Your local sky

Altitude and azimuth

Goal: understand the transformation from sky coordinates to your coordinates.

Two coordinate systems

Equatorial: right ascension and declination. Fixed to the stars, the same for everyone on Earth. This is what sun.position() and moon.position() return.

Horizontal: altitude and azimuth. Angle above your horizon, and compass bearing. Depends on where you are and what time it is.

Every "where do I look?" question is a conversion from the first to the second.

The hour angle

The bridge is local sidereal time, how far the sky has turned at your longitude:

hour_angle = local_sidereal_time - right_ascension

Hour angle is zero when the object is on your meridian, due south or north and at its highest. Negative before, positive after. It effectively is a clock running on star time.

Then two spherical-trigonometry formulae:

sin(altitude) = sin(lat)·sin(dec) + cos(lat)·cos(dec)·cos(H)

tan(azimuth) = sin(H) / (cos(H)·sin(lat) − tan(dec)·cos(lat))

That is the whole conversion. Everything else (refraction, parallax) is a correction on top.

Refraction

Air bends light, lifting objects slightly. It is negligible overhead and about 0.57° at the horizon, larger than the Sun itself.

The consequence: when you see the Sun touching the horizon, it is geometrically already fully below it. Every sunrise you have ever watched, you were looking at something that had not happened yet.

Moonfield defines sunrise at a geometric altitude of −0.833°: −0.567° for refraction, −0.267° for the Sun's radius, since sunrise means the upper limb.

Run

moonfield now
moonfield frame --facing SE

Checkpoint

• I can name both coordinate systems and say what each is fixed to
• I know what hour angle means and when it is zero
• I know refraction is ~0.57° at the horizon
• I can explain why a "setting" Sun has already set

Next: Why your latitude matters.