Tagged ‘time‘

Adventures In Time And Space 4: Royal Observatory At Greenwich

The Prime Meridian near Flamsteed House

The Prime Meridian near Flamsteed House

The Royal Observatory at Greenwich is on a hill in Greenwich Park in London and is the location of the Prime Meridian. The observatory was commissioned in 1675 by King Charles II for the purposes of celestial navigation and cartography. The king appointed John Flamsteed as the first Astronomer Royal to serve as the director of the new observatory.

The Prime Meridian passes through the Greenwich Observatory complex and is marked by a stainless steel strip in the courtyard. In recent times, a green laser also marks the location and shines across the night sky. The Prime Meridian is part of a geographic coordinate system. This coordinate system is useful for making maps because every location on Earth can be identified by its latitude and longitude.

The latitude is an angular measurement ranging from 0° at the Earth’s equator to either +90° at the north pole or −90° at the south pole. Lines of latitude are circles of differing circumferences on the Earth’s surface. The largest circle is called a great circle and it is the equator. Lines of latitude also are called parallels because the circles are parallel to each other. The equator divides the Earth into the Northern Hemisphere and the Southern Hemisphere. On the Earth’s surface, each degree of latitude corresponds to a distance of about 111 kilometers.

The longitude is an angular measurement ranging from 0° at the prime meridian to either +180° eastward or −180° westward. All meridians are halves of great circles which converge at the north and south poles. The prime meridian and its opposite, the 180th meridian at 180° longitude, together form a great circle around the sphere of the Earth and divides it into the Eastern Hemisphere and the Western Hemisphere. Because lines of longitude converge at the poles, each degree of longitude corresponds to a different distance on the Earth’s surface as the latitude changes. At the equator, the distance is about 111 kilometers, but this distance gets smaller until it reaches 0 kilometers at the poles.

For further precision, each degree of latitude and longitude (°) is divided into 60 minutes (‘), each of which is further divided into 60 seconds (”), e.g., San Antonio, Texas is located at 29°25′26″ N and 98° 29′ 37″ W. These coordinates also can be expressed as decimal fractions, e.g., San Antonio is 29.42412 and -98.49363.

Unlike the equator, which is the one great circle perpendicular to the Earth’s axis of rotation, the location of the prime meridian is arbitrary, and can be part of any great circle that runs through both poles. Throughout history, it was common practice to choose a nation’s capital or some other popular location, so different maps had different prime meridians. Finally, it was decided in 1884 to have delegates from 25 nations meet in Washington, DC, for the International Meridian Conference. The delegates voted to adopt Greenwich as the location for the universal Prime Meridian.

Map of the Prime Meridian at the Royal Observatory Greenwich (south is up)

Map of the Prime Meridian at the Royal Observatory Greenwich (south is up)

Once Greenwich was chosen as the universal Prime Meridian, the longitude at any location can be determined by calculating the time difference between that location and Greenwich. Since a day has 24 hours and a circle has 360°, then the sun moves across the sky at a rate of 15° per hour. As a simple example, if a location is six hours behind the time at Greenwich, then that location is near 90° west longitude. Obviously, a chronometer set to Greenwich time and the local time need to be known.

GPS shows 0.00149 degrees (about 5.3 seconds) due to IERS Meridian being about 100 meters eastward

GPS shows 0.00149 degrees (about 5.3 seconds) due to IERS Meridian being about 100 meters eastward

So why doesn’t the Greenwich Prime Meridian show 0° longitude? The reason has to do with the fact that the Earth is not really a perfect sphere and that, until recently, most maps had to shift their lines of latitude and longitude until they matched local surface measurements to some reasonable amount.

