{"action":"created","comment":{"url":"https://api.github.com/repos/aerospaceresearch/orbitdeterminator/pulls/comments/214745125","pull_request_review_id":151861864,"id":214745125,"node_id":"MDI0OlB1bGxSZXF1ZXN0UmV2aWV3Q29tbWVudDIxNDc0NTEyNQ==","diff_hunk":"@@ -0,0 +1,1842 @@\n+\"\"\"Implements Gauss' method for three topocentric right ascension and\n+declination measurements of celestial bodies. Supports both Earth-centered and\n+Sun-centered orbits.\"\"\"\n+\n+import numpy as np\n+from astropy.coordinates import Longitude, SkyCoord\n+from astropy.coordinates import solar_system_ephemeris, get_body_barycentric\n+from astropy import units as uts\n+from astropy import constants as cts\n+from astropy.time import Time\n+from datetime import datetime, timedelta\n+import matplotlib.pyplot as plt\n+from mpl_toolkits import mplot3d\n+from poliastro.stumpff import c2, c3\n+from astropy.coordinates.earth_orientation import obliquity\n+from astropy.coordinates.matrix_utilities import rotation_matrix\n+import argparse\n+\n+# declare astronomical constants in appropriate units\n+au = cts.au.to(uts.Unit('km')).value\n+mu_Sun = cts.GM_sun.to(uts.Unit('au3 / day2')).value\n+mu_Earth = cts.GM_earth.to(uts.Unit('km3 / s2')).value\n+c_light = cts.c.to(uts.Unit('au/day'))\n+earth_f = 0.003353\n+Re = cts.R_earth.to(uts.Unit('km')).value\n+\n+# load JPL DE432s ephemeris SPK kernel\n+# 'de432s.bsp' is automatically loaded by astropy, via jplephem\n+# 'de432s.bsp' is about 10MB in size and will be automatically downloaded if not present yet in astropy's cache\n+# for more information, see astropy.coordinates.solar_system_ephemeris documentation\n+solar_system_ephemeris.set('de432s')\n+\n+#compute rotation matrices from equatorial to ecliptic frame and viceversa\n+obliquity_j2000 = obliquity(2451544.5) # mean obliquity of the ecliptic at J2000.0\n+rot_equat_to_eclip = rotation_matrix( obliquity_j2000, 'x') #rotation matrix from equatorial to ecliptic frames\n+rot_eclip_to_equat = rotation_matrix(-obliquity_j2000, 'x') #rotation matrix from ecliptic to equatorial frames\n+\n+# set output from printed arrays at full precision\n+np.set_printoptions(precision=16)\n+\n+# convention:\n+# a: semi-major axis\n+# e: eccentricity\n+# taup: time of pericenter passage\n+# Euler angles:\n+# omega: argument of pericenter\n+# I: inclination\n+# Omega: longitude of ascending node\n+\n+#rotation about the z-axis about an angle `ang`\n+def rotz(ang):\n+    cos_ang = np.cos(ang)\n+    sin_ang = np.sin(ang)\n+    return np.array(((cos_ang,-sin_ang,0.0), (sin_ang, cos_ang,0.0), (0.0,0.0,1.0)))\n+\n+#rotation about the x-axis about an angle `ang`\n+def rotx(ang):\n+    cos_ang = np.cos(ang)\n+    sin_ang = np.sin(ang)\n+    return np.array(((1.0,0.0,0.0), (0.0,cos_ang,-sin_ang), (0.0,sin_ang,cos_ang)))\n+\n+#rotation from the orbital plane to the inertial frame\n+#it is composed of the following rotations, in that order:\n+#1) rotation about the z axis about an angle `omega` (argument of pericenter)\n+#2) rotation about the x axis about an angle `I` (inclination)\n+#3) rotation about the z axis about an angle `Omega` (longitude of ascending node)\n+def orbplane2frame_(omega,I,Omega):\n+    P2_mul_P3 = np.matmul(rotx(I),rotz(omega))\n+    return np.matmul(rotz(Omega),P2_mul_P3)\n+\n+def orbplane2frame(x):\n+    return orbplane2frame_(x[0],x[1],x[2])\n+\n+# get Keplerian range\n+def kep_r_(a, e, f):\n+    return a*(1.0-e**2)/(1.0+e*np.cos(f))\n+\n+def kep_r(x):\n+    return kep_r_(x[0],x[1],x[2])\n+\n+# get cartesian positions wrt orbital plane\n+def xyz_orbplane_(a, e, f):\n+    r = kep_r_(a, e, f)\n+    return np.array((r*np.cos(f),r*np.sin(f),0.0))\n+\n+def xyz_orbplane(x):\n+    return xyz_orbplane_(x[0],x[1],x[2])\n+\n+# get cartesian positions wrt inertial frame from orbital elements\n+def xyz_frame2(a,e,f,omega,I,Omega):\n+    return np.matmul( orbplane2frame_(omega,I,Omega) , xyz_orbplane_(a, e, f) )\n+\n+def xyz_frame(x):\n+    return np.matmul( orbplane2frame(x[3:6]) , xyz_orbplane(x[0:3]) )\n+\n+# get mean motion from mass parameter (mu) and semimajor axis (a)\n+def meanmotion(mu,a):\n+    return np.sqrt(mu/(a**3))\n+\n+# get mean anomaly from mean motion (n), time (t) and time of pericenter passage (taup)\n+def meananomaly(n, t, taup):\n+    return np.mod(n*(t-taup), 2.0*np.pi)\n+\n+# compute eccentric anomaly (E) from eccentricity (e) and mean anomaly (M)\n+def eccentricanomaly(e,M):\n+    M0 = np.mod(M,2*np.pi)\n+    E0 = M0 + np.sign(np.sin(M0))*0.85*e #Murray-Dermotts' initial estimate\n+    # 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