Computed sky · The gist
Why the sundial and the clock disagree
A sundial and a clock can sit more than a quarter of an hour apart, and this essay works out exactly why, by hand, by separating the two things that cause it and then adding them back together.
This is the short way in. The essay has the working, the sources and the sky.
A sundial tells the time from a shadow. A clock tells the time from a machine. They do not match, and there are three separate reasons.
The first is that a whole country keeps one clock. India's clock is set for a line of longitude at 82 and a half degrees east. That is a decision about paperwork, not about the sky.
The second is where you stand. The earth turns fifteen degrees in an hour, so one degree of longitude is four minutes of time. Jaipur sits nearly seven degrees west of India's line, so the sun arrives there about 27 minutes later than the clock suggests, and that gap never changes.
Take those two away and something is still left over, and the leftover is the strange one. It is not the same every day. It grows and shrinks through the year and then comes back. Its name is the equation of time. Equation here is an old word for a correction, not an equals sign.
The leftover has two causes, and they are independent.
One: the earth's path round the sun is not a circle. It is very slightly squashed. The earth moves a little faster when it is nearer the sun, in early January, and a little slower when it is further away, in early July. So the sun does not cross the sky at a steady pace.
Two: the earth's axis is tilted by about 23 and a half degrees. A clock measures the earth spinning on that axis. The sun travels along a line that is tilted against it. Near the solstices all of the sun's daily shift counts towards the time; near the equinoxes some of it is spent going north or south instead.
The essay works out each cause on its own for real dates, then adds them. Sometimes they cancel out exactly, and on those days the shadow and the clock agree. On 3 November 2026 they both push the same way, and the shadow runs 16 minutes and 27 seconds ahead.
Words decoded
- sundial
- an instrument that gives the time from the shadow of a fixed edge
- apparent solar time
- the time the shadow keeps; noon is the moment the sun is due south of you
- mean solar time
- the time a clock keeps; it runs on an imaginary sun that moves at a perfectly even rate
- equation of time
- apparent solar time minus mean solar time, which is the shadow's reading minus the clock's
- ecliptic
- the line the sun appears to travel along through the year
- eccentricity
- how far an orbit is from a circle; the earth's is 0.0167, which is very nearly round
- perihelion and aphelion
- the points where the earth is nearest to and furthest from the sun, in early January and early July
- obliquity
- the tilt of the earth's axis against the plane of its orbit, about 23 degrees 26 minutes of arc
- equation of the centre
- the amount by which the real sun runs ahead of or behind an evenly moving one
- right ascension
- the address of a point in the sky measured round the equator, which is the direction a clock counts in
- Julian Day
- a plain running count of days that astronomy programs use in place of dates
- bhujāntara and udayāntara
- the Sanskrit names for these same two corrections in classical Indian astronomy
Twice a week
Essays like this one, Tuesdays and Saturdays. One email per essay, and the archive is never mailed out. Subscriptions open shortly; the RSS feed is live now.
Nothing else arrives, ever.