2. Early Precision Time Measurement
• Late 1630s – Galileo Galilei
observed that a pendulum took the
same time to swing through a wide
arc as a narrow arc.
• Mid 1720s – John Harrison
improved accuracy of pendulum
clock to 1/5 second per day.
• Pendulum clocks must be
stationary, thus no precision timing
at sea.
3. Navigation at Sea
Where Am I?
• Latitude – how far north or south of the
equator? (easy)
• Longitude – how far east or west of the
prime meridian? (hard)
• 1707 – Isles of Scilly –
British fleet lost (1400+)
4. Methods of Determining Position
• Triangulation – Latitude (north/south)
– Sextant used to measure vertical angle between
horizon and sun at highest point (or Polaris (a.k.a.
the “north star”) at night)
5. Methods of Determining Position
• The “Longitude Problem”
– East/West location determination much harder
than latitude. Longitude determination required
knowing precise time at Greenwich (Prime
Meridian = zero longitude).
– Voyages could last months.
– John Harrison worked from 1735 to 1772 (37
years) building 5 “sea clocks” (chronometers) for
precision timing at sea. { 1/3 second per day }
6.
7. Enter: Quartz
• 1880 - Piezoelectricity first
demonstrated by brothers
Pierre & Jacques Curie.
• When piezoelectric material is
subjected to mechanical stress,
(e.g. bending) it creates electrical charge.
• Inverse also true (apply charge to bend).
• “Feedback” employed to sustain resonance at
very stable frequency & low power.
8. A quartz crystal “tuning fork”
resonator in a wristwatch
resonates with very stable
frequency (32,768 cycles per
second. A counter is used to
divide down to one pulse per
second.
Typical drift of quartz watch:
~ 1 second per day.
9. The “Gold Standard” of Precision Time
Measurement: Atomic Clock
• The “cosmic oscillator” improved upon the
quartz oscillator.
– changes in the energy levels of atoms release
electromagnetic radiation of very specific
frequencies.
– atoms don’t wear out, change their properties
over time, or have small differences due to
manufacturing imprecision.
• 1948 - First “atomic clock” built by Harold
Lyons at National Bureau of Standards (NBS).
10. Atomic Clock Precision Proves Theories
of Relativity
• Albert Einstein predicted Special Relativity
(kinematic time dilation) in 1905, and General
Relativity (gravitational time dilation) in 1915.
– Kinematic: Time passes relatively
slower at high speed.
– Gravitational: Time passes slower
in stronger gravitational fields.
• 1971 - Hafele-Keating Experiment
– Used cesium clocks to prove both
theories
11. Precise Time Yields Position (again)
• Trilateration – determining locations of points
by measurement of distances, using the
geometry of circles, spheres or triangles.
Cell phone trilateration –
• Measure transit time for radio
signal between tower and phone.
(Time yields distance).
• Known distance to tower provides
circle of possible locations.
• Determine distance to more
towers for more circles & find
intersections of circles.
12. GPS – Precision Timing for All
• Cesium 133 atomic clocks
on-board each GPS satellite
for extremely precise time
synchronization.
• Constellation of satellites in
circular orbits 20,000 km
above earth surface.
• Radio signals broadcast from satellites include
the exact time at which the signal was
transmitted, as well as the ephemeris data for
the satellite.
13. GPS Precision Navigation & Timing
• Exact location of satellite is calculated from
ephemeris data included in the signal.
• Just like cellular towers, except in 3-D –
replace circles of possible positions with
spheres.
• 4th satellite provides receiver clock calibration.
• More GPS receivers in the world used for time
synchronization than for determining position.
Editor's Notes
Period of pendulum swing determined by length of rod & mass of weight – rod length adjusted to “tune”. Accuracy was affected by expansion & contraction of pendulum rod due to temperature changes. Harrison created pendulum rod of alternating brass and iron rods so that their thermal expansions/contractions counteracted each other, keeping length constant.Pendulum clocks reined for
Gridlines overlaying earth show latitude & longitude for precise mapping. Not knowing precisely where you are can be very dangerous at sea. Scilly naval disaster of 1707- led to the sinking of a British naval fleet off the Isles of Scilly. With four large ships and more than 1,400 sailors lost in stormy weather, it was one of the worst maritime disasters in the history of the British Isles. It was later determined that the main cause of the disaster was the navigators' inability to accurately calculate their positions.
Sun at highest point over Greenwich at noon GMT. Earth rotates 360 degrees every 24 hours – thus, if it is 6 pm in Greenwich when the sun is at highest point over you, you know your longitude is ¼ way around the world = 90 degrees west. Every second your clock is off will misplace your longitude by as much as 1 nautical mile (nm) { clock 5 minutes slow? -> as much as 300 nautical miles error! }
Resonant frequency determined by shape & size of quartz plate. Size changes relatively little with temperature fluctuations.
The first quartz clock was built in 1927 by Warren Marrison and J.W. Horton at Bell Telephone Laboratories. Since the 1980s when the advent of solid state digital electronics allowed them to be made compact and inexpensive, quartz timekeepers have become the world's most widely-used timekeeping technology.
Atomic oscillators use the discrete (quantum physics) energy levels in atoms and molecules as the source of their resonance frequency. An electromagnetic field at a particular frequency can boost an atom from one energy level to a higher one. Or, an atom at a high energy level can drop to a lower level by emitting energy at that frequency.Current cesium133-based atomic clock at National Institute of Standards & Technology (NIST) in Boulder, CO is accurate to 1 second in 100 million years.
JodepheHafele (physicist) and Richard Keating (astronomer) took four cesium-beam atomic clocks around the world on commercial airliners (east, then west) and compared the time on the clocks to others left stationary on the ground. Special Relativity predicted the clocks on the eastbound airplane would lose ~184 nanoseconds (ns) while the clocks on the westbound plane would gain 96 ns compared to the clocks on the ground due to time travelling faster in the plane travelling against the earth’s rotation and slower in the plane travelling with the earth’s rotation. Also, General Relativity predicted the clocks on the airplanes would gain ~140 to 180 ns due to the relatively weaker gravitational field of the earth at altitude compared to the clocks on the ground. The results agreed perfectly with the theories.
What does precise time measurement give us??? Precise position, again.Trilateration, in contrast to triangulation, does not involve the measurement of angles, but rather distances.Precise clocks expensive & large – if phone clock is off, circles will be larger or smaller, throwing off solution.Note cool trick that allows us to use cheap clocks in phones – add one more tower into play. Adjust clock to make four circles intersect. This way, the cheap clock can be calibrated regularly, synchronizing it exactly with the time standard.
Ephemeris data is orbital information that allows the receiver to calculate the precise position of the satellite.Radio signals travel at speed of light ~ 300,000 km/s (186,000 miles/second)Clocks are so precise, we must adjust for relativity to re-synch them with time on surface (Boulder).
Synchronized time necessary for power companies, communications, banking…GPS video: http://www.youtube.com/watch?v=EOwMkFsJXRI
