Sidereal time, or what the sky reads on your clock, the gist

Sidereal time, or what the sky reads on your clock

The earth takes 23 hours 56 minutes to turn once, not 24, and this essay carries one birth moment from a wall clock to the clock the sky actually keeps, using nothing harder than multiplication.

This is the short way in. The essay has the working, the sources and the sky.

Your clock and the sky disagree by 3 minutes 56 seconds every single day. That is why the stars you saw at nine last night are in that spot at four minutes to nine tonight, and why a year of nights brings the whole sky back round.

A day is one turn of the earth. But you have to measure that turn against something, and the answer depends on what you pick.

Measure it against the Sun, from midday to midday, and you get 24 hours. That is the day your clock keeps. Measure it against a star, from the moment the star is due south to the next time it is due south, and you get 23 hours, 56 minutes and 4 seconds. That is the sidereal day, and it is shorter.

Why shorter? Because the earth is also going round the Sun. In one year it makes one full lap. So in a year the earth turns 365.2422 times as far as the Sun is concerned, and 366.2422 times as far as the stars are concerned. One extra turn. Divide 24 hours in the ratio of those two numbers and the sidereal day drops straight out.

Sidereal time is the reading on the sky's own clock. Its useful meaning is simple: it tells you which part of the sky is due south of you right now. Astronomers give every point of the sky an address, counted in hours, and your sidereal time is the address of whatever is crossing the line from north to south over your head.

The essay then does one full conversion, digit by digit. It takes a birth at 09:12 in the morning on 22 July 2009 in Ujjain. Subtract five and a half hours to reach Greenwich time. Fetch the day number for that date. Count 3,490 days from a published starting value. Add 3 minutes 56.5554 seconds of drift for each of those days. Add the hours since midnight, multiplied by 1.0027379. Add the city's longitude, converted to hours. Answer: 4 hours 45 minutes 15 seconds.

Then it says which digits are shaky and why, and stops before the ascendant, which is the next piece of work.

Words decoded

solar day: one turn of the earth measured against the Sun, averaging 24 hours
sidereal day: one turn measured against the stars, 23h 56m 4.09s
meridian: the imaginary line running from due north, over your head, to due south
right ascension: the address of a point in the sky, counted in hours, the sky's version of longitude
sidereal time: the right ascension of whatever is crossing your meridian at this instant
Greenwich mean sidereal time: the same reading, but for Greenwich, from which every other place is worked out
Universal Time: clock time at Greenwich, the scale all this arithmetic runs on
Julian Day: a plain running count of days that astronomy programs use instead of dates
precession: the slow westward drift of the sky's zero point, about one degree every seventy-two years
ascendant, or lagna (लग्न): the point of the sky rising in the east at a given moment, computed from sidereal time and latitude

Why anyone should careIf you have ever been handed an astrology chart, this is the step nobody shows you, and it is the step everything else leans on. It is also completely ordinary arithmetic. Nothing in it is secret, nothing in it is a matter of opinion, and a patient person with a sheet of paper can check the answer.

Read it properly, 8 min Sidereal time, or what the sky reads on your clock