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Calculating Solar Position: A Guide to Declination, Hour Angle, and Local Solar Noon

This guide discusses calculating the solar position using declination and hour angle for locations like ASMS. It covers the significance of elliptical orbits and axial tilt in determining solar noon, explaining the Equation of Time and timezone offsets. Additionally, it offers formulas for converting coordinates using declination, hour angle, and latitude, as well as practical applications for determining solar positions for specific dates and times. Engage in computations for local solar noon and verify results with calculators or spreadsheets.

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Calculating Solar Position: A Guide to Declination, Hour Angle, and Local Solar Noon

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  1. Sun Position Calculations Paul Calder Flinders University

  2. Declination • If orbit was circular -23.45 cos(360/365 * (N+10)) • Since orbit is actually (slightly) elliptical, use 3rd order harmonic year angle ( degrees) = N * 360/365 declination ( degrees) = 0.39637 - 22.9132 cos  + 4.02543 sin  - 0.38720 cos 2 + 0.05197 sin 2 - 0.15453 cos 3 + 0.08490 sin 3

  3. Hour Angle • Timezone offset • 12 noon is not "high noon" • Equation of time • Compensate for elliptical orbit • Compensate for axial tilt • Hour angle • H = time + TZO + EOT

  4. Timezone Offset • Where is CST "correct"? • What longitude? • What towns are nearest? • When is ASMS "local solar noon"? • Should Adelaide switch to TZ+10? • What other parts of the world have half-hour timezones?

  5. The Equation of Time 0.017189 + 0.428108 cos  - 7.351407 sin  - 3.349466 cos 2 - 9.361774 sin 2 http://www.analemma.com/

  6. Converting Coordinates input: latitude  declination  hour angle H calculate sin a = sin  sin  + cos  cos  cos H = P cos A cos a = cos  sin  – sin  cos  cos H = Q sin A cos a = -cos  sin H = R azimuth (A) = atan2(Q, R) altitude (a) = atan2( sqrt(Q*Q + R*R), P)

  7. Your Turn! • Compute the sun position from the front door of ASMS at 10am on May 10 • Using your calculator • Check using the spreadsheet • Compare with on-line calculators

  8. Next Week

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