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