{Note: If your browser does not distinguish
between "a,b" and "α, β" (the Greek letters
"alpha, beta")
then I am afraid you will not be able to make much sense of the
equations on this page.}
Since refraction affects zenith angle, The standard formula for the altitude of an object
is: If a = 0° (the object is on horizon, either
rising or setting), This gives the semi-diurnal arc H: Knowing the Right Ascension of the object, and its
semi-diurnal arc, However, refraction means that this simplified
formula is not accurate, Furthermore, "sunrise" and "sunset"
generally refer to the moment So sunrise and sunset actually occur when the Sun has
altitude -0°50' Since the atmosphere scatters sunlight, the sky does
not become dark instantly at sunset; In summer, astronomical twilight will last all night,
for any place with latitude above 48.6°. Exercise: The Sun is at declination -14°.
If the Sun is on the local
meridian at 12:03, And when will astronomical
twilight start and finish? Click here
for the answer. Previous section:
Refraction
it
generally changes both the Right Ascension and declination of an
object.
It also affects the time the object appears to rise and
set.
sin(α) = sin(δ)sin(φ) + cos(δ) cos(φ)
cos(H)
then this equation becomes:
cos(H) = -
tan(φ) tan(δ)
the
time between the object crossing the horizon, and crossing the
meridian.
we can find the Local Sidereal Time of meridian
transit,
and hence calculate its rising and setting times.
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.
when the top of the Sun's
disc is just on the horizon.
The formula would give us the time of
rising or setting
for the centre of the Sun's disc.
So
we must also allow for the semi-diameter of the Sun's disc,
which is 16 arc-minutes.
(34' for refraction, and another 16' for the
semi-diameter of the disc).
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.
What will be its hour angle at sunrise
(the moment the top
edge of the Sun first appears over the horizon),
at a latitude of
+56°20'?
what time is sunrise?
and what time is
sunset?
Next section: Geocentric parallax
Return to index