feat: add Besselian year calculation

doc/source/_assets/timescale-refs.bib

@@ -15,6 +15,20 @@ @book{Dershowitz:2007cc
 publisher = {Cambridge University Press},
 edition = {3},
 }
+@article{Desai:2015jr,
+author = {Desai, S and Wahr, J and Beckley, B},
+title = {{Revisiting the pole tide for and from satellite altimetry}},
+journal = {Journal of Geodesy},
+year = {2015},
+month = dec,
+volume = {89},
+number = {12},
+issn = {0949-7714},
+url = {https://doi.org/10.1007/s00190-015-0848-7},
+doi = {10.1007/s00190-015-0848-7},
+pages = {1233--1243},
+publisher = {Springer Science and Business Media LLC},
+}
 @article{Fairhead:1990vz,
 author = {Fairhead, L and Bretagnon, P},
 title = {{An analytical formula for the time transformation TB-TT}},
@@ -49,6 +63,19 @@ @techreport{Kaplan:2005kj
 institution = {US Naval Observatory},
 pages = {116},
 }
+@article{Lieske:1979wv,
+author = {Lieske, J H},
+title = {{Precession matrix based on IAU (1976) system of astronomical constants}},
+journal = {Astronomy and Astrophysics},
+year = {1979},
+month = mar,
+volume = {73},
+number = {3},
+url = {https://ui.adsabs.harvard.edu/abs/1979A&A....73..282L},
+key = {1979A&A....73..282L},
+pages = {282--284},
+note = {Provided by the SAO/NASA Astrophysics Data System},
+}
 @book{Meeus:1991vh,
 author = {Meeus, J H},
 title = {{Astronomical Algorithms}},

test/test_time.py

@@ -245,6 +245,27 @@ def test_sidereal():
     expected = 20.96154017401333
     assert np.isclose(expected, 24.0*ts.st).all()
 
+def test_besselian():
+    """Test that the Besselian year matches expected outputs
+    """
+    # Besselian years
+    B = np.array([1900.0, 1950.0, 2000.0])
+    # create timescale from Besselian year
+    ts = timescale.from_besselian(B)
+    # expected Julian date for Besselian year 1900
+    # from table 1 of Lieske (1979)
+    expected = np.array([2415020.31352, 2433282.42345905, 2451544.5333981])
+    assert np.isclose(expected, ts.utc).all()
+    # check Besselian year
+    assert np.isclose(ts.B, B).all()
+    # check inverse conversions
+    JD = np.array([2415020.0, 2433282.5, 2451545.0])
+    ts = timescale.from_julian(JD)
+    # check Besselian year from Julian date
+    # from table 1 of Lieske (1979)
+    expected = np.array([1899.999142, 1950.00021, 2000.001278])
+    assert np.isclose(expected, ts.B).all()
+
 def test_epochs():
     """Test that the epoch conversions match expected outputs
     """

timescale/__init__.py

@@ -20,6 +20,13 @@ def from_deltatime(*args, **kwargs):
 # Julian dates
 def from_julian(ut1, **kwargs):
     return timescale.time.Timescale(ut1 - 2400000.5)
+# Besselian years
+def from_besselian(B, **kwargs):
+    """Wrapper for creating a ``Timescale`` object from Besselian years
+    """
+    # convert Besselian year to MJD
+    MJD = 15019.81352 + (B - 1900.0) * 365.242198781
+    return timescale.time.Timescale(MJD)
 # calendar dates
 def from_calendar(*args, **kwargs):
     """Wrapper for ``timescale.time.Timescale().from_calendar``

timescale/time.py

@@ -17,6 +17,7 @@
 
 UPDATE HISTORY:
     Updated 07/2025: verify Bulletin-A entries are not already in merged file
+        add Besselian year conversion to Timescale class
     Updated 03/2025: added attributes for ut1_utc and gps_utc
     Updated 02/2025: added GLONASS as delta time option
         update GPS seconds calculation for output from timescale object
@@ -1073,13 +1074,28 @@ def T(self):
         """
         _jd_j2000 = _jd_mjd + _mjd_j2000
         return (self.tt - _jd_j2000)/self.century
+
+    @timescale.utilities.reify
+    def B(self):
+        """Time in Besselian years :cite:p:`Lieske:1979wv`
+        """
+        return 1900.0 + (self.MJD - 15019.81352) / 365.242198781
 
     @timescale.utilities.reify
     def ut1(self):
         """Universal Time (UT) as Julian Days
         """
         # convert UT1-UTC to days
         return self.utc + self.ut1_utc/self.day
+
+    @timescale.utilities.reify
+    def ut2(self):
+        """UT0 corrected for polar motion and seasonal variation
+        """
+        theta = 2.0*np.pi*self.B
+        ut2_ut1 = 0.022*np.sin(theta) - 0.012*np.cos(theta) - \
+            0.006*np.sin(2.0*theta) + 0.007*np.cos(2.0*theta)
+        return self.ut1 + ut2_ut1
 
     @timescale.utilities.reify
     def utc(self):