It was only until the existence of artificial satellites that maps finally could be adjusted to the center of the Earth’s mass and not to various local surfaces. The current coordinate system, the World Geodetic System, was established in 1984 (WGS 84) and measures global surface locations to within ±1 meter or better. WGS 84 showed that the Greenwich Prime Meridian was actually about 5.3 seconds or about 100 meters west of 0° longitude. The new meridian is known as the International Reference Meridian and is maintained by the International Earth Rotation and Reference Systems Service (IERS). It is the reference meridian of the Global Positioning System (GPS) run by the United States Department of Defense.

The IERS Reference Meridian is about 5.3 seconds (about 100 meters) east of the Greenwich Meridian

The IERS Reference Meridian is about 5.3 seconds (about 100 meters) east of the Greenwich Meridian

Adventures In Time And Space 3: Everyday

Noah Kalina

Noah takes a photo of himself every day for 6 years.

New York artist Noah Kalina created an awesome montage of pictures that he took once a day of himself for 2356 days. He started on January 11, 2000 and finished on July 31, 2006. His video everyday displays the photographs at a rate of six per second.

This time span covers about 6.5 years of Noah’s life, or maybe one-thirteenth of an average human life span. To put this amount of time in perspective, 6.5 years would be roughly the time a human would develop from a baby to a child in the first grade, the time spent in university earning a graduate degree, and it would be the time needed for Pioneer 11 to reach Saturn.

Adventures In Time And Space 1: Powers Of Ten

Powers of Ten (1977)

Powers of Ten (1977)

One of the things that makes science so awesome is knowing that all of the wonders of the universe exist all around us but we can notice only a small part of it. We humans are trapped in both time and space by the limitations of our senses. We go about our daily lives using measurement scales that range (in time) from about a second to about a year and (in space) from about a millimeter to about a kilometer.

But events in the universe occur at much smaller and at much larger measurement scales than within these normal human ranges. Science has had to establish a common framework in order to make sense of a far more detailed universe. We use a scale of numbers with a fixed ratio called an order of magnitude.

To make it easy on us, we express the orders of magnitude in factors of ten, i.e., ten multiplied by itself a certain number of times. Each order of magnitude is either ten times larger or ten times smaller than the one next to it, e.g., if a number differs from another number by one order of magnitude, then it is ten times different than the other number; if they differ by two orders of magnitude, then the numbers differ by a factor of 100.

We can use scientific notation to show the order of magnitude in an easy way. If the order of magnitude of a number, say, 2300 is three, then we can express this as 2.3 x 103. If the number was 23000 instead, then it would be 2.3 x 104 and have an order of magnitude of four.

Why bother? Because doing it this way helps us handle very large and very small numbers and gives us a way to compare the scale of things.

The designers Charles and Ray Eames wanted to show this relative scale of the universe. They made a film using the orders of magnitude in factors of ten. They started with humans (naturally) and zoomed outwards from Earth towards the edge of the observable universe. They then zoomed inward towards a single atom and the quarks inside it. In 1977, their film Powers of Ten: A Film Dealing with the Relative Size of Things in the Universe and the Effect of Adding Another Zero was their awesome result:

Powers of Ten (for length)
The examples given are sizes that are within the range of lengths that exist between each order of magnitude. For example, the sizes of elephants, FM radio waves, and humans fall in descending order between one decameter (ten meters) and one meter.

10−18 attometer (quintillionth of meter)
0.000,000,000,000,000,001 (e.g., quark)

10−15 femtometer (quadrillionth of meter)
0.000,000,000,000,001 (e.g., uranium nucleus, proton, neutron)

10−12 picometer (trillionth of meter)
0.000,000,000,001 (e.g., carbon atom, x-rays, gamma rays)

10−9 nanometer (billionth of meter)
0.000,000,001 (e.g., virus, DNA, visible light)

10−6 micrometer (millionth of meter)
0.000,001 (e.g., human hair, white blood cell, bacterium)

10−3 millimeter (thousandth of meter)
0.001 (e.g., rice grain, ant, sand grain)

10−2 centimeter (hundredth of meter)
0.01 (e.g., hummingbird, chicken egg, penny)

