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1. How do I convert right ascension and declination to altitude and azimuth?

Given the hour angle H of the object with right ascension RA and declination DEC, and the observer's latitude LAT:

azimuth = atan2(sin(H), cos(H) * sin(LAT) - tan(DEC) * cos(LAT))

altitude = asin(sin(LAT) * sin(DEC) + cos(LAT)* cos(DEC) * cos(H))

where "atan2(x,y)" is C-library function equivalent to "atan(x/y)".

Bill Owen (wmo@wansor.jpl.nasa.gov) offers the following comments:

For the azimuth, it might be better to multiply both numerator and denominator by cos(DEC). Granted that the answer should turn out the same either way, since 0/something = something else/infinity, but you'll avoid the overflow that would otherwise result when you compute tan(DEC) near the poles.

Also, the formula you have here is zero when you're looking south. Although there are different conventions, the most common one reckons azimuth eastward from *north*.

Combine these nits, and the formula I use is:

azimuth = atan2 (-sin(H)*cos(DEC), cos(LAT)*sin(DEC) - sin(LAT)*cos(DEC)*cos(H) )

2. What's the hour angle?

Given an object with right ascension RA and the observer's longitude LONG, and the sidereal time at Greenwich ST:

H = ST - LONG - RA

where LONG is positive to the west and ST is represented as an angle. If you measure longitude to the east:

H = ST + LONG - RA.

3. How do I predict the ocean tides?

This is not commonly done by amateurs. See Observer's Handbook 2000 page 157.

4. How do I calculate the date of Easter?

Many people know the following formula:

Easter is the first Sunday after the first full Moon following the vernal equinox.

Caution! This is "astronomical Easter", and it is usually, but not always, the same day as "ecclesiastical Easter", which is the date used by the churches and printed on calendars. "Ecclesiastical Easter" is determined by a formula codified many years ago.

Here is the method published in the Explanatory Supplement.

Perform integer math and drop all remainders. It is valid for any Gregorian year "Y":

C = Y / 100
N = Y - 19 * (Y / 19)
K = (C - 17) / 25
I = C - C / 4 - (C - K) / 3 + 19 * N + 15
I = I - 30 * (I / 30)
I = I - (I / 28) * (1 - (I / 28) * (29 / (I + 1)) * ((21 - N) / 11))
J = Y + Y / 4 + I + 2 - C + C / 4
J = J - 7 * (J / 7)
L = I - J
M = 3 + (L + 40) / 44
D = L + 28 - 31 * (M / 4)

"M" is the month number (3 -> March, 4 -> April) and "D" is the day of the month.

There is a short BASIC program at
http://www.skypub.com/software/software.html

See also the informative Royal Observatory leaflet on Easter at:
http://www.rog.nmm.ac.uk/leaflets/easter/easter.html

There is an HTML Ecclesiatical Calendar generator at:
http://cssa.stanford.edu/~marcos/ec-cal.html

See also the Calendar FAQ at: http://www.watch-inc.com/articles/faqs-about-calendars.html

Tidbits: the pattern of Gregorian Easter days, one year to the next, repeats in a cycle 5,700,000 years long. March 22 is the earliest date of Easter, April 25 is the latest, and April 19 is the most frequent.

5. How fast does that comet (or asteroid) move?

From Harald Lang (lang@math.kth.se).

The current speed of a body like a comet orbiting the sun, or in a hyperbolic or parabolic orbit, is:

2 * pi * sqrt(2/r - (1-e)/q) AU/year

where r is the current distance in AU to the sun, q is the perihelion distance in AU, and e is the eccentricity of the orbit.

6. How do I find my longitude and latitude?

Here are some sites that give longitude and latitude information.

It has been suggested to me that the following precisions are appropriate for the applications shown: 100 miles for most skyviewing work, 2 miles for accurately predicting Iridium flares, 50 feet for occultation work.

United States:
    + Census TMS Home Page http://tiger.census.gov/
    + Mapblast http://www.mapblast.com/
    + National Atlas of the United States of America
       http://www-atlas.usgs.gov/scripts/start.html
    + U.S. Gazetteer
       http://www.census.gov/cgi-bin/gazetteer
    + You could also download and install Google Earth on your PC.
       http://earth.google.com/

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