,35999.0498,-.00015},{.016751,-.41e-4,0},1.00000013, {101.22083,1.71918,.00045},{0,0,0},{0,0,0}}, {{295.0,60,0},{0,0,0},71.137866,{0,0,0},{0,0,0},{0,0,0}}, {{134.7,50,0},{0,0,0},80.331954,{0,0,0},{0,0,0},{0,0,0}}, {{114.6,40,0},{0,0,0},93.216975,{0,0,0},{125,0,0},{5.5,0,0}} }; /* utility functions and global variables */ double pi = 3.141592653589792907377; double rad(double gr) {return pi * gr / 180.0;} double gra(double ra) {if (ra<0) ra=ra+2*pi; return fmod((180.0 * ra / pi), 360.0);} double terms(double T, ThreeTerms thiselement) {return thiselement.term1 + thiselement.term2 * T + thiselement.term3 * T * T;} /* rectangular to polar coordinates */ Polar r2p (Vector rect) { Polar pole; pole.r = sqrt((rect.x * rect.x + rect.y * rect.y + rect.z * rect.z)); if (pole.r==0) pole.r = 1.7e-9; if (rect.x==0) rect.x = 1.7e-9; pole.phi = atan2(rect.y, rect.x); pole.theta = asin(rect.z / pole.r); return pole; } /* polar to rectangular coordinates */ Vector p2r (Polar pole) { Vector rect; rect.x = pole.r * cos(pole.theta) * cos(pole.phi); rect.y = pole.r * cos(pole.theta) * sin(pole.phi); rect.z = pole.r * sin(pole.theta); return rect; } /* Julian date */ double jd(int d, int m, int y, double gmt) { if (m <= 2) {m += 12; y--;} return 3.0 - floor(y / 100) + floor(floor(y / 100) / 4) + floor(y * 365.25) + floor(30.6001 * (m + 1)) + 1720993.5 + d + gmt / 24.0; } /* T */ double T(double jd) {return (jd - 2415020.5) / 36525;} /* heliocentric position vector of planet */ Vector helio_planet(double T, Orbit thisorbit) { double m,e,ea,in,v,a,b; int count; Vector anomaly_vec,helio_vec; Polar anomaly_pol,helio_pol; m = rad(gra(rad(terms(T, thisorbit.M)))); e = terms(T, thisorbit.e); /* solve Kepler's equation */ ea = m; for (count=1;count<6;count++) ea = m + e * sin(ea); /* calculate true anomaly */ anomaly_vec.x = thisorbit.a * (cos(ea) - e); anomaly_vec.y = thisorbit.a * sin(ea) * sqrt(1 - e * e); anomaly_vec.z = 0; anomaly_pol = r2p(anomaly_vec); /* reduce to ecliptic */ a = gra(anomaly_pol.phi) + terms(T, thisorbit.PA); m = rad(terms(T, thisorbit.node)); v = gra(rad(a + gra(m))); b = rad(v); in = rad(terms(T, thisorbit.incl)); a = atan(cos(in) * tan(b - m)); if (a<pi) a = a + pi; a = gra(a + m); if (fabs(v - a) > 10) a = a - 180; /* heliocentric lat & long */ helio_pol.phi = rad(gra(rad(a))); helio_pol.theta = atan(sin(helio_pol.phi - m) * tan(in)); helio_pol.r = rad(thisorbit.a) * (1 - e * cos(ea)); /* helio polar to rect */ helio_vec = p2r(helio_pol); return helio_vec; } /* geocentric longitude, latitude and distance */ Position planet(double T, int thisplanet) { Vector earth_helio; Vector thisplanet_helio; Vector thisplanet_geo_vec; Polar thisplanet_geo_pol; Position thisposition; /* calculate heliocentric position of earth: */ earth_helio = helio_planet(T, orbits[EARTH]); if (thisplanet!=EARTH) { thisplanet_helio = helio_planet(T, orbits[thisplanet]); /* calculate geocentric position: */ thisplanet_geo_vec.x = thisplanet_helio.x - earth_helio.x; thisplanet_geo_vec.y = thisplanet_helio.y - earth_helio.y; thisplanet_geo_vec.z = thisplanet_helio.z - earth_helio.z; } else { thisplanet_geo_vec = earth_helio; } thisplanet_geo_pol = r2p(thisplanet_geo_vec); thisposition.longitude = gra(thisplanet_geo_pol.phi); thisposition.latitude = gra(thisplanet_geo_pol.theta); thisposition.distance = gra(thisplanet_geo_pol.r); if (thisplanet==EARTH) thisposition.longitude = gra(thisplanet_geo_pol.phi + pi); if (thisposition.latitude>180) thisposition.latitude-=360; return thisposition; } int main() { double t; int months; int years; Position persefone; Position hermes; Position demeter; years=1800; for (months=1;years<2100;months++) { if (months>12) {months=1;++years;}; t = T(jd(1, months, years, 0)); persefone = planet(t, PERSEFONE); hermes = planet(t, HERMES); demeter = planet(t, DEMETER); printf("%i,%i,%03.2f,%03.2f,%03.2f,%02.2f\n", months,years, persefone.longitude,hermes.longitude,demeter.longitude,demeter.latitude); } return 0; }

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