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Is there an equation which calculates how long the moon is visible on any given day/night at a given location, if we know where we are, which day it is and which phase of the moon it is?
Answer 1:

It is certainly possible to calculate (or at least estimate!) how long the moon is visible on any given day from a given location using an algorithm comprised of a series of calculations. However, I'm not actually sure whether or not that algorithm could be reduced to a single equation. Most calculations I have heard of use some amount of approximation, or even an iterative approach to finding the solution. There are many online calculators that can be used for these types of calculations. One of my favorite resources for astronomical information (besides www.nasa.gov) is from the U.S. Naval Observatory, and I'm sure they have more information on this topic there.

Answer 2:

Regarding your question about an equation for the time the moon is visible at any given day and location, as far as I know, there is no such equation. In astronomy, you usually work with a set of procedures to find answers to questions like yours. First you would need to know the declination and right ascension (RA), in this case, of the Moon. These are like latitude and longitude for a place on earth. In fact, the declination of the body is the latitude of that point on earth for which the celestial body in question is at its zenith, i.e. straight overhead. For the longitude of said place, you need to combine RA and sidereal time (a clock measuring day relative to the stars instead of the Sun) at that instant. For the so called 'fixed stars', the declination and RA can be taken as fixed (they vary very slowly due to the star's proper motion and to the change in orientation of Earth's axis (precession), which moves like the axis of a spinning top, describing a cone. One revolution of earths axis takes about 25000 years, so it can be neglected). In the case of the planets, they change according to their motion around the sun, and in the case of the Sun, its declination and RA change according to the Earth's motion around the Sun. In the case of the Moon, they change according to its motion around the earth which is quite more complicated than that of the planets around the Sun, given the forces of attraction of both, the Earth and the Sun. Once you know the declination and RA of a body, along with the latitude and longitude of a given place on Earth it is a standard astronomical procedure to find the Rising and Setting times for that body. Again, in the case of the moon (and to a lesser extent, the Sun) you need to take into account the not so small change in declination and RA between Rising and Setting, so that makes it yet more complicated. To top it all, in the particular case of the Moon, you also need to take parallax into account, given the relative short distance between the Earth and the Moon. To better understand parallax, take the following example. Imagine you are standing to the left of a friend, and you see a not so distant object right in front of you. Your friend would need to turn a little to the left in order to see the same object also straight ahead. Another example of parallax is the difference in what you see when you first close your right eye with your left eye open and then quickly switch to an open right eye and a closed left one.

Going back to the fixed stars, if a star lies on the equatorial plane (i.e., the imaginary plane where the equator lies) the star will be exactly 12 sidereal hours (about 11h58m solar) above the horizon, regardless of where on Earth you are. In the case of the Sun, at the time of the equinoxes (beginning of spring and beginning of fall) it lies on the equatorial plane and the Sun (more accurately, its centre) is 12 solar hours above the horizon, regardless of your place on earth. At other times of the year, the declination of the Sun can be as far as 23.5 degrees north (beginning of summer) or south (beginning of winter), giving rise to the difference in the length of a day. These differences are greater the further away you are from the equator.

As a final note, if you live somewhere along the equator, the difference between Rising and Setting times, regardless of date, are:
-stars, always 12 sidereal hours (11h58m),
-the Sun, 12h (with small variations)
If you have a Handheld Computer running on Palm OS3.5 or OS5 you will find the following of great interest: www.aho.ch .

Please feel free to write back regarding any further question you may have. If you are still interested, I will try to find some software for you to try on your computer. One more thing you may want to do is have your students perform the calculations using their scientific calculators according to the excellent book by Peter Duffet-Smith, "Practical Astronomy with your Calculator"


You may also have a look at


under Science-> Astronomy and space, on the left panel.
I hope this helps...

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