Phase 1 — The Initial Request
Given a location at latitude 40.65 degrees and longitude -75.27 degrees, can you create a table that for each day of the year gives the local time at which the azimuth of the sun is 259 degrees?
A quick exploration of the solar geometry, then code that uses the ephem library to compute sun position in 30-second steps for every day of 2026, scanning for azimuth crossings and interpolating to the exact moment.
observer.date = t.strftime('%Y/%m/%d %H:%M:%S')
sun = ephem.Sun(observer)
az = math.degrees(float(sun.az))
if prev_az < target_az <= az:
frac = (target_az - prev_az) / (az - prev_az)
exact_utc = prev_t + timedelta(seconds=30 * frac)
Key insight surfaced mid-computation: azimuth 259° is only reachable from late February through mid-October at this latitude — 136 winter days return N/A because the sun sets before swinging that far west.
Phase 2 — Iterative Refinement
Can you replace the N/A entries with the sunset times for each date?
Added a get_sunset() helper using ephem.Observer.next_setting(), then wove sunset times into the 136 N/A rows, colour-coded in warm amber so they're visually distinct from the azimuth-crossing rows.
I notice you left dashes for 4 dates for the enter/sunrise times; why is that?
Diagnosed the bug: on June 8, 9 and July 3, 4, sunrise azimuth is ~58.94° — just below 59° — so the code didn't flag it as "already past the target." But the actual crossing happens at alt≈0°, right at the horizon, which the −2° altitude guard clipped.
Fix: treat any sunrise azimuth within 1° of the target as a "sunrise" entry.
Phase 3 — The Real Use Case Emerges
The application is actually determining when the sun stops hitting windows facing southeast (169 degrees on the compass) so I can know when window shades can be opened.
The geometry clicked: 169° + 90° = 259°. Once the sun passes that azimuth, it's no longer shining through the window — the table already gives exactly the right answer, just with a newly understood meaning.
It would be useful to know when the sun becomes visible through the window in the morning, i.e., when the sun first reaches 59 degrees (169 − 90), or the sunrise time if the sun rises at an angle already greater than 59 degrees.
Added a morning scan column. In winter, sunrise is already past 59° so the window gets sun from the moment the sun rises. Around the summer solstice, the sun rises well to the northeast and only swings around to 59° later — on June 21 not until 5:39 AM EDT.
Phase 4 — Correction
I made a mistake — instead of 59 degrees, the azimuth for sun entry should be 79 degrees (169 − 90). Can you regenerate the spreadsheet using that value?
One-line change — TARGET_AZ_AM = 79.0 — and a full regeneration. On June 21 the sun now enters the window at 7:52 AM EDT instead of the earlier (wrong) time. All 365 rows clean, no dashes.
Phase 5 — Going Deeper
Can you come up with a mathematical function that will take as inputs a longitude, latitude and azimuth angle and output the local time when the sun will be at the specified azimuth?
Derived the closed-form solution using spherical trigonometry. The key relationships:
The ± in the quadratic gives two roots — morning and afternoon crossings. Solar declination δ and Equation of Time (EoT) are computed from day-of-year using Spencer (1971) Fourier series.
Phase 6 — Two Python Modules
Can you share the Python code that does this even more accurately?
Extracted and cleaned the ephem-based core into a standalone module with a clear public API:
find_azimuth_times(lat, lon, target_az, date)
→ list of {local_time, hour_angle, altitude_deg, period, tz_label}
azimuth_time(lat, lon, target_az, date, period='PM')
→ datetime | None
Accurate to a few arcseconds via VSOP87 planetary theory inside ephem. Timing errors well under a minute.
Can you create Python code which does the same thing but doesn't use the ephem library? Lower accuracy is OK.
Three bugs found and fixed during development of the stdlib-only version:
Bug 1 — Wrong quadratic coefficient signs (C was negated). Bug 2 — Wrong azimuth formula (sin/cos form instead of Meeus tan form). Bug 3 — Wrong longitude correction sign in the time conversion.
Final results vs. ephem reference:
2026-06-21 az=259° PM 4:00 PM EDT ← ephem: 4:00 PM EDT ✓ 2026-06-21 az= 79° AM 7:52 AM EDT ← ephem: 7:52 AM EDT ✓ 2026-03-15 az=259° PM 6:15 PM EDT ← ephem: 6:11 PM EDT (Δ4 min) 2026-10-13 az=259° PM 6:14 PM EDT ← ephem: 6:17 PM EDT (Δ3 min)