diff --git a/skyfield/sgp4lib.py b/skyfield/sgp4lib.py
index fd2d3fc..cc76bcc 100644
--- a/skyfield/sgp4lib.py
+++ b/skyfield/sgp4lib.py
@@ -263,8 +263,6 @@ class EarthSatellite(VectorFunction):
         i = jd.argsort()
         return ts.tt_jd(jd[i]), v[i]
 
-_second = 1.0 / (24.0 * 60.0 * 60.0)
-
 def theta_GMST1982(jd_ut1):
     """Return the angle of Greenwich Mean Standard Time 1982 given the JD.
 
@@ -278,8 +276,8 @@ def theta_GMST1982(jd_ut1):
     t = (jd_ut1 - T0) / 36525.0
     g = 67310.54841 + (8640184.812866 + (0.093104 + (-6.2e-6) * t) * t) * t
     dg = 8640184.812866 + (0.093104 * 2.0 + (-6.2e-6 * 3.0) * t) * t
-    theta = (jd_ut1 % 1.0 + g * _second % 1.0) * tau
-    theta_dot = (1.0 + dg * _second / 36525.0) * tau
+    theta = (jd_ut1 % 1.0 + g / DAY_S % 1.0) % 1.0 * tau
+    theta_dot = (1.0 + dg / (DAY_S * 36525.0)) * tau
     return theta, theta_dot
 
 _zero_zero_minus_one = array((0.0, 0.0, -1.0))
diff --git a/skyfield/tests/test_earth_satellites.py b/skyfield/tests/test_earth_satellites.py
index fbb0524..54b6651 100644
--- a/skyfield/tests/test_earth_satellites.py
+++ b/skyfield/tests/test_earth_satellites.py
@@ -5,6 +5,7 @@ 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
+from skyfield.timelib import julian_date
 
 iss_tle0 = """\
 1 25544U 98067A   18184.80969102  .00001614  00000-0  31745-4 0  9993
@@ -63,7 +64,7 @@ from ..constants import DEG2RAD
 
 arcminute = DEG2RAD / 60.0
 arcsecond = arcminute / 60.0
-second = 1.0 / (24.0 * 60.0 * 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
@@ -76,25 +77,28 @@ def test_appendix_c_conversion_from_TEME_to_ITRF():
     vTEME = array([-4.746131487, 0.785818041, 5.531931288])
     vTEME = vTEME * 24.0 * 60.0 * 60.0  # km/s to km/day
 
-    ts = api.load.timescale()
-    jd_ut1 = ts.tt(2004, 4, 6, 7, 51, 28.386 - 0.439961).tt
+    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)
 
-    meter = 1e-3
+    epsilon = 5e-8  # Why not 1e-8, which would match all of their digits?
 
-    assert abs(-1033.47938300 - rITRF[0]) < 0.1 * meter
-    assert abs(+7901.29527540 - rITRF[1]) < 0.1 * meter
-    assert abs(+6380.35659580 - rITRF[2]) < 0.1 * meter
+    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 * second
+    vITRF_per_second = vITRF / seconds_per_day
 
-    assert abs(-3.225636520 - vITRF_per_second[0]) < 1e-4 * meter
-    assert abs(-2.872451450 - vITRF_per_second[1]) < 1e-4 * meter
-    assert abs(+5.531924446 - vITRF_per_second[2]) < 1e-4 * meter
+    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():
     ts = api.load.timescale(builtin=True)