# -*- coding: utf-8 -*- from numpy import array from skyfield import api from skyfield.api import EarthSatellite, load from skyfield.constants import AU_KM, AU_M from skyfield.sgp4lib import TEME_to_ITRF, VectorFunction from skyfield.timelib import julian_date line1 = '1 25544U 98067A 18184.80969102 .00001614 00000-0 31745-4 0 9993' line2 = '2 25544 51.6414 295.8524 0003435 262.6267 204.2868 15.54005638121106' # Here are numbers from HORIZONS, which I copied into the test below: # #Ephemeris / WWW_USER Wed Jul 4 19:16:45 2018 Pasadena, USA / Horizons #... #2458303.500000000 = A.D. 2018-Jul-04 00:00:00.0000 TDB # X = 2.633404251158200E-05 Y = 1.015087620439817E-05 Z = 3.544778677556393E-05 # VX=-1.751248694205384E-03 VY= 4.065407557020968E-03 VZ= 1.363540232307603E-04 #2458304.500000000 = A.D. 2018-Jul-05 00:00:00.0000 TDB # X =-2.136440257814821E-05 Y =-2.084170814514480E-05 Z =-3.415494123796893E-05 # VX= 2.143876266215405E-03 VY=-3.752167957502106E-03 VZ= 9.484159290242074E-04 # TODO: try with array of dates def test_iss_against_horizons(): ts = api.load.timescale() s = EarthSatellite(line1, line2) hp = array([ [2.633404251158200E-5, 1.015087620439817E-5, 3.544778677556393E-5], [-2.136440257814821E-5, -2.084170814514480E-5, -3.415494123796893E-5], ]).T hv = array([ [-1.751248694205384E-3, 4.065407557020968E-3, 1.363540232307603E-4], [2.143876266215405E-3, -3.752167957502106E-3, 9.484159290242074E-4], ]).T two_meters = 2.0 / AU_M three_km_per_hour = 3.0 * 24.0 / AU_KM t = ts.tdb(2018, 7, 4) p = s.at(t) assert abs(p.position.au - hp[:,0]).max() < two_meters assert abs(p.velocity.au_per_d - hv[:,0]).max() < three_km_per_hour t = ts.tdb(2018, 7, [4, 5]) p = s.at(t) assert abs(p.position.au - hp).max() < two_meters assert abs(p.velocity.au_per_d - hv).max() < three_km_per_hour # The following tests are based on the text of # http://www.celestrak.org/publications/AIAA/2006-6753/AIAA-2006-6753-Rev2.pdf appendix_c_example = """\ TEME EXAMPLE 1 00005U 58002B 00179.78495062 .00000023 00000-0 28098-4 0 4753 2 00005 34.2682 348.7242 1859667 331.7664 19.3264 10.82419157413667 """ from ..constants import DEG2RAD arcminute = DEG2RAD / 60.0 arcsecond = arcminute / 60.0 seconds_per_day = 86400.0 # Note that the following test is based specifically on Revision 2 of # "Revisiting Spacetrack Report #3" AIAA 2006-6753 (earlier versions of # the PDF use different numbers): # # http://www.celestrak.org/publications/AIAA/2006-6753/AIAA-2006-6753-Rev2.pdf def test_appendix_c_conversion_from_TEME_to_ITRF(): rTEME = array([5094.18016210, 6127.64465950, 6380.34453270]) vTEME = array([-4.746131487, 0.785818041, 5.531931288]) vTEME = vTEME * 24.0 * 60.0 * 60.0 # km/s to km/day jd_utc = julian_date(2004, 4, 6, 7, 51, 28.386) d_ut1 = -0.439961 jd_ut1 = jd_utc + d_ut1 / 86400.0 xp = -0.140682 * arcsecond yp = 0.333309 * arcsecond rITRF, vITRF = TEME_to_ITRF(jd_ut1, rTEME, vTEME, xp, yp) epsilon = 5e-8 # Why not 1e-8, which would match all of their digits? assert abs(-1033.47938300 - rITRF[0]) < epsilon assert abs(+7901.29527540 - rITRF[1]) < epsilon assert abs(+6380.35659580 - rITRF[2]) < epsilon vITRF_per_second = vITRF / seconds_per_day epsilon = 7e-8 # Why not 1e-9, which would match all of their digits? assert abs(-3.225636520 - vITRF_per_second[0]) < epsilon assert abs(-2.872451450 - vITRF_per_second[1]) < epsilon assert abs(+5.531924446 - vITRF_per_second[2]) < epsilon def test_appendix_c_satellite(): lines = appendix_c_example.splitlines() ts = api.load.timescale() sat = EarthSatellite(lines[1], lines[2], lines[0], ts) t = ts.tt_jd(sat.epoch.whole + 