Simplified Sidereal Time

While preparing for a full moon / blue moon, I was looking at an algorithm for calculating sidereal time and had a mini epiphany. The algorithm is basically an elaborate modulo operation. Modulo is generally applied to integer values, but it can be used with decimal numbers and even fractions.

For the algorithm that I have generally used, a lot of the calculations are only for converting the date to some linear expression of time. The calendar that is usually used does not express time linearly.

The amount of time from the beginning of one month to the beginning of another month could be 28 to 31 days. With linear representations of dates, a subtraction operation is all that is needed to know the amount of time between two moments in time.

In JavaScript, this linear representation of time is shown by calling getTime() on a date object. The time value for 2019 January 10 @16:40:20 UTC  is 1547138420000. This value is the number of milliseconds since another date and time. This time and date is also 00:00:00 Sidereal time. The number of milliseconds in a sidereal day (23 hours 56 minutes 4.1 seconds) is 86164100. For any date after 2019-01-10T16:40:20 we could get the Sidereal time by doing the following:

  • Acquire the getTime() value for the date in question.
  • Subtract 1547138420000 from that value.
  • Get the modulo 86164100 for the resulting value.
  • Multiply the result by 24/86164100.

The result of these operations is the sidereal time in decimal. If you want to convert it to hour:minute:second format do the following:

var hour = Math.floor(result);
var minute = (result % 1) * 60;
var second = (minute % 1) * 60;
minute = Math.floor(minute)