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## Experimental Methods in Astronomy

by: Virgil Bartell

45

0

2

# Experimental Methods in Astronomy AST 4700

Marketplace > University of Central Florida > Astronomy > AST 4700 > Experimental Methods in Astronomy
Virgil Bartell
University of Central Florida
GPA 3.68

Yanga Fernandez

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COURSE
PROF.
Yanga Fernandez
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Astronomy

This 2 page Class Notes was uploaded by Virgil Bartell on Thursday October 22, 2015. The Class Notes belongs to AST 4700 at University of Central Florida taught by Yanga Fernandez in Fall. Since its upload, it has received 45 views. For similar materials see /class/227568/ast-4700-university-of-central-florida in Astronomy at University of Central Florida.

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Date Created: 10/22/15
Summary of coordinate conversion formulae AST 47005263 Spring 20107 Handout 6 1 Basic formulae for spherical trig Consider a spherical triangle with sides 17b7 and c7 and with opposite angles A7B7 and C There are two basic formulae to remember sin a sin b sin 0 sin A sin B sin 07 and cosc cosacosb sinasinbcosC cosb cosacoscsinasinccosB cosa cosccosb sincsinbcosA These are the law of sines and the law of cosines There are really only two formulae here 7 no need to remember every combination 2 F mmrorial to Horizon x Let H and 6 be the hour angle and declination We cannot use the right ascension a but we7ll see later on that there7s an easy relationship between a and H The hour angle is de ned as the amount of time before or after the object has transited When an object rises7 it has 712h lt H lt 0 or equivalently7 12h lt H lt 24h H increases through the night At transit7 H 0 When an object sets7 0 lt H lt 12 h To nd altitude a and azimuth A7 the formulae are sina sin6sin cos cosabcosH7 sin6 7 sin bsina cosA cos cosa and 7 cos 6 sin H s1nA cosa where b is the observers latitude At UCF7s location7 286 To do the reverse problem7 where you know a and A and you want to nd H and 6 the formula are very similar sin6 sinasin gt cosacos z cosA7 i 7 i i 6 COS H W cos b cos 6 7 and 7 cos a sin A sin H cos 6 1 L 3 F auaforial to Ecliptic 1 To nd ecliptic latitude B and ecliptic longitude A the formulae are sin sin 6cos E 7 cos 6sin E sina cos 6 cos 04 cos A cos B and s1n67cos6s1n sin A sin 6 cos B where E is the obliquity of Earth7s axis with respect to the plane of the ecliptic At the standard epoch in use 20000 6 23 26 21quot For the reverse problem of deriving Oz and 6 from A and B the formulae are sin 6 sin cos 6 cos sin 6 sin A cos A cos B cosa cos 6 and cos6s1n67s1n sina sin 6 cos 6 1 L 4 F auarorial to GalactiCI To nd the galactic latitude b and the galactic longitude Z the formulae are sinb sin 6g sin 6 cos 6g cos 6 cosa 7 04g COS i Ame cos6sina 7 04g cos b 7 and 6 6 b sin 7 sin gsin Z 7 DO 9 7 sm d cos 6g cos b where 046 12h51m263s 6g 27 07 42quot and node 32 55 55quot These are all refering to the standard epoch 20000 Speci cally 046 and 6g indicate the location of North Galactic Pole and node refers to the offset of the longitude zero point from the celestial equator For the reverse problem of deriving Oz and 6 from b and Z the formulae are sin 6 sin 6g sin b cos 6g cos b sin 7 Awe COSW i a 7 sinb 7 sin gsin G 7 cos 6g cos 6 and Z Z b cos 7 node cos s1na 046 7 COS6 5 Why always two formulae for the Iongitudes 04 A A and 7 Since the cos 1 aka arccos function only returns values between 0 and 180 degrees one has no way of knowing whether the longitude really is in that range or between 180 and 360 degrees This ambiguity can be eliminated with calculation of the sine If the sine is positive then the cos 1 function will return the right longitude If the sine is negative then cos 1 returns the wrong longitude the right longitude in that case is 360 minus that wrong longitude

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