# Amplitudes

An amplitude is the bearing of a celestial body as it rises or sets, illustrated in Figure 7.2 and Figure 7. 2b. To calculate a body's amplitude you need to know

1. Its declination

Lacking tables you need a calculator that can handle simple trigonometry. The general formula is:

Amplitude = sin~] (sin declination of body/cos your latitude).

Even if the declination and your latitude have different names, ie, one is north and the other is south, all the figures are taken as positive. Once you have the answer you will need to convert it into a bearing as shown in Figures 7.3, 7.3b and 7.4.

you are facing due north. It is straightforward to interpolate other cardinal points and bearings and to use the passage of the sun during the day to confirm your direction. It is rare for the sun to rise due east or set due west.

7.0 Facing South

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7.1 The Sun at Noon

7.2 Seasonal Path of the Sun

Even before doing your sums you know that north must be somewhere to starboard. After a couple of days on a long passage you will be right to within about 5°.

7.2b Amplitude by Rising Sun

An amplitude is taken when a celestial body is exactly on the horizon. Imagine you are watching the sun rise at 41 °N and the sun's declination is 23.5°N.

Amplitude = sin~] (sin 23.5 divided by cos 41) = sin-1 (0.3987 divided by 0.7547) = sin-1 (0.5283) = 31.8899 ° Call this 32°

Sin-1is calculator speak. What it means is that when you have finished dividing the sine of a body's declination by the cosine of your latitude then you hit the shift key on your calculator immediately followed by the sine key.

The exact keystrokes will vary from calculator to calculator. The shift key is sometimes called the mode key. Read the instructions to discover yours.

By the rules in Figure 7.4 the sun was rising so the amplitude is east.

The declination was north so the amplitude is north.

This translates your amplitude to a bearing of E32°N.

This is shorthand for saying the bearing was 32° north of east (Figure 7.3b). In 360 nomenclature east is 090° and 32° north from that is

If the sun had been setting the bearing would have been W32°N (Figure 7.3b). In 360 nomenclature west is 270° so

If the declination had been south then the bearing would have been W32°S and

Laid out like this it all looks more complicated than it is in practice. If you do not have a compass then twice-a-day amplitudes of the sun will give you a known direction. Added to finding north at noon it adds up to three checks each day. If you have a compass then amplitudes are a useful means of checking its accuracy.

7.3 Amplitudes Worked Example 7.3b Amplitudes and Bearings

If you know the declination of several stars then you can check your direction throughout the night. On a practical note, the sun lets you know it is coming over the horizon. A rising star is halfway up the sky before you have noticed it. Setting stars are best for amplitudes.

 Serial Rule 1 Amplitudes are east when the body is rising 2 Amplitudes are west when the body is setting 3 Amplitudes are north (of east or west) when the declination is north 4 Amplitudes are south when the declination is south.

7.4 Converting Amplitudes to Bearings

7.4 Converting Amplitudes to Bearings