Calculating Differences

Alcyone Ephemeris can operate in a special difference mode. The current mode, normal or difference (interval) is indicated in the status bar.

In the difference mode all ephemeris data are calculated as changes of the respective values over a specified time of (a) Differences per hour, (b) Differences per day or (c) the Differences per interval of the ephemeris calculation or (d) the current selected interval (all differences positive). Differences of one hour or one day can be selected and shown regardless of the interval of the ephemeris calculation.

Special considerations for (c) and (d) are explained below. The difference shown in line n, whether one hour, one day or the selected interval, applies to the change in the interval between line n and line n - 1. To switch between normal mode (No differences) and a difference mode, or select Ephemeris -> Differences from the main menu or click the current mode in the status bar and select the difference mode.

Note on difference mode for Differences per interval and Differences per interval (all differences positive): There are some peculiarities in the calculation of differences of longitude and right ascension for longer intervals, which is why two forms of calculation are provided: the normal form Differences per interval and the form Differences per interval (all differences positive), which is applied only to differences of longitude and right ascension. In order to calculate differences that cross through 360° = 0°, the range +180°...360° = 0°...+180° is transformed to -180°...0°...+180°, and then numbers within this range are subtracted. (For right ascension in hours, the range +12h...24h = 0h...+12h is transformed to -12h...0h...+12h.) For example, the positive difference 10° - 345° = 25° is transformed to 10° - (-15°) = 25°. The negative difference 238° - 240° = -2° is calculated as -122° - (-120°) = -2°. This works for all differences less than 180°. However, if the difference exceeds 180°, the result is a negative (360° - difference). For example, the difference 240° - 25° = 215°, is computed as -120° - 25° = -145°, which is 360° - 215°. In order to give the correct, positive result, it is necessary to add 360°, that is, -145° + 360° = 215°, which is what is done when Differences per interval (all differences positive) is selected. But in this way, there are no negative differences, so that retrograde differences of -1° or -2° appear as 359° and 358°, which is clearly not desirable. For most purposes, it is best to use the form selected interval, and only where the differences exceed 180° is Differences per interval (all differences positive) preferable, for example, for intervals close to or exceeding one-half of a body's tropical period, as 13-14 days for the moon, 182-183 days for the sun. However, both forms have their applications and some experimenting will show the capabilities of the two ways of computing with the selected interval.