10−1 decimeter (tenth of meter)
0.1 (e.g., baseball bat, basketball, cell phone)

100 meter (one meter)
1 (e.g., elephant, FM radio waves, human)

101 decameter (ten meters)
10 (e.g., football field, blue whale, house)

102 hectometer (hundred meters)
100 (e.g., Eiffel Tower, Boeing 747 airplane)

103 kilometer (thousand meters)
1,000 (e.g., Grand Canyon, AM radio waves)

106 megameter (million meters)
1,000,000 (e.g., Jupiter, Earth, Texas)

109 gigameter (billion meters)
1,000,000,000 (e.g., Deneb, Arcturus, Sun)

1012 terameter (trillion meters)
1,000,000,000,000 (e.g., Stingray Nebula, Kuiper Belt)

1015 petameter (quadrillion meters)
1,000,000,000,000,000 (e.g., Orion Nebula, Oort Cloud)

1018 exameter (quintillion meters)
1,000,000,000,000,000,000 (e.g., Large Magellanic Cloud, Tarantula Nebula, Eagle Nebula)

1021 zettameter (sextillion meters)
1,000,000,000,000,000,000,000 (e.g., Local Group, Milky Way Galaxy)

1024 yottameter (septillion meters)
1,000,000,000,000,000,000,000,000 (e.g., Virgo Supercluster)

1027 zennameter (octillion meters)
1,000,000,000,000,000,000,000,000,000 (e.g., observable universe)

Incidentally, 10100 is the number googol. Mathematician Edward Kasner’s nine-year-old nephew coined the word and Edward mentioned it in his 1940 book Mathematics and the Imagination. Of course, this power of ten was the inspiration for the name of the company Google.

The Powers of Ten film from the Office of Charles and Ray Eames was a landmark film. It even became a 2004 couch gag on the opening sequence of The Simpsons (The Ziff Who Came to Dinner):

If we want to show the relative scale of events and not of sizes, then we can use the powers of ten to get a sense of how long events take. We can show how fast atoms react with each other and then go towards larger and larger time scales until we reach the grand age of the observable universe:

Powers of Ten (for time)
The examples given are events that occur within the range of times that exist between each order of magnitude.
For example, the time between normal human heartbeats takes between one decisecond (tenth of second) and one second.

10−18 attosecond (quintillionth of second)
0.000,000,000,000,000,001  (e.g., transfer of electron between atoms)

10−15 femtosecond (quadrillionth of second)
0.000,000,000,000,001  (e.g., chemical reaction time)

10−12 picosecond (trillionth of second)
0.000,000,000,001  (e.g., lifetime of hydronium ion in water)

10−9 nanosecond (billionth of second)
0.000,000,001  (e.g., light travels 30 centimeters or one foot)

10−6 microsecond (millionth of second)
0.000,001  (e.g., strobe light flash)

10−3 millisecond (thousandth of second)
0.001 (e.g., wing flap of honey bee)

10−2 centisecond (hundredth of second)
0.01 (e.g., camera shutter speed)

10−1 decisecond (tenth of second)
0.1 (e.g., human eye blink)

100 second (one second)
1 (e.g., time between human heartbeats)

101 decasecond (ten seconds)
10 (e.g., )

102 hectosecond (hundred seconds)
100 (e.g., )

103 kilosecond (thousand seconds)
1,000 (e.g., class period, movie, concert, football game)

106 megasecond (million seconds)
1,000,000  (e.g., calendar month, grading cycle)

109 gigasecond (billion seconds)
1,000,000,000  (e.g., human life span)

1012 terasecond (trillion seconds)
1,000,000,000,000 (e.g., complete cycle of the equinoxes)

1015 petasecond (quadrillion seconds)
1,000,000,000,000,000 (e.g., length of geologic period)

1018 exasecond (quintillion seconds)
1,000,000,000,000,000,000 (e.g., age of universe)