Since refraction affects zenith angle, it changes both the Right Ascension and declination of an object. It also affects the time the object appears to rise and set.
The standard formula for the altitude of an object is:
If a = 0° (the object is on horizon), then we have:
This gives the semi-diurnal arc H:
the time between the object crossing the horizon, and crossing the meridian.
Knowing the Right Ascension of the object, and its semi-diurnal arc, we can find the Local Sidereal Time of meridian transit, and hence calculate its rising and setting times.
However, refraction means that this simplified formula cannot be used, since the altitude should be, not 0°, but -0°34'. This is not too important for stars, which are rarely observed close to the horizon. But it makes an important difference in calculating the times of rising and setting of the Sun.
Furthermore, "sunrise" and "sunset" generally refer to the moment when the top of the Sun's disc is just on the horizon. So we must also allow for the semi-diameter of the Sun's disc, which is 16 arc-minutes.
So sunrise and sunset actually occur when the Sun has altitude -0°50' (34' for refraction, and another 16' for the semi-diameter of the disc).
Since the atmosphere scatters sunlight, the sky does not become dark instantly at sunset; there is a period of twilight.
During civil twilight, it is still light enough
to carry on ordinary activities out-of-doors;
this continues until the Sun's altitude is -6°.
During nautical twilight, it is dark enough to see the brighter
stars, but still light enough to see the horizon, enabling sailors to measure
stellar altitudes for navigation;
this continues until the Sun's altitude is -12°.
During astronomical twilight, the sky is still too light for making
reliable astronomical observations;
this continues until the Sun's altitude is -18°.
Once the Sun is more than 18° below the horizon, we have astronomical
darkness.
The same pattern of twilights repeats, in reverse, before sunrise.
In summer, astronomical twilight will last all night, for any place with latitude above 49°.
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