The 2,116th Meeting of the Society

March 17, 2000

Time Measurement

Robert A. Nelson

President, Satellite Engineering Research Corporation

About the Lecture

The measurement of time is central to advanced engineering and communication systems. The precision of time dissemination is now at the nanosecond level and is expected to reach a picosecond within a decade. The history of clocks will be summarized, various time scales will be described, and the origin of the leap second will be discussed. The effects of the special and general theories of relativity on time transfer algorithms are significant in modern timekeeping systems and their magnitudes will be illustrated. The Global Positioning System is a significant universal source of time. Its principles of measurement will be given and its current status and future growth will be discussed.

About the Speaker

Robert A Nelson is president of Satellite Engineering Research Corporation, an engineering consulting firm in Bethesda, Maryland. Mr. Nelson holds the degree of Ph.D. in physics from the University of Maryland and is a licensed Professional Engineer. He is also a lecturer in the Department of Aerospace Engineering at the University of Maryland. Mr. Nelson is co-author of the textbook Satellite Communication Systems Engineering (Prentice-Hall, 1993) and is Technical Editor of Via Satellite magazine. His publications include a variety of technical papers and reports on the application of relativity to high precision time transfer systems.


President Spargo called the 2116th meeting to order at 8:15 p.m. on March 17, 2000. The Recording Secretary read the minutes of the 2115th meeting and they were approved. The speaker for the 2116th meeting was Robert A. Nelson. The title of his presentation was “Time and Its Measurement in the New Millennium”. In our civilization the measurement of time is central to advanced our engineering and communication systems. The precision of our measurement and dissemination of time is now at the nanosecond level and is expected to reach a picosecond within a decade. We know that the length of the tropical year is 365.242190 days. The incommensurability of the length of the day, the period of the lunar orbit, and the length of the year have presented a challenge to every civilization that has tried to construct a calendar. Our calendar is based on the Roman calendar, more or less as it was established by Julius Caesar in 46 BC This calendar had 365 days with one day added every fourth year. In 325 AD the Roman calendar became inextricably linked to the Christian religion when the council of Nicaea established the rules for the celebration of Easter. The Jewish religion celebrated Passover based on a lunar calendar so that its date in the Roman calendar always changed. The Council decided that Christians should celebrate Easter on the first Sunday after the first full-moon on or after the vernal equinox which was set at March 21st. The fixing of the number of the year occurred in 532 when abbot Dionysius Exiguus, while working on Easter calculations for Pope John I, set that year then known as 248 anno Diocletiani as the year 532 anno Domini based on his estimation of the supposed birth date of Jesus. This did not however gain wide usage until the Venerable Bede published his histories in 725. At the same time he also introduced the reckoning of years BC, unfortunately without the benefit of the number zero resulting in recurring mass confusion about the proper start of our centuries and millennia. Because the Julian calendar had exactly 365.25 days per year, it gained about one day every 100 years and by 1582 the vernal equinox was occurring on March 10 or 11 instead of on the 21st as the Council of Nicaea had decreed, thus throwing off the celebration of Easter. The reform of Pope Gregorian XIII in 1582 removed those 10 excess days, and by establishing that years divisible by 100 would not be leap years unless they were divisible by 400, set the length of the calendar year at 365.2425 days. The first quadricentennial leap day was observed 17 days ago. Another leap day correction of the calendar will not be necessary for more than 3000 years. This Gregorian calendar was soon adopted in all Catholic countries, and slowly over the next two hundred years by Protestant countries. The Protestant British Empire adopted the new style calendar in 1752, dropping 11 days after February 19 and at the same time moved the observance of the new year date from March 25 to January 1 (thus causing subsequent confusion about the celebration of the birthday of George Washington). The subdivision of the day into 24 hours is first recorded by Hipparchus in about 130 BC. A standard system for subdividing the day was not widely accepted until mechanical clocks were introduced in the 14th century and the hour was divided into minutes and seconds. The minute was named from partes minuta prima, the first small part, and the second was named from partes minuta secunda, the second small part. In the 17th century Galileo discovered the regularity of the pendulum by comparing it with the regularity of his own pulse. Galileo's discovery was utilized by Christian Huygens in 1657 when he invented the pendulum clock. The current standard of time measurement is the cesium atomic clock. The Naval Observatory employs 50 cesium clocks to maintain military time. It is accurate to one part in 1014. The hydrogen MASER clock can keep time accurate to one part in 1016. The mean solar second is defined as 1/86,400 of the mean the solar day, but the measurement of the mean solar day is not standard or portable. The ephemeris second was defined in 1956 as 1/31,556,925.9747 of the tropical year 1900 as measured by the astronomer Simon Newcomb, the second president of the Philosophical Society of Washington. In 1967 the 13th General Conference On Weights And Measures defined the atomic second as the duration of 9,192,631,770 transitions of the two hyperfine levels of the ground state of the 133Cs atom. This is fine but the earth's rotation slows by 1.4 millisecond per day per century. How do we know the earth is slowing? Because we have ancient eclipse records such as the eclipse of 484 BC in Greece. It is tidal friction that is slowing the earth's rotation, and increasing the period of the moon's orbit. Simon Newcomb was unaware of this slowing, and the midpoint of the measurements he used was about 1820 so the epoch when one mean solar day equaled 86,400 seconds was 1820. The length is now 86,400.0024 seconds, meaning that 0.0024 seconds accumulates per second per year. Universal Time based on astronomical observation was established in 1956 with three levels of correction. UT0 is universal time at a local observatory. UT1 is UT0 corrected for polar motion. UT2 is UT1 corrected for seasonal variations in rotation. International Atomic Time (TAI) based on atomic clocks was defined to be in agreement with UT1 on the epoch January 1, 1958. Coordinated Universal Time (UTC) was established on January 1, 1972. It keeps time within 0.9 seconds of UT1 by means of leap seconds. Terrestrial dynamic time (TDT) was adopted in 1976 and incorporates corrections for gravitation from the law of general relativity. The global positioning system constellation must disseminate both time and position. There are 24 satellites orbiting in six different planes. Each satellite completes an orbit in approximately 12 hours. Four satellites are required for each GPS determination. The GPS time scale is synchronized with UTC. The time scale origin was Jan. 5/6, 1980 and binary rollover is 1024 weeks. The first rollover occurred on August 21, 1999. The second rollover will occur on May 25, 2019. The GPS signals use two frequency standards, 1575.42 MHz. and 1227.60 MHz. The GPS signal requires corrections for both general and special relativistic effects. One correction is a gravitational red shift due to high orbits of +45 microseconds per day. The second correction is time dilation due to orbital velocity of -7 microseconds per day. The net correction is +38 microseconds per day. There is an orbital eccentricity correction of 46 nanoseconds and finally a correction for rotation of the earth during time of flight of approximately 133 nanoseconds. In conclusion as humans project beyond this planet, the measurement of time kept by atomic clocks will find their replace the paradigm of astronomical motion in the clock work universe. Mr. Nelson kindly answered questions from the floor. President Spargo thanked Mr. Nelson for the society. The President then announced the next meeting and made the usual parking announcement and adjourned the 2116th meeting to the Annual Meeting of the Society at 9:30 p.m. Attendance: 53 Temperature: 5.9°C Weather: partly cloudy Respectfully submitted, John S. Garavelli Recording Secretary