diff --git a/skyfield/sgp4lib.py b/skyfield/sgp4lib.py
index 8957ab5b..2f152cf0 100644
--- a/skyfield/sgp4lib.py
+++ b/skyfield/sgp4lib.py
@@ -103,7 +103,9 @@ def __init__(self, line1, line2, name=None, ts=None):
         else:
             year = two_digit_year + 1900
 
-        self.epoch = ts.utc(year, 1, satrec.epochdays)
+        whole_days = int(satrec.epochdays)
+        seconds = (satrec.epochdays - whole_days) * DAY_S
+        self.epoch = ts.utc(year, 1, whole_days, 0, 0, seconds)
 
         self._setup(satrec)
 
@@ -131,8 +133,8 @@ def from_satrec(cls, satrec, ts):
         # be unified to always use epochyr and epochdays.
         whole, fraction = divmod(satrec.jdsatepoch, 1.0)
         year, month, day = compute_calendar_date(whole)
-        day += 0.5  # convert integer Julian day into Julian date float
-        self.epoch = ts.utc(year, month, day + fraction + satrec.jdsatepochF)
+        seconds = (0.5 + fraction + satrec.jdsatepochF) * DAY_S
+        self.epoch = ts.utc(year, month, day, 0, 0, seconds)
 
         self._setup(satrec)
         return self
diff --git a/skyfield/tests/test_earth_satellites.py b/skyfield/tests/test_earth_satellites.py
index c23c2d8a..2b1478c1 100644
--- a/skyfield/tests/test_earth_satellites.py
+++ b/skyfield/tests/test_earth_satellites.py
@@ -207,3 +207,20 @@ def _at(self, t):
         True, True, True, False,
         True, True, True, False,  # Last two fake sats can see each other.
     ]
+
+def test_tle_epoch_matches_sgp4_library():
+    from numpy import asarray
+    from sgp4.api import Satrec
+    from skyfield.constants import DAY_S
+    line1 = '1 55910U 23035C   23076.01808579 -.00000195  00000-0  00000+0 0  9994'
+    line2 = '2 55910  44.0037 312.8770 0004210 247.2472 260.1626 14.90311335    06'
+    ts = api.load.timescale(builtin=True)
+    satrec = Satrec.twoline2rv(line1, line2)
+    sat = EarthSatellite(line1, line2, ts=ts)
+    fraction = sat.epoch.tai_fraction - sat.epoch._leap_seconds() / DAY_S
+    offset_s = ((sat.epoch.whole - satrec.jdsatepoch)
+                + (fraction - satrec.jdsatepochF)) * DAY_S
+    assert abs(offset_s) < 1e-9
+    _, r_library, _ = satrec.sgp4(satrec.jdsatepoch, satrec.jdsatepochF)
+    r_epoch, _, _ = sat._position_and_velocity_TEME_km(sat.epoch)
+    assert abs(asarray(r_epoch) - r_library).max() < 1e-12