7/24/2019 Terbit, Tenggelam Dan Twilight

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BAB 13

SUNRISE, SUNSET AND TWILIGHT

Since refraction affects zenith angle, it changes both the Right Ascension and declination of anobject. It also affects the time the object appears to rise and set.

The standard formula for the altitude of an object is:

( ) ( ) ( ) ( ) ( ) ( )Hcoscoscossinsinsin +=

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 -034'. This is not too important for stars, which are rarely observed close to thehorizon. But it makes an important difference in calculating the times of rising and setting of theSun.

Furthermore, "sunrise" and "sunset" generally refer to the moment when the top of the Sun's disc isjust 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 -050' (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 aperiod of twilight.

During civil twilight, it is still light enough to carry on ordinary activities out-of-doors; this continuesuntil the Sun's altitude is -6.During nautical twilight, it is dark enough to see the brighter stars, but still light enough to see thehorizon, enabling sailors to measure stellar altitudes for navigation; this continues until the Sun'saltitude 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.

7/24/2019 Terbit, Tenggelam Dan Twilight

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