Newcomb's Tables of the Sun

Newcomb's Tables of the Sun

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Newcomb's Tables of the Sun is the short title and running head of a work by the American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 astronomer and mathematician Simon Newcomb
Simon Newcomb
Simon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...

 entitled "Tables of the Motion of the Earth on its Axis and Around the Sun" on pages 1–169 of "Tables of the Four Inner Planets" (1895), volume VI of the serial publication
Astronomical Papers prepared for the use of the American Ephemeris and Nautical Almanac. The work contains Newcomb's mathematical development of the position of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

 in the Solar System
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

, which is constructed from classical celestial mechanics
Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...

 as well as centuries of astronomical measurements. The bulk of the work, however, is a collection of tabulated precomputed values that provide the position of the sun at any point in time.

Newcomb's
Tables were the basis for practically all ephemerides of the Sun published from 1900 through 1983, including the annual almanacs of the U.S. Naval Observatory and the Royal Greenwich Observatory. The tables are seldom used now; since the Astronomical Almanac
Astronomical Almanac
The Astronomical Almanac is an almanac published by the United States Naval Observatory and Her Majesty's Nautical Almanac Office, containing solar system ephemeris and catalogs of selected stellar and extragalactic objects....

 for 1984 they have been superseded by more accurate numerically-integrated ephemerides developed at Jet Propulsion Laboratory
Jet Propulsion Laboratory
Jet Propulsion Laboratory is a federally funded research and development center and NASA field center located in the San Gabriel Valley area of Los Angeles County, California, United States. The facility is headquartered in the city of Pasadena on the border of La Cañada Flintridge and Pasadena...

, based on much more accurate observations than were available to Newcomb. Also, the tables did not account for the effects of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

 which was unknown at the time. Nevertheless, his tabulated values remain accurate to within a few seconds of arc to this day.

Newcomb's work was no small accomplishment, especially considering that it predated the advent of digital computers by more than a half century. Emphasis is often placed on the tables themselves, rather than the underlying theory. The latter may turn out to be the more enduring work because the formulas he developed are still used in astronomical software and other computer algorithms.

Newcomb developed similar formulas and tables for the other planets; those of the inner planets have proved to be the most accurate.

Expressions


Certain expressions have been cited in a number of other works over a long period, and are listed below. Newcomb assigns the symbol T to the time since "1900, Jan. 0, Greenwich Mean noon", measured in Julian centuries of 36,525 days.

Sun's geometric mean longitude


The Sun's geometric mean longitude
Ecliptic coordinate system
The ecliptic coordinate system is a celestial coordinate system that uses the ecliptic for its fundamental plane. The ecliptic is the path that the sun appears to follow across the celestial sphere over the course of a year. It is also the intersection of the Earth's orbital plane and the celestial...

, freed from aberration
Aberration of light
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...

 is given as
L = 279° 41' 48.04" + T + 1.089 T2


Authors citing this expression include Borkowski (p. 12) and the Nautical Almanac Offices of the United Kingdom and United States (p. 98).

Fictitious mean Sun


Newcomb gives the Right ascension
Right ascension
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...

 of the fictitious mean Sun, affected by aberration (which is used in finding mean solar time) as
τ
Tau
Tau is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300.The name in English is pronounced , but in modern Greek it is...

 = 18h 38m 45.836s + s T + 0.0929s T2


Authors citing this expression include McCarthy & Seidelmann (p. 13) and the Nautical Almanac Offices of the United Kingdom and United States (p. 73).

Discontinuance


By 1970 the astronomical community recognized the need for improved ephemerides, which are used to prepare national almanacs. The changes required were
  • a new fundamental catalog of stars to replace FK4
  • the use of improved values of astronomical constants that had been discovered
  • a better definition and practical realization of ephemeris time
    Ephemeris time
    The term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:...

     which would take advantage of atomic time
  • a new epoch
    Epoch (astronomy)
    In astronomy, an epoch is a moment in time used as a reference point for some time-varying astronomical quantity, such as celestial coordinates, or elliptical orbital elements of a celestial body, where these are subject to perturbations and vary with time...

     to replace 1950.0


It was decided to introduce as many changes as possible at one time in a consistent system, and the new system would go into effect for the 1984 edition of the ephemerides. "The majority of the resolutions were prepared and adopted by the General Assembly of the IAU at the 1976 and 1979 meetings."

The new fundamental ephemeris was prepared by the Jet Propulsion Laboratory
Jet Propulsion Laboratory
Jet Propulsion Laboratory is a federally funded research and development center and NASA field center located in the San Gabriel Valley area of Los Angeles County, California, United States. The facility is headquartered in the city of Pasadena on the border of La Cañada Flintridge and Pasadena...

 and named DE200/LE200
DE400
DE400 are designations for the more recent members of a series of astronomical ephemerides produced by numerical integration at the Jet Propulsion Laboratory...

. It uses numerical integration
Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of...

.

Works cited

  • Borkowski, K. M. "The Tropical Year and Solar Calendar". Journal of the Royal Astronomical Society of Canada 85 no. 3 (1990): 121–130.
  • McCarthy, D. D.
    Dennis McCarthy (scientist)
    Dr. Dennis D. McCarthy is a former Director of Time at the United States Naval Observatory. Dr. McCarthy also works for the International Earth Rotation and Reference Systems Service. -References:...

     & Seidelmann, P. K.
    TIME from Earth Rotation to Atomic Physics. (Weinheim: Wiley-VCH, 2009).
  • [U.S.] Nautical Almanac Office and HM Nautical Almanac Office
    HM Nautical Almanac Office
    Her Majesty's Nautical Almanac Office , now part of the United Kingdom Hydrographic Office, was established in 1832 on the site of the Royal Greenwich Observatory , where the Nautical Almanac had been published since 1767...

    . "The Improved IAU System", a supplement bound with
    The Astronomical Almanac for the Year 1984. (Washington and London: U.S. Government Printing Office and Her Majesty's Stationery Office, 1983).
  • Nautical Almanac Offices of the United Kingdom and United States of America. Explanatory Supplement to the Ephemeris. (London: Her Majesty's Stationery Office, 1961).
  • Newcomb, Simon
    Simon Newcomb
    Simon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...

    .
    Tables of the Four Inner Planets, 2nd ed. (Washington: Bureau of Equipment, Navy Dept., 1898).