Magnetic Declination from Sun's Bearing

This explanation details how to determine the magnetic declination using the provided magnetic bearing of the sun at noon.

Declination Concepts Explained

• Magnetic Bearing: The angle measured clockwise from the Magnetic North direction to the line of sight of an object.
• Magnetic Declination: The angle between the direction of True North (geographic north) and the direction of Magnetic North. This angle varies depending on location and time. It is specified as East (E) or West (W) declination.
• Sun at Noon: At local apparent noon, the sun reaches its highest point in the sky. For observers in the Northern Hemisphere, the sun is approximately due South at this time. The true bearing to the sun is therefore approximately 180°.

Calculating Declination Steps

We are given the following information:

• The magnetic bearing of the sun at noon is $179^{\circ}$.
• We assume the sun is exactly due South at local noon, which means its true bearing is $180^{\circ}$.

The magnetic declination is the angle between True North and Magnetic North. Let's denote this declination as $D$.

If Magnetic North is East of True North, the declination '$D$' is positive (East). If Magnetic North is West of True North, the declination '$D$' is negative (West).

We can establish the relationship using angles measured clockwise from True North:

• Angle from True North to the Sun = $180^{\circ}$ (True Bearing)
• Angle from True North to Magnetic North = $D$ (Declination)
• Angle from Magnetic North to the Sun = $179^{\circ}$ (Magnetic Bearing)

The relationship between these angles is:

Angle (True North $\rightarrow$ Sun) = Angle (True North $\rightarrow$ Magnetic North) + Angle (Magnetic North $\rightarrow$ Sun)

Substituting the known values:

$180^{\circ}$ = $D$ + $179^{\circ}$

To find the declination $D$, we rearrange the equation:

$D$ = $180^{\circ}$ - $179^{\circ}$

$D$ = $1^{\circ}$

Since the resulting value for $D$ is positive, it indicates that Magnetic North is $1^{\circ}$ East of True North.

Declination Result

Therefore, the magnetic declination is $1^{\circ}$ East.