Course / Checking the compass by the Sun

Part II · First sights · Page 1 of 3

Where the Sun rises

The Sun rises due east and sets due west only at the equinoxes. The rest of the year it rises north or south of east by its amplitude, which depends on its declination and your latitude. Since the amplitude can be worked out, the rising or setting Sun gives a true bearing to check the compass against.

Predict In June (declination 23° N), where does the Sun rise at 50° N?

NESWrises 061°sets 299°A = 28.9°A = 28.9°
Your horizon from above, north up. The amplitude is measured from east or west toward the pole of the Sun's declination.
Amplitude: sin A = sin dec ÷ cos lat
28.9° N
Sun rises at
061°
Sun sets at
299°

The higher the latitude, the further north of east and west the Sun rises and sets.

sin amplitude = sin declination ÷ cos latitude

Take the bearing when the Sun's lower limb is about half a diameter above the horizon: then its center is on the true (celestial) horizon, which is what the formula assumes.