How is the angle of inclination of the sun measured on the vernal or autumnal equinox at noon related to the latitude of our location here on earth. Use a picture that includes the earth and the sun in your explanation.

I'm completly lost

On the two equinoxes, the sun is midway between the north and south celestial poles. At noon on those dates (in the northern hemisphere), the inclination angle of the sun above the (southern) horizon equals the latitude.

A southern latitudes, the noon inclination angle is measured from the northern horizon, and a similar relation applies. The noon inclination angle (measured from north) equals the southern latitude.

thank you

I was wrong and careless. The latitude is the complement of the inclination angle at noon on the equinoxes. It is 90 degrees at the equator and zero degrees at the poles at that time.

Subtract the inclination angle from 90 degrees to get the latitude.

No worries! I'll do my best to explain it to you step by step, and I'll also provide a visual representation to help you understand.

First, let's start by understanding what the angle of inclination of the sun refers to. The angle of inclination is the angle between the sun's rays and a horizontal plane, usually measured at local noon.

To understand how it is related to the latitude of our location on Earth, we need to consider the Earth's axial tilt. The Earth's axis is tilted about 23.5 degrees relative to its orbital plane.

Here's a step-by-step explanation of how the angle of inclination is related to latitude:

1. Imagine that we are observing the Earth from space. The Earth is represented as a circle, and the Sun is shining light rays onto it.

2. Let's focus on a specific moment when the Earth is experiencing either the vernal (spring) or autumnal (fall) equinox. During these equinoxes, the Earth's axis is neither tilted toward nor away from the Sun, resulting in equal day and night lengths worldwide.

3. On the equator (0 degrees latitude), the Sun is directly overhead at noon. The angle of inclination here is 0 degrees.

4. As we move away from the equator towards higher latitudes, the angle of inclination increases. This means that the Sun's rays become more slanted and less perpendicular to the Earth's surface.

5. At the Tropic of Cancer (approximately 23.5 degrees north latitude) during the summer solstice, the angle of inclination reaches its maximum of 90 degrees. This means that the Sun is directly overhead at noon.

6. Beyond the Tropic of Cancer and moving towards the North Pole, the angle of inclination starts decreasing again.

7. At the Arctic Circle (approximately 66.5 degrees north latitude) during the winter solstice, the angle of inclination is 0 degrees again. This means that the Sun does not rise above the horizon at all, creating a polar night.

To help visualize this process, check out this image:

```
(Sun)
/
/
| | |
——————————————— Earth ————————————————
| | |
\ |
\Latitude
\
\
```

In this image, the Earth is shown as a circle, and the sun's rays are represented by the angled lines hitting the Earth's surface. As you can see, the angle of inclination increases as we move away from the equator towards higher latitudes.

So, in summary, the angle of inclination of the sun at noon on the vernal or autumnal equinox is related to the latitude of our location on Earth. As we move away from the equator towards higher latitudes, the angle of inclination increases, indicating that the sun's rays become more slanted relative to the Earth's surface.

I hope this explanation and visual representation have helped clarify things for you!