Timing: Part 1 - Sidereal Or Solar?

The subjects of timing, synchronizing and broadcasting are inseparable and in this new series John Watkinson will look at the fundamentals of timing, areas in which fundamental progress was made, how we got where we are and where we might be going.

However the message is conveyed, analog or digital, whether recorded, broadcast or sent down a wire, it is fundamental to audio and moving images that the result should be presented with a particular time base, in most cases the original one.

The importance of timing is not restricted to broadcasting, but is also vital in a number of other areas, such as science, propulsion, communications, defense, navigation, business and agriculture. In all of those fields there has been steady technological progress and often developments in one field have been adopted in another. A good example is the atomic clock that defines the timing for TV broadcasts. This treatment of timing will necessarily have to be broad.

The accuracy of timing technology has steadily increased. It is difficult to say whether timing technology advanced to meet demand, or whether advances in timing became enabling technology in some other field.

What is time? Difficult to say. It's not tangible like a substance and whilst it flows onwards like a river, time doesn't need a medium to operate in. Time is perhaps best thought of as a dimension in which motion or change is possible. In other words change results in any parameter you can think of becoming a function of time.

The motion of elementary particles allows matter to exist. The propagation of electromagnetic waves, whether from natural sources or from TV transmitters is strongly linked to time and the speed of light c, which has some very interesting characteristics. Electromagnetic waves can travel through a vacuum, but it is possible to think of time as a kind of framework in which they propagate.

Fig.1 - The Earth's axis of rotation is inclined with respect to the ecliptic by about 23 degrees. This inclination is responsible for the seasons.

Fig.1 - The Earth's axis of rotation is inclined with respect to the ecliptic by about 23 degrees. This inclination is responsible for the seasons.

The existence of matter and the possibility of change are all that is needed for evolution to take place, and at any point in evolutionary time what went before and what is to come cannot be the same.

Life evolved on a peculiar planet that rotates on its own axis as well as orbiting the sun. The plane in which the Earth orbits is called the ecliptic. Fig.1 shows that the axis of rotation, the polar axis, is not at right angles to the ecliptic, but is inclined at about 23 degrees. The angular momentum of the turning Earth causes it to act like a giant gyroscope, so the polar axis is steady, at least in the short term, with respect to the stars.

All of the basic timing of life on Earth follows from that. Before artificial light, most things had to be done in daylight and much life evolved to sleep at night. The day became the basic unit of time and remains so for many purposes. The inclination of the polar axis is responsible for the seasons, which were important for agriculture, as plant life had evolved to grow in the summer.

That inclination is also responsible in high latitudes for Vitamin D deficiency and lack of immunity to viruses in the winter, with the average mortality rate showing a sinusoidal component peaking in the winter. The inclination of the polar axis also sets the locations of the Tropics of Cancer and Capricorn and of the Arctic and Antarctic Circles. One orbit of the Sun, four seasons, is a year.

Fig.2 - A suspended mass is supported by the tension T and influenced by the force of gravity mg. The resultant is a restoring force proportional to the displacement. A simple pendulum has a constant period for small angles determined by gravity and length. It was the first accurate timekeeping method.

Fig.2 - A suspended mass is supported by the tension T and influenced by the force of gravity mg. The resultant is a restoring force proportional to the displacement. A simple pendulum has a constant period for small angles determined by gravity and length. It was the first accurate timekeeping method.

Although they are completely different in size, the sun and the moon are also at completely different distances, so by coincidence they subtend roughly the same angle to a viewer on the Earth. The casual observer might think the sun and the moon went around the Earth. This is not so surprising in an era when many casual observers thought the Earth was flat.

Galileo built an early telescope and used it to figure out what was going on. He realized that the Earth went around the sun and not vice versa. Instead of being praised for his tremendous discovery, he was slapped under house arrest as this idea was incompatible with the views of the time.

