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Light-second

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Template:Unit of length A light-second is a unit of length useful in astronomy, telecommunications and relativistic physics. It is defined as the distance that light travels in free space in one second, and is equal to exactly 299,792,458 metres. It is just over 186,282 miles and almost 9.84×108 feet.

Just as the second forms the basis for other units of time, the light-second can form the basis for other units of length, ranging from the light-nanosecond (just under one U.S. or imperial foot) to the light-minute, light-hour and light-day, which are sometimes used in popular science publications. The more commonly used light-year is also presently defined to be equal to precisely 31557600 light-seconds, since the definition of a year is based on a Julian year (not Gregorian year) of exactly 365.25 days, each of exactly 86400 SI seconds.[1]

Definition of the metre

The metre is the length of the path traveled by light in vacuum during a time interval of 1⁄299792458 of a second.

This definition fixes the speed of light in vacuum at exactly 299792458 m/s, and hence the light-second at exactly 299,792,458 m.[2]

Use in telecommunications

Communications signals on Earth rarely travel at precisely the speed of light in free space, but distances in fractions of a light-second are still useful for planning telecommunications networks as they indicate the minimum possible delay between sender and receiver.

  • One light-nanosecond is almost 300 millimetres (299.8 mm, 5 mm less than one foot), which limits the speed of data transfer between different parts of a large computer.
  • One light-microsecond is about 300 metres.
  • The mean distance, over land, between opposite sides of the Earth is 66.8 light-milliseconds.
  • Communications satellites are typically 1.337 light-milliseconds (low earth orbit) to 119.4 light-milliseconds (geostationary orbit) from the surface of the Earth. Hence there will always be a delay of at least a quarter of a second in a communication via geostationary satellite (119.4ms times 2); this delay is just perceptible in a transoceanic telephone conversation routed by satellite.

Use in astronomy

The yellow shell indicating one light-day distance from the Sun compares in size with the positions of Voyager 1 and Pioneer 10 (red and green arrows respectively). It is larger than the heliosphere's termination shock (blue shell) but smaller than Comet Hale-Bopp's orbit (faint orange ellipse below). Click on the image for a larger view and links to other scales.
The faint yellow sphere centred on the Sun has a radius of one light-minute. For comparison, sizes of Rigel (the blue star in the top left) and Aldebaran (the red star in the top right) are shown to scale. The large yellow ellipse represents Mercury's orbit.

The light-second is a convenient unit for measuring distances in the inner Solar System, because it corresponds very closely to the radiometric data used to determine them (the match is not exact for an Earth-based observer because of a very small correction for the effects of relativity). The value of the astronomical unit in light seconds is a fundamental measurement for the calculation of modern ephemerides (tables of plantary positions): it is usually quoted as "light-time for unit distance" in tables of astronomical constants, and its currently accepted value is 499.004786385(20) s.[3][4]

  • The mean diameter of the Earth is about 0.0425 light-seconds.
  • The average distance from the Earth to the Moon is about 1.282 light-seconds.
  • The diameter of the Sun is about 4.643 light-seconds.
  • The average distance from the Earth to the Sun is 499.0 light-seconds.

Multiples of the light-second can be defined, although apart from the light-year they are more used in popular science publications than in research works. For example, a light-minute is 60 light-seconds and the average distance from the Earth to the Sun is 8.317 light-minutes.

Unit Definition Distance Example
  m km miles  
light-second   2.997924580×108 m 2.998×105 km 1.863×105 miles average distance from the Earth to the Moon is about 1.282 light-seconds
light-minute 60 light-seconds 1.798754748×1010 m 1.799×107 km 1.118×107 miles average distance from the Earth to the Sun is 8.317 light-minutes
light-hour 60 light-minutes
= 3600 light-seconds		 1.079252849×1012 m 1.079×109 km 6.706×108 miles semi-major axis of Pluto's orbit is about 5.473 light-hours
light-day 24 light-hours
= 86400 light-seconds		 2.590206837×1013 m 2.590×1010 km 1.609×1010 miles Sedna is currently 0.52 light-days from the Sun; on an orbit that varies from a perihelion of 0.44 light-days to an aphelion of 5.41 light-days
light-week 7 light-days
= 604800 light-seconds		 1.813144786×1014 m 1.813×1011 km 1.127×1011 miles The Oort cloud is thought to extend between 41 and 82 light-weeks out from the Sun
light-year 365.25 light-days
= 31557600 light-seconds		 9.460730473×1015 m 9.461×1012 km 5.879×1012 miles Proxima Centauri is the nearest star to the Sun, about 4.24 light-years away

References

  1. ^ IAU Recommendations concerning Units
  2. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 112, ISBN 92-822-2213-6, archived (PDF) from the original on 2021-06-04, retrieved 2021-12-16
  3. ^ Standish, E. M. (1998), JPL Planetary and Lunar Ephemerides, DE405/LE405 (PDF), JPL IOM 312.F-98-048.
  4. ^ McCarthy, Dennis D.; Petit, Gérard, ed. (2004), "IERS Conventions (2003)", IERS Technical Note No. 32, Frankfurt: Bundesamts für Kartographie und Geodäsie, ISBN 3-89888-884-3{{citation}}: CS1 maint: multiple names: editors list (link).

See also

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