Calculates leap seconds for an instant (#54)

To know the difference between universal time (UT) and dynamical time
(TD), we need to be aware of the leap seconds to take into account.

This supports leap seconds from 1800-01-01 to 2024-01-01 (with the most
recent leap second being added on 2017-01-01).

lib/astronoby/util/time.rb

@@ -21,6 +21,62 @@ def self.decimal_hour_to_time(date, decimal)
 
         ::Time.utc(date.year, date.month, date.day, hour, minute, second).round
       end
+
+      # @param instant [Numeric, Time, Date, DateTime]
+      # @return [Integer, Float] Number of leap seconds for the given instant
+      def self.terrestrial_universal_time_delta(instant)
+        # Source:
+        #  Title: Astronomical Algorithms
+        #  Author: Jean Meeus
+        #  Edition: 2nd edition
+        #  Chapter: 10 - Dynamical Time and Universal Time
+
+        jd = case instant
+        when Numeric
+          instant
+        when ::Time, ::Date, ::DateTime
+          Epoch.from_time(instant)
+        else
+          raise IncompatibleArgumentsError,
+            "Expected a Numeric, Time, Date or DateTime object, got #{instant.class}"
+        end
+
+        return 69 if jd >= 2457754.5
+        return 68 if jd >= 2457204.5
+        return 67 if jd >= 2456109.5
+        return 66 if jd >= 2454832.5
+        return 65 if jd >= 2453736.5
+        return 64 if jd >= 2451179.5
+        return 63 if jd >= 2450814.5
+
+        theta = ((jd - Epoch::J1900) / 365.25) / 100.0
+        if (2415020.5...2450814.5).cover?(jd) # 1900 - 1997
+          return -2.44 +
+              87.24 * theta +
+              815.20 * theta**2 -
+              2_637.80 * theta**3 -
+              18_756.33 * theta**4 +
+              124_906.15 * theta**5 -
+              303_191.19 * theta**6 +
+              372_919.88 * theta**7 -
+              232_424.66 * theta**8 +
+              58_353.42 * theta**9
+        elsif (2378496.5...2415020.5).cover?(jd) # 1800 - 1899
+          return -2.5 +
+              228.95 * theta +
+              5_218.61 * theta**2 +
+              56_282.84 * theta**3 +
+              324_011.78 * theta**4 +
+              1_061_660.75 * theta**5 +
+              2_087_298.89 * theta**6 +
+              2_513_807.78 * theta**7 +
+              1_818_961.41 * theta**8 +
+              727_058.63 * theta**9 +
+              123_563.95 * theta**10
+        end
+
+        0.0
+      end
     end
   end
 end

spec/astronoby/util/time_spec.rb

@@ -28,4 +28,40 @@
       end
     end
   end
+
+  describe "::terrestrial_universal_time_delta" do
+    it "returns the number of seconds between TT and UT for a given Julian Day" do
+      epoch = 2437665.5 # 1962-01-01T00:00:00
+
+      delta = described_class.terrestrial_universal_time_delta(epoch).round(2)
+
+      expect(delta).to eq 34.56
+    end
+
+    it "returns the number of seconds between TT and UT for a given Time object" do
+      time = Time.utc(1977, 1, 1) # 2443144.5
+
+      delta = described_class.terrestrial_universal_time_delta(time).round(2)
+
+      expect(delta).to eq 46.98
+    end
+
+    it "returns the number of seconds between TT and UT for a given Date object" do
+      date = Date.new(1980, 1, 1) # 2444239.5
+
+      delta = described_class.terrestrial_universal_time_delta(date).round(2)
+
+      expect(delta).to eq 50.07
+    end
+
+    context "when the Julian Day is out of range" do
+      it "returns 0" do
+        date = Date.new(1700, 1, 1) # 2341972.5
+
+        delta = described_class.terrestrial_universal_time_delta(date)
+
+        expect(delta).to eq 0
+      end
+    end
+  end
 end