Merge pull request #7530 from ayshih/small_tilt

Fixed an inaccuracy in the HME<->HEE transformation

changelog/7530.bugfix.rst

@@ -0,0 +1 @@
+Fixed an inaccuracy in the implementation of `~sunpy.coordinates.HeliocentricEarthEcliptic` and `~sunpy.coordinates.GeocentricSolarEcliptic` such that the Earth was not exactly in the XY plane, but rather had an error of up ~10 meters.

sunpy/coordinates/_transformations.py

@@ -589,7 +589,8 @@ def _rotation_matrix_reprs_to_reprs(start_representation, end_representation):
     A = start_representation.to_cartesian()
     B = end_representation.to_cartesian()
     rotation_axis = A.cross(B)
-    rotation_angle = -np.arccos(A.dot(B) / (A.norm() * B.norm()))  # negation is required
+    # Calculate the angle using both cross and dot products to minimize numerical-precision issues
+    rotation_angle = -np.arctan2(rotation_axis.norm(), A.dot(B))  # negation is required
 
     if rotation_angle.isscalar:
         # This line works around some input/output quirks of Astropy's rotation_matrix()

sunpy/coordinates/tests/test_transformations.py

@@ -695,6 +695,13 @@ def test_hme_hee_sunspice():
     assert_quantity_allclose(new.distance, old.distance)
 
 
+def test_hee_earth():
+    # The Earth in HEE should have negligible Z component
+    times = parse_time('2013-08-10 12:00') + np.arange(10) * u.s
+    earth_hee = get_earth(times).heliocentricearthecliptic
+    assert_quantity_allclose(0*u.m, earth_hee.cartesian.z, atol=1e-4*u.m)
+
+
 def test_hee_hee():
     # Test HEE loopback transformation
     obstime = Time('2001-01-01')