SPACETRC / ASTRONOMY INSTRUMENTS LAB
Measure an angle.
Calculate the sky.
Explore altitude and shadow geometry together. Change latitude, declination and hour angle; compare the drawing with the numerical calculation.
φ / δ / H
Change the measurement.
See the geometry.
Initial model: latitude 41°, declination 20°, meridian transit H = 0°.
- Altitude a
- Horizon status
- Hour angle from meridian
- Ideal horizontal shadow length
H / 15 expresses the angle in hours; it is not a time zone or wristwatch reading.
Inspect the calculation
sin a = sin φ · sin δ + cos φ · cos δ · cos H
- Degree inputs are converted to radians.
- The right-hand side is evaluated and clamped to [−1, 1] against rounding error.
- The inverse sine is evaluated and converted back to degrees.
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Shadow model: L = h / tan a. It applies for 0° < a ≤ 90°, assuming flat horizontal ground and a vertical gnomon. No finite shadow is calculated at the horizon.
The model omits atmospheric refraction, parallax, terrain, body radius and instrument error. The drawing shows altitude relative to the horizon; it does not show azimuth.
Move from drawing to measurement.
Meridian experiment
Set H = 0°. Record how altitude changes as the difference between latitude and declination changes.
The horizon boundary
Increase the hour angle. When does the result fall below zero? Why is the shadow model not used for negative altitude?
Read a historical instrument
Look for an angle scale, sighting line and pivot in an astrolabe drawing. Explain which details this educational diagram leaves out.
Calculation source: U.S. Naval Observatory · Altitude and azimuth ↗