Topic 8 - Amplitude Of Sun 412b4t

Module: Topic 8:

Principles of Navigation Amplitude of Sun

MA0539

Objective: 1.

Calculate the Amplitude of the Sun.

Amplitude The amplitude of a body is the angular distance between the body and the prime vertical at the time of theoretical rising or setting. The prime vertical is the great circle on the celestial sphere which es through the observer's zenith and the east and west points of the rational horizon. Theoretical rising or setting of a body occur when the centre of the body is on the observer's rational horizon, East or West of the meridian. At these times, the true zenith distance is 90º and true altitude of the body is zero. If the true altitude of the Sun is 0 0, the observed altitude of the Sun’s lower limb, for an observer at sea level will be about 18’ because of semi-diameter correction and refraction. True Alt. of Sun Parallax

-

Apparent altitude Refraction

+

SD

+ -

Dip, @ sea-level

+

Obs. Alt. of Sun’s LL

00º 00.0' 0.2' --------00º 00.2' 00º 34.5' --------00º 34.3' 16.0 --------00º 18.3' 0.0’ --------00º 18.3'

The bearing amplitude of a body is the arc of the horizon contained between east and a rising body or between west and a setting body. The amplitude uses east and west as its origin.

W

The diagram shows the path of body X with a northerly declination, dXd, and the path of body

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Module: Topic 8:

Principles of Navigation Amplitude of Sun

MA0539

Y, with a southerly declination, DYD. Thus, the amplitude of body X rising is angle EZd and the amplitude of body Y rising is angle EZD. The amplitude of bodies X and Y setting would be angle WZd, and angle WZD, respectively. Clearly a body will always rise and set on a northerly bearing when its declination is north, and will rise and set on a southerly bearing when its declination is south. The amplitude, therefore, is always named the same as the body's declination. Finding the amplitude of the Sun is a quick and simple method of determining com error. Theoretical sunrise occurs when the centre of the Sun is on the observer's rational horizon. However, refraction, which is maximum at zero altitude, makes the Sun appear to rise about 35 minutes above the horizon when it is theoretically at an altitude of zero degrees. This value of 35 minutes roughly corresponds to the diameter of the Sun; to allow for this, amplitudes should be taken when the Sun's centre is about the Sun's diameter clear of the horizon. In other words, there should be a clearance about the Sun's semi-diameter between the horizon and the Sun's lower limb at the time of amplitude. The true amplitude may be calculated from the formula: sin Amplitude = sin Declination x sec Latitude. This formula is deduced from Napier's Rules for the solution of right-angled spherical triangles. The problem is much more readily solved by extracting the true amplitude directly from prepared amplitude tables. The L.M.T. of sunrise and sunset for any observer is listed in the Nautical Almanac for cer tain latitudes at three-day intervals. One must interpolate between the listed latitudes in order to obtain an accurate time of sunrise or sunset in intermediate latitudes. Example 1:

Sunrise dec 17d 08 h d (0.5) Dec Sin Amp Amp Amplitude True Azimuth Gyro brg Gyro Error

17 Jan 92: Lat 12º N Long 030ºW: Sin Amp

=

Sec Lat

x

GMT

=

17 d 08 h 23m

Gyro bearing 114ºG

Sin Dec

S 20º 51.8' 0.2' S 20º 51.6' = Sec 12º X Sin 20º 51.6’ = 1.0223 X 0.3561 = 0.3640 = 21.3º =E 21.3º S 111.3º T (90º + 21.3º = 111.3º) 114.0º G 2.7º H

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Module: Topic 8:

Principles of Navigation Amplitude of Sun

MA0539

You will note that amplitude is not named the same way as the azimuth. Amplitude is named East when the body is rising and West when the body is setting and North or South according to the declination of the body. In this case, the body is rising and the declination is South, therefore, the amplitude is named E and S. Summarise:

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