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From: Mac Oglesby[SMTP:[EMAIL PROTECTED]
Sent: vrijdag 27 december 1996 17:49
To: sundial
Subject: Computation of sunrise, sunset angles
Both Mayall (p.244) and Rohr (p.91) give the formula for finding the hour
angle of the sun at sunset or sunrise as
cos HA = tan L tan D
where HA is the hour angle in degrees of the sun at its rising or setting,
L is the latitude of the place, and D is the declination of the sun.
When I run a latitude of 43 and a declination of -23.44 through my
calculator or on a computer spreadsheet, I get a result of 113.8478 for the
hour angle! A declination of 0 (with the same latitude) gives an hour
angle of 90, which looks good, but 23.44 yields an hour angle of 66.1522
degrees!
A friend has suggested that the formula should be corrected to read
cos HA = - tan L tan D
and that there is a misprint in both books. Has anyone else noticed this?
Mac Oglesby
Dear Mac,
It depends on what point of zero-reference for the hour angle HA is taken:
1. Rohr, Mayall:
Hour angle HA1 is measured from the north (zero) to the east
(positive).
Resulting formulae: cosHA1 = +tanL.tanD
2. Otherwise
Hour angle HA2 is measured from the south (zero)
Resulting formulae: cosHA2 = -tanL.tanD
(Note: cos(a+180)=cos(a-180)=-cos(a), giving the same result)
Regards,
Hans Sassenburg
