A Treatise On Spherical Astronomy

Cover A Treatise On Spherical Astronomy
A Treatise On Spherical Astronomy
Robert S Robert Stawell Ball
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Ex. 3. Show that the maximum effects of annual parallax on the right ascension and declination of a star are given by the expressions or sec 8(1- cos 2 a sin 2 cos 2 o)^, where o- is the coefficient of annual parallax, o> is the obliquity of the ecliptic, and a, 8, X are the right ascension, declination, and latitude of the star.
[Math. Trip. I. ] The maximum value of (iv) for any real value of is a- sec 8 (cos 2 a cos 2 a> + sin 2 a) 2 = o- sec 8 (1 - cos 2 a sin 2 )$, and the maximum va
...lue of (v) for any real value of is or {(cos 8 sin eo - sin 8 cos o> sin a) 2 + sin 2 8 cos 2 a}^ = o- {(sin 8 cos u> - cos 8 sin cos 2 a}^ = o- (sin 2 X + sin 2 a> cos 2 o) .
Ex. 4. Show that the general effect of the annual parallax of a star is to alter its position in the small ellipse which it appears to describe annually owing to aberration, and for a given star state how this alteration varies with the time of year. [Math. Trip. L] Let 8 be the sun, S Q (Fig.


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