diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 4ce8112..3e2c96c 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -3,6 +3,14 @@ Changelog
 
 .. currentmodule:: skyfield.positionlib
 
+1.24 — The future
+-----------------
+
+* Fix: improved the accuracy with which velocity is converted between
+  the Earth-fixed ITRF frame that rotates with the Earth and the
+  inertial GCRS frame that does not.  In particular, this should make
+  Earth satellite velocities more accurate.
+
 1.23 — 2020 July 9
 ------------------
 
diff --git a/skyfield/tests/test_positions.py b/skyfield/tests/test_positions.py
index a10650b..ab8cc54 100644
--- a/skyfield/tests/test_positions.py
+++ b/skyfield/tests/test_positions.py
@@ -1,8 +1,9 @@
 import numpy as np
-from skyfield import api, constants
+from skyfield import api
+from skyfield.constants import DAY_S
 from skyfield.earthlib import earth_rotation_angle
 from skyfield.functions import length_of
-from skyfield.positionlib import ICRF, _GIGAPARSEC_AU
+from skyfield.positionlib import ICRF, ITRF_to_GCRS2, _GIGAPARSEC_AU
 from skyfield.starlib import Star
 
 def test_subtraction():
@@ -89,15 +90,17 @@ def test_position_from_radec():
     p = api.position_from_radec(6, 0)
     assert length_of(p.position.au - [0, 1, 0]) < 1e-16
 
-def test_itrf_vector():
+def test_velocity_in_ITRF_to_GCRS2():
     ts = api.load.timescale(builtin=True)
-    t = ts.utc(2019, 11, 2, 3, 53)
-    top = api.Topos(latitude_degrees=45, longitude_degrees=0,
-                    elevation_m=constants.AU_M - constants.ERAD)
-    x, y, z = top.at(t).itrf_xyz().au
-    assert abs(x - 0.7071) < 1e-4
-    assert abs(y - 0.0) < 1e-14
-    assert abs(z - 0.7071) < 1e-4
+    t = ts.utc(2020, 7, 17, 8, 51, [0, 1])
+    r = np.array([(1, 0, 0), (1, 1.0 / DAY_S, 0)]).T
+    v = np.array([(0, 1, 0), (0, 1, 0)]).T
+    r, v = ITRF_to_GCRS2(t, r, v)
+    r0, r1 = r.T
+    v0 = v[:,0]
+    actual_velocity = r1 - r0
+    stated_velocity = v0 / DAY_S
+    assert length_of(actual_velocity - stated_velocity) < 4e-9
 
 # Test that the CIRS coordinate of the TIO is consistent with the Earth Rotation Angle
 # This is mostly an internal consistency check
diff --git a/skyfield/tests/test_topos.py b/skyfield/tests/test_topos.py
index 0c47237..90ab999 100644
--- a/skyfield/tests/test_topos.py
+++ b/skyfield/tests/test_topos.py
@@ -1,13 +1,40 @@
 from numpy import abs
 
-from skyfield.api import load
-from skyfield.toposlib import Topos
+from skyfield import constants
+from skyfield.api import Topos, load
+from skyfield.functions import length_of
 
 angle = (-15, 15, 35, 45)
 
 def ts():
     yield load.timescale()
 
+def test_velocity():
+    # It looks like this is a sweet spot for accuracy: presumably a
+    # short enough fraction of a second that the vector does not time to
+    # change direction much, but long enough that the direction does not
+    # get lost down in the noise.
+    factor = 300.0
+
+    ts = load.timescale(builtin=True)
+    t = ts.utc(2019, 11, 2, 3, 53, [0, 1.0 / factor])
+    jacob = Topos(latitude_degrees=36.7138, longitude_degrees=-112.2169)
+    p = jacob.at(t)
+    velocity1 = p.position.km[:,1] - p.position.km[:,0]
+    velocity2 = p.velocity.km_per_s[:,0]
+    print(length_of(velocity2 - factor * velocity1))
+    assert length_of(velocity2 - factor * velocity1) < 0.0007
+
+def test_itrf_vector():
+    ts = load.timescale(builtin=True)
+    t = ts.utc(2019, 11, 2, 3, 53)
+    top = Topos(latitude_degrees=45, longitude_degrees=0,
+                elevation_m=constants.AU_M - constants.ERAD)
+    x, y, z = top.at(t).itrf_xyz().au
+    assert abs(x - 0.7071) < 1e-4
+    assert abs(y - 0.0) < 1e-14
+    assert abs(z - 0.7071) < 1e-4
+
 def test_beneath(ts, angle):
     t = ts.utc(2018, 1, 19, 14, 37, 55)
     # An elevation of 0 is more difficult for the routine's accuracy