This section is a collection of small tools which allow you to make a variety of astronomical calculations. We offer maps of the sky, the phases of the Moon as well as computational tools. From time to time we add whatever seems appropriate. As a working limit, we have chosen not to require more than four items for any calculation (if you will accept the notion that a latitude and a longitude together form is a single item - a location). We don't produce more output than will conveniently occupy a pop-up message box.

These tools should not be relied upon for extended time periods or for high precision work. In many cases, the techniques give only approximate answers by ignoring minor factors such as the disturbances of the planets (perturbations) and slowly changing variables such as the tilt of the Earth's orbit. Round off errors accumulate when times deviate greatly from the present.

Star Maps This tool shows you the sky above Frosty Drew Observatory at any date or time, approximately. It defaults to right now, but you can change to any other date and/or time.		Moon Phases This tools will show you the phase of the Moon for any date or time, approximately. It defaults to right now, but you can change to any other date and/or time.
Calculating Ephemerides A facility for calculating the position of objects in solar orbit with reasonable accuracy is available. You can calculate the position of planets, comets, asteroids and unpowered spacecraft as long as the objects stay well away from planets. It supports all the orbits due solely to the Sun's gravity alone (circular, elliptical, parabolic and hyperbolic).		Conversion & Dimensional Analysis Tool This tool converts from many systems of measurements to many others. Complex composite measurements (volts, pressures etc.) are supported. You can perform algebraic manipulations of these expressions (+,-, * , / and exponentiation). A information page explains this tool.
Dates and Times The FDO utility tools allow a very rich set of ways to specify dates. A complete explanation of the ways you can specify dates and times is available. Some conversions require a single date. Use the upper field. For ranges of dates, you will need to enter both fields. You may select either the 24 hour display format or the AM/PM display format. 24 hour      AM/PM
Convert Angles to Various Formats This application converts angles you specify (in any format) to any or all of the formats you specify by the check boxes in the adjacent column.      For information on angle formats:		Display Format for Angles This tool doesn't do any computations by itself. It merely tells other tools how to display results. If you turn off all the flags, you will see the decimal format. If you specify hour angle display, elevations will appear in sexagesimal format as is customary. Sexagesimal format       123°34'56" 24 hour angle format      8h 14m 20s Radian format                 2.15962R Circle portion format      34.3284% Decimal format               123.58222
Spherical and Cartesian Coordinates This tool transforms spherical to Cartesian coordinates and vice versa. Traditionally, the X axis points towards the First Point of Aries (the point where the Sun is located at the first instant of Spring in the northern hemisphere). The Y axis is at right angles to the North. The Y axis is at right angles measured counterclock wise looking down from the North. λ is measured in degrees from the First Point of Aries. β is measured up or down from the circumferential plane which is perpendicular to North. ρ is the radius distance.		Fill either group of boxes with appropriate values. The buttons associated with each group determine whether the conversions are from Cartesian to Spherical and vice versa. X= Y= Z= λ= β= ρ=
Elongations Did you ever wonder how far apart in degrees two objects are in the sky? If you ever wondered how Venus was above the Sun or how wide is the bowl of the Big Dipper, this is what you are asking. If you supply two coordinate pairs, this tool will tell you how many degrees separate them. While the two coordinate need not be in the same format, they both be in the same system (both Equatorial, or both Ecliptic or both Horizon). Long= Lat.  = Long= Lat.  =		Great Circle Distances This is almost the same as the tool as Elongations except that a planetary radius must be supplied. The default is for the Earth in kilometers. Long= Lat.  = Long= Lat.  = Radius =
Combined Stellar Magnitudes Ever wonder how bright a binary star composed of a first and a sixth magnitude star would be together. How about a cluster composed of 10000 twelth magnitude star? How bright are all the stars in the sky togather? Here is a tool to calculate this for you. If you want to enter many stars of the same magnitude prefix the magnitude with the count and an asterisk (no blanks allowed). So 500*9 would mean 500 ninth magnitude stars. The default is an approximation of all the stars in the sky at one time. Notice that they don't even match Venus at its brightest!		Planetary Conjunctions This little tool calculates how long any two bodies in orbit about the sun will take to reach their current angular positions again relative to each other. The defaults are Mercury and Earth. Mercury's "year" is just about 88 days, but because the Earth is moving, getting into the same alignment takes about 116 days. Inner planet= Outer planet=
Atmospheric Density Ever wonder how much of the atmosphere of Earth is above or below a given altitude? OK, so you haven't. Well just in case you ever do, here is an easy tool that gives a reasonable approximation. Temperature = (F°/C°/K°).         Altitude = (mi/km/ft/m).		Atmospheric Refraction That pesky stuff we've evolved to breath can muck up seeing in lots of ways. However one problem can be relieved by this tool. Ever try to find a dim object near the horizon only to find it was bent upwards by several arc minutes? This tool will tell you approximately how much. More precise calculations require an analysis of air densities and temperatures at multiple levels.
Radius, Distance and Angle Fill in any two of the three fields to the left. Fill in two of the boxes below and place a "?" in the third box. You should specify units for the radius and the distance boxes, even if one of them has a "?". α = r = D=   The defaults describe the Earth as seen from the Moon.		This tool is really many tools in one. This tool calculates the missing item. It displays the angle, the visible portion of the surface, the distance to the horizon along the sphere's surface,and the distances to the nearest and farthest visible points as well as the radius. If you regard the sphere as flattened, this tools works quite well for calculating sizes and distances to nebulae, galaxies and globular clusters.
Equatorial to Ecliptic Coordinates The Earth equatorial plane tilts at approximately 23°26' to the plane of the Ecliptic (Earth's orbit about the Sun). Translating from one system to the other can be just a wee bit tedious, and fraught with peril for the unwary. Here is a tool to do this chore. α = δ =		Ecliptic to Equatorial Coordinates If you know the coordinates something relative to the Ecliptic but want the position expressed as a Right Ascension and Declination (the Equatorial coordinate system), here is the tool for you. It is, of course, the inverse of the tool to the left. λ = β =
Horizontal to Equatorial Coordinates Look in the sky - it a bird, it a plane, its Super Nova! Fine, but how do you tell people elsewhere in the world where to look? Translate from your local horizontal coordinates to the standard Equatorial coordinates. Here is a tool to do this chore. See Note 1.          Azimuth =          Altitude =       Longitude =          Latitude = Date & Time =		Equatorial To Horizontal Coordinates The first northern hemisphere Super Nova has just been reported giving its Equatorial coordinates  "Great" you say "but where do I look?" You want to know where it is in YOUR sky tonight  Here is the tool  It is, of course, the inverse of the tool to the left. See Note 1.                     α =                     δ =      Longitude =         Latitude = Date & Time =

Note 1: The tools to switch between horizontal and equatorial coordinates require both the time (Date & Time) and the location of the user on Earth (Latitude and Longitude) The default location is Frosty Drew observatory next Friday night. Together the time and location resolve the position of the local horizon.