A- On Dec .21, what is the noon sun angle for someone at 54 degree N lat.?

B- In what horizon ( part of the sky using compass directions) is the noon sun?

Isn't Dec 21 the shortest day of the year? Hint: what makes it the shortest day of the year?

To find the noon sun angle on Dec. 21 for someone at 54 degrees N latitude, we need to consider the tilt of the Earth's axis and the position of the Sun in the sky.

On December 21, the winter solstice occurs in the Northern Hemisphere, which marks the shortest day of the year. This is due to the tilt of the Earth's axis away from the Sun.

To calculate the noon sun angle, we can use the concept of solar zenith angle. The solar zenith angle is the angle between the Sun and the observer's zenith (directly overhead point).

To calculate the solar zenith angle, we can use the following formula:

Solar zenith angle = 90 degrees - latitude + declination of the Sun

For Dec. 21, the declination of the Sun can be approximated to -23.5 degrees.

For a latitude of 54 degrees N, we can substitute these values into the formula:

Solar zenith angle = 90 degrees - 54 degrees + (-23.5 degrees)
= 12.5 degrees

So, the noon sun angle on Dec. 21 for someone at 54 degrees N latitude is approximately 12.5 degrees.

Now, moving on to the second part of your question, the direction of the noon sun depends on the observer's position and the season.

On December 21, the noon sun is in the southern part of the sky for observers in the Northern Hemisphere. Since you mentioned being at 54 degrees N latitude, the noon sun would be positioned in the southern part of the sky using compass directions. The exact compass direction would primarily depend on your specific location within the 54 degrees N latitude.

To determine the precise compass direction, you can use a compass or a smartphone app with a compass function. Stand facing north and determine the direction in which the Sun is located at noon. That direction would correspond to the southern part of the sky.

In summary, on December 21, the noon sun angle for someone at 54 degrees N latitude is approximately 12.5 degrees, and the noon sun is in the southern part of the sky using compass directions.