What is a Mean Sun and mean Solar Day?

A day is the time it takes for the Earth to rotate on its axis. Divide this by 24 hours and each hour by 60 minutes and you can say what time it is. If only it were that simple.

What we have defined above is the local sidereal time, LST. (sidereal = determined by the motion of stars)

If we observe the stars revolving around the pole star a sidereal day is the time it takes any star to complete one revolution. A sidereal day is, however, 4 minutes longer than a solar day. Why?

As the Earth rotates all the stars in the sky appear to move from west. Relative to the Earth the Sun orbits the Earth on the ecliptic so it actually moves from east to west against the other stars by about a degree a day. The difference works out to 4 minutes a day which is why a mean solar day is 4 minutes greater than a sidereal day.

(A star on the celestial equator rises in the east and set in the west. Imagine the Sun was a lot fainter than it is so that we could see all the other stars behind it throughout the day. It rises in the east too but would move slightly slower than all the other stars. Four minutes a day slower.)

Just to make things even more complicated the length of a solar day varies throughout the year also.

This is because

  1. The Earths axis of rotation is tilted and,
  2. The Earth’s orbit is not circular but elliptical.

A Mean Solar Day is 24 hours. An apparent day may be between 20 to 30 seconds shorter or longer than this due to the effects above but obviously, for the sake of timekeeping, it is sensible to use an average.

The mean sun is an imaginary sun which matches a mean solar day exactly. It orbits the Earth at a constant rate so that every day is the same length.

The Equation of Time

Universal time (clock time) is based on the motion of an imaginary “mean sun”. This can differ from local solar time, even on the Greenwich meridian, by about 15 minutes over the course of the year. (Note- the difference between a solar day and 24 hours may only be up to 30 seconds but the difference can add up day after day reaching a peak of +14 minutes or -16 minutes).

The Equation of Time is a means of calculating the difference for any particular date. The easiest way to do it is to enter your data into a computer program and let it calculate it all for you. There is one at http://www.go.ednet.ns.ca/~larry/orbits/jsjdetst.html

One must also take into account your longitude as the Sun will be at its highest for people at different longitudes. For every degree east of the time zone meridian ( 0 if you live in the UK) you must subtract 4 minutes from your local time.

Standard Time = Sundial Time - Equation of Time - Longitude Correction

Time Summary

  • Greenwich Mean Time – the mean solar time on the zero meridian that passes through Greenwich. Often referred to as Universal Time.
  • Standard Time – the local mean solar time. Clock time if you live in the same time zone as Greenwich.
  • Local Sidereal Time – the local time calculated using the stars. Up to 4 minutes different to the local mean solar time.
  • Local Apparent Time – the time according to your sundial.

Did you know

Before the invention of the railways different big cities in the UK had their own times. e.g. there was London time, Birmingham time and Edinburgh time, all of which were slightly different by a few minutes. It was the need for accurate timetables which created the need for Greenwich Mean Time.