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Hello,
Latitude and declination are closely related. In fact, in some sense,
declination is latitude on the sky. For example, if your latitude is
40 degrees, then stars at declination=40 degrees will pass straight
overhead (or through the zenith) at your location (of course, any
given star will only be straight overhead momentarily; because the
Earth is rotating, the stars appear to drift from East to West
across the sky).
If you moved to a different latitude on the Earth, the same star would
not pass through the zenith. For example, if you moved 10 degrees
South (to latitude=30 degrees), the star would be 10 degrees south of
your zenith at the highest point of its track across the sky.
Does that make sense? Good. The next step is to actually determine the
range of latitudes from which this star can be seen more than 20
degrees off of the horizon. Well, 20 degrees off the horizon is the
same as (90-20) = 70 degrees away from the zenith. So, if you moved
70 degrees north or south from the original location, the star will
just barely be 20 degrees above the horizon at the highest point of
its orbit. 40 degrees N - 70 degrees = -30 degrees, or 30 degrees
South (roughly the latitude of northern Chile). Any further South
than that, and you will never see this star above an altitude of 20
degrees. Further south than -50 degrees, and you'll never see this
star at all!
But wait, what about moving the other way? 40 degrees N + 70 degrees
degrees North, and you can't go further North than that! There is no
rational solution in this case, because no matter how far North you
go, stars at +40 degrees declination will always be more than 20
degrees above your horizon at some point in their track across the
sky. In fact, if you were at the north pole, this star would always
be 50 degrees above the horizon; from there the stars circle the sky
at constant altitude, never rising or setting!
The second part of the question, regarding the range of dates that the
star could be observed, is more tricky. The other celestial
coordinate (right ascension) is analogous to longitude on the Earth.
However, because the Earth is rotating and the sky is not, the two
coordinates cannot easily be tied together like declination and
latitude can, because at any position on the Earth, while your
longitude remains constant, the apparent drift of the sky means that
you will see stars with different right ascension at different times.
For example, let's say we are again at 40 degrees North latitude,
observing the same star while it is at our zenith. Let's say we are
at longitude 100 degrees West, and it is midnight. If we wait an
hour, the rotation of the Earth makes the star appear to drift, and
we'll see it roughly 15 degrees West of the zenith (the Earth rotates
once (360 degrees) in 1 day (24 hours). 360 degrees/24 hours is 15
degrees per hour).
So, in a way, the stars and the sky are like a big clock, because
their east-west position in the sky is intimitely connected to the
rotation of the Earth. In fact, we base our entire system of time
measurement on the apparent drift of a particular star in the sky: the
Sun. There's an additional complication, however: The Sun doesn't
drift across the sky like the rest of the stars. Since we are in
orbit around the Sun, the direction of the Sun with respect to all the
other stars changes over the course of a year. Thus, "normal" time,
which is Sun-based time, is slightly different that sidereal time,
which is time based on the stars. This means that while our star was
at the zenith at midnight today, the same star will reach the zenith
about 4 minutes before midnight tomorrow. This is because our clock
time is connected to the position of the sun, which appears to be
slowly drifting past the other stars (again, due to our orbital motion
around the Sun). Whew! The combination of Earth's rotation and
orbital motion is sure making this complicated! But, you can try to
picture these motions in your mind, and then tie them to what you see in
the sky, and it all becomes a beautiful celestial dance.
I still haven't specifically addressed the second question, however.
How do you get a range of dates that a star can be observed from a
certain location on the Earth above altitude=20 degrees in the sky,
if you only know its right ascension? There are the additional
constraints that both the Sun and the moon need to be below the
horizon. I have explained the connection of right ascension to both
longitude and time, but I have not shown how to plug in the numbers
and get an answer. The equation that we need is called "the equation
of time", and it's complicated. It basically says the same things
I've already explained, but in the language of mathematics. Since
this answer is quickly becoming an entire college course on astronomy,
I am going to bow out short of answering the question numerically.
If you really need to know the answer, there are a number of things
you can do. First, you can look up the right ascension of the zenith
for any location, at any time on any date in a book called the
Astronomical Almanac (actually, they publish only the right ascension
of the zenith for longitude=0 degrees, but it's easy to add your
longitude). Second, you can look in one of the fine amateur astronomy
magazines (Astronomy or Sky and Telescope are the most popular), which
show monthly sky charts, so you can see at a glance what is going to
be up. If you collect 12 monthly magazines, you will be able to see
what the stars will look like at any time over the year (although the
planet positions will be wrong if the magazines are not from the
current year). Third, you can get computer software that will show
you the sky at any time, from anywhere on the Earth. Skyglobe is
nice, and it's shareware (by the way, when professional astronomers
plan observing runs, they typically use one of these three methods rather
than using the equation of time directly). Finally, you can go to your
local library or bookstore and read all about celestial coordinates
and the equation of time.
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