3.0, sat.epoch.tt_fraction) # First, a crucial sanity check (which is, technically, a test of # the `sgp4` package and not of Skyfield): are the right coordinates # being produced by our Python SGP4 propagator for this satellite? rTEME, vTEME, error = sat._position_and_velocity_TEME_km(t) # TODO: This used to be accurate to within 1e-8 but lost precision # with the move to SGP4 2.0. Is the difference an underlying change # in the algorithm and its results? Or something else? epsilon = 1e-4 assert abs(-9060.47373569 - rTEME[0]) < epsilon assert abs(4658.70952502 - rTEME[1]) < epsilon assert abs(813.68673153 - rTEME[2]) < epsilon # TODO: Similar to the above, this used to be 1e-9. Then the Time # object started storing UTC as seconds, and it got worse. epsilon = 5e-8 assert abs(-2.232832783 - vTEME[0]) < epsilon assert abs(-4.110453490 - vTEME[1]) < epsilon assert abs(-3.157345433 - vTEME[2]) < epsilon def test_epoch_date(): # Example from https://celestrak.org/columns/v04n03/ s = appendix_c_example.replace('00179.78495062', '98001.00000000') lines = s.splitlines() sat = EarthSatellite(lines[1], lines[2], lines[0]) assert sat.epoch.utc_jpl() == 'A.D. 1998-Jan-01 00:00:00.0000 UTC' def test_target_number(): s = EarthSatellite(line1, line2) assert s.target == -125544 def test_is_sunlit(): # Yes, a positionlib method; but it made sense to test it here. ts = api.load.timescale() t = ts.utc(2018, 7, 3, 0, range(0, 60, 10)) s = EarthSatellite(line1, line2) eph = load('de421.bsp') expected = [True, False, False, False, True, True] assert list(s.at(t).is_sunlit(eph)) == expected # What if we observe from a topos rather than the geocenter? topos = api.Topos('40.8939 N', '83.8917 W') assert list((s - topos).at(t).is_sunlit(eph)) == expected def test_is_venus_behind_earth(): # Like the previous test: a satellite-focused positionlib method. # Just for fun, we ask whether the Sun is behind the earth, so this # measures the same celestial circumstance as the previous test. ts = api.load.timescale() t = ts.utc(2018, 7, 3, 0, range(0, 60, 10)) s = EarthSatellite(line1, line2) eph = load('de421.bsp') expected = [False, True, True, True, False, False] p = (eph['earth'] + s).at(t).observe(eph['sun']).apparent() assert list(p.is_behind_earth()) == expected def test_is_another_satellite_behind_earth(): # See if the method works with a pure geometric difference. ts = api.load.timescale() t = ts.utc(2018, 7, 3, 0, range(0, 60, 10)) s = EarthSatellite(line1, line2) # The "other satellite" is fictitious: the ISS offset by one day. s2 = EarthSatellite(line1.replace('184.80969102', '185.80969102'), line2) expected = [True, True, True, True, True, True] p = (s - s2).at(t) assert list(p.is_behind_earth()) == expected def test_behind_earth_thoroughly(): class FakeSat(VectorFunction): center = 399 target = None zero = array([0,0,0]) def __init__(self, r): self.r = array(r) def _at(self, t): return self.r, self.zero, None, None ts = api.load.timescale() t = ts.utc(2023, 4, 8, 1, 25) # Earth's equatorial radius is around 6378 km. sats = [ FakeSat([-9e5 / AU_KM, 0, 0]), # far left of Earth FakeSat([-8e5 / AU_KM, 0, 0]), # left of Earth FakeSat([0, 0, 0]), # center of Earth FakeSat([8e5 / AU_KM, 0, 0]), # right of Earth FakeSat([9e5 / AU_KM, 0, 0]), # farther right of Earth ] verdicts = [ (s2 - s1).at(t).is_behind_earth() for s1 in sats for s2 in sats if s2 is not s1 ] assert verdicts == [ False, True, True, True, # First two fake sats can see each other. False, True, True, True, True, True, True, True, True, True, True, False, True, True, True, False, # Last two fake sats can see each other. ]