@@ -96,6 +96,8 @@ API Changes
 
 - ``astropy.time``
 
+  - Correct use of UT in TDB calculation [#1938, #1939].
+
 - ``astropy.units``
 
   - ``Quantity`` now converts input to float by default, as this is
 
@@ -810,12 +810,13 @@ def _get_delta_tdb_tt(self, jd1=None, jd2=None):
                     jd2 = self._time.jd2
 
             # First go from the current input time (which is either
-            # TDB or TT) to an approximate UTC.  Since TT and TDB are
-            # pretty close (few msec?), assume TT.
+            # TDB or TT) to an approximate UT1.  Since TT and TDB are
+            # pretty close (few msec?), assume TT.  Similarly, since the
+            # UT1 terms are very small, use UTC instead of UT1.
             njd1, njd2 = erfa_time.tt_tai(jd1, jd2)
             njd1, njd2 = erfa_time.tai_utc(njd1, njd2)
-            # TODO: actually need to go to UT1 which needs DUT.
-            ut = njd1 + njd2
+            # subtract 0.5, so UT is fraction of the day from midnight
+            ut = day_frac(njd1 - 0.5, njd2)[1]
 
             # Compute geodetic params needed for d_tdb_tt()
             elon = 0. if self.lon is None else self.lon.to(u.radian).value
 
@@ -168,8 +168,8 @@ def test_transforms(self):
         assert t.tai.iso == '2006-01-15 21:25:10.500000'
         assert t.tt.iso == '2006-01-15 21:25:42.684000'
         assert t.tcg.iso == '2006-01-15 21:25:43.322690'
-        assert t.tdb.iso == '2006-01-15 21:25:42.684372'
-        assert t.tcb.iso == '2006-01-15 21:25:56.893951'
+        assert t.tdb.iso == '2006-01-15 21:25:42.684373'
+        assert t.tcb.iso == '2006-01-15 21:25:56.893952'
 
     def test_creating_all_formats(self):
         """Create a time object using each defined format"""
 
@@ -572,9 +572,9 @@ TT, UT1, UTC).  This requires auxilliary information (latitude and longitude).
   >>> t.tcg.iso
   '2006-01-15 21:25:43.322690'
   >>> t.tdb.iso
-  '2006-01-15 21:25:42.684372'
+  '2006-01-15 21:25:42.684373'
   >>> t.tcb.iso
-  '2006-01-15 21:25:56.893951'
+  '2006-01-15 21:25:56.893952'
 
 Sidereal Time
 -------------