Prevent satellite find_events() from exiting early

The discrete finder, as it narrowed in on N events, was watching only
how tightly it was bracketing the first event, on the assumption that
they were all bracketed by roughly equal intervals.  But for satellite
find_events(), this is not the case: their brackets are not the same
size, so all intervals need watching.  Fixes #1000.

Author: brandon-rhodes

CHANGELOG.rst

@@ -30,12 +30,19 @@ Next version
 
   So Skyfield now encourages code to ask for ``position.xyz`` instead.
   An advantage is that the new name is self-documenting: the name
-  reminds the user that it is a 3-vector with Cartesian components.
+  reminds the user that it is a 3-vector of Cartesian components.
 
 * Fix: the :meth:`~skyfield.sgp4lib.EarthSatellite.find_events()` Earth
   satellite method was returning an empty list of events if the only
-  event in the time period was a sole rising or setting.  It should now
-  find them successfully.
+  event in the time period was a lone rising or setting.  It should now
+  detect and return them.
+  `#996 <https://github.com/skyfielders/python-skyfield/issues/996>`_
+
+* Fix: the :meth:`~skyfield.sgp4lib.EarthSatellite.find_events()` Earth
+  satellite method, faced with a single pass that was very close to the
+  start time, was returning an inaccurate setting time.  It should now
+  return an accurate setting time.
+  `#1000 <https://github.com/skyfielders/python-skyfield/issues/1000>`_
 
 * Fix: bodies with Kepler orbits (like comets and asteroids) were
   incorrectly returning positions with only a single dimension if given

skyfield/searchlib.py

@@ -65,10 +65,7 @@ def _find_discrete(ts, jd, f, epsilon, num):
         starts = jd[indices]
         ends = jd[indices + 1]
 
-        # Since we start with equal intervals, they all should fall
-        # below epsilon at around the same time; so for efficiency we
-        # only test the first pair.
-        if ends[0] - starts[0] <= epsilon:
+        if (ends - starts).max() <= epsilon:
             y = y[indices + 1]
             # Keep only the last of several zero crossings that might
             # possibly be separated by less than epsilon.

skyfield/tests/test_satellite_events.py

@@ -141,3 +141,21 @@ def run_sat(name, line1, line2, number_events_expected):
         '2 41105   5.0153  78.6193 0002491 153.4123  31.4253  1.00270890 31881',
         1,
     )
+
+def test_earth_satellite_pass_very_close_to_start_time():
+    ts = load.timescale()
+    t0 = ts.utc(2024, 9, 5)
+    t1 = ts.utc(2024, 9, 6)
+    observer = wgs84.latlon(+48.6622, +34.8862, 0)
+    satellite = EarthSatellite(
+        '1 38707U 12039A   24247.82317651  .00138984  00000-0  16635-2 0  9998',
+        '2 38707  97.4945 189.8924 0007050 108.0286 252.1739 15.60479551673427',
+        'KANOPUS', ts,
+    )
+    t, y = satellite.find_events(observer, t0, t1, 70.0)
+    assert list(y) == [0, 1, 2]
+    assert t.utc_strftime() == [
+        '2024-09-05 00:00:32 UTC',
+        '2024-09-05 00:00:50 UTC',
+        '2024-09-05 00:01:08 UTC',  # was 00:02:56 before bug was fixed
+    ]