The first attempt at measuring time was the sundial, which was only a formalized way of monitoring how shadows would move around with the sun. The sundial has a shadow-forming bar called a gnomon that should be parallel to the polar axis. The sundial shows local solar time, which means the time implied from the angle of the sun at the location of the sundial. This means that the reading of a sundial is a function of longitude. As the Earth rotates at 15 degrees per hour, it follows two sundials 15 degrees of longitude apart will read one hour different. Each one is correct for its own location.

Whist there were many attempts to measure time using the dripping of water and the burning of calibrated candles, the first successful alternative to the sundial was the pendulum, no more than a weight suspended so it can swing. Fig.2 shows that gravity provides a restoring force that, for small angles, is proportional to the displacement. That is the requirement for simple harmonic motion: mechanical sinusoidal oscillation.

The first timekeepers, invented in the Netherlands, were mechanisms that would sustain the motion by providing synchronized impulses, like a proud parent pushing a child on a swing. A pendulum one meter long has a period of very nearly two seconds, one second each way, and the meter came close to being defined in that way. As the Earth is not spherical, gravity on the surface isn’t constant, so the idea was dropped.

In a non-technical world that got dark at night the manufacture of a timekeeping machine was difficult and expensive and no one could read it after sunset. The solution that allowed the most people to know the time irrespective of daylight was to arrange for the timekeeping machine to strike a loud bell every hour.

From the Latin clocca, meaning a bell, came the French cloche and the German glokke. That caused these timekeepers to be called clocks, a term that is used loosely today to mean any kind of timekeeper. To a horologist, a clock is something that strikes. Anything else is a timepiece.

A pendulum has angular momentum, which is a vector quantity. External effects cause the plane of the pendulum to precess, just as a gyroscope does. The effect was used by Foucault to demonstrate the rotation of the Earth at the Pantheon in Paris. The plane of a freely suspended pendulum rotates at a constant rate with respect to the Earth.

Fig.3 An Earth day of 24hrs is the time taken for the sun to return overhead the same geographical position (GP) and requires about one degree more than a whole turn. A sidereal day, the length of an absolute rotation, is about four minutes shorter than an Earth day.

Fig.3 An Earth day of 24hrs is the time taken for the sun to return overhead the same geographical position (GP) and requires about one degree more than a whole turn. A sidereal day, the length of an absolute rotation, is about four minutes shorter than an Earth day.

At either of the Poles, the plane of a Foucault pendulum would stay locked in space and the Earth would turn beneath it. One complete rotation of the Earth on its axis, whose length is a sidereal day, causes the stars to reappear in the same place, which is important to astronomy. However, that is not the same as a solar day. Fig.3 shows that as the Earth rotates the same way as it orbits, it has to complete slightly more than one revolution to face the Sun again each day.

As there are about 365 days in a year, the extra motion needed corresponds to about one degree, taking four minutes. The sidereal day then has a period of 23 hours 56 minutes in solar time and there are about 366 sidereal days, or absolute earth rotations, in a year.

Early clocks were not very accurate and only had hour hands. They were regularly reset by reference to a sundial. Gradually clocks became more accurate. It was understood that the length of the pendulum had to be kept constant for accurate timing, and that led to the invention by John Harrison of the gridiron pendulum that used rods of dissimilar metal whose thermal expansion cancelled out and kept the pendulum length constant.

These accurate clocks then showed that the length of the solar day was not constant. This could only happen if the Earth's orbit around the sun were completely circular, whereas it is elliptical and slightly eccentric.

Conservation of energy requires that the orbital velocity of the Earth fall as it gets farther away from the sun; where potential energy increases and kinetic energy decreases. Johannes Kepler worked out the principles in the early 1600s. As orbital speed varies, the angle between the sun and the Earth swept out in one day also varies, so the with respect to a constant-speed timepiece the time of the midday sun will change throughout the year. A clock that ran true to the average of all midday sun timings was working in mean time.

A clock in the Royal Observatory at Greenwich in England would be running at Greenwich Mean Time (GMT), which is the mean solar time on the Greenwich Meridian, where zero degrees of longitude is considered to be.

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