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Astrometry and Cosmology

  • Chapter
Astrophysical Formulae

Abstract

For reference purposes, the earth’s surface at sea level may be represented by revolving an ellipse of eccentricity, e, and major axis, a e, about the polar axis. The flattening factor, f, or ellipticity, is related to the eccentricity, e,by the equation

$${e^2} = 2f - {f^2}$$
(5-1)

, The flattening factor is alternatively called the ellipticity or the oblateness factor. The major axis, a e, is the equatorial radius, which is related to the polar radius, a p, by the equation

$${a_p} = {a_e}\left( {1 - f} \right) = {a_e}{\left( {1 - {e^2}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}$$
(5-2)

and the mean radius, < a> is given by

$$\left\langle a \right\rangle = {\left( {a_e^2{a_p}} \right)^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}}}$$
(5-3)

.

“There is not, in strictness speaking, one fixed star in the heavens, ... there can hardly remain a doubt of the general motion of all the starry systems, and consequently of the solar one amongst the rest.”

Sir F. W. Herschel, 1753

“A luminous star, of the same density as the Earth, and whose diameter should be two hundred and fifty times larger than that of the Sun, would not, in consequence of its attraction, allow any of its rays to arrive at us. It is therefore possible that the largest luminous bodies in the universe may, through this cause, be invisible.”

P. S. Laplace, 1798

“The laws of physical phenomena must be the same for a fixed observer as for an observer who has a uniform motion of translation relative to him.... There must arise an entirely new kind of dynamics which will be characterized above all by the rule that no velocity can exceed the velocity of light.”

H. Poincaré, 1904

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Lang, K.R. (1980). Astrometry and Cosmology. In: Astrophysical Formulae. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21642-2_5

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  • DOI: https://doi.org/10.1007/978-3-662-21642-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55040-2

  • Online ISBN: 978-3-662-21642-2

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