# Calculate Sun Angle: Length of Object by Shadow

• Ba
In summary, the angle the sun is in the sky at a certain time of day is based on two components, one that varies with a 24 hour period, and one that varies with the season.
Ba
Can somebody explain how to calculate the sun's angle in the sky at a certain time of day? It is wanted to calculate the length of an object by it's shadow.

It's based on the law of cosines from spherical trigonometry. The site http://www.krysstal.com/sphertrig.html has what you want about the shadow, but you have to scroll past a lot of stuff about great circle distances and the direction of Mecca.

The easiest way to get the angle it set up a short stick you can measure, then compute the angle. You can then apply that to an object you wish to find the height of. You need to work fast, the angle is always changing.

A planetarium program will tell you if you don't feel like calculating it...

russ_watters said:
A planetarium program will tell you if you don't feel like calculating it...

Aww, that's no fun! See Asimov's story "The Feeling of Power".

Well, I will say you haven't lived until you've done celestial navigation... after a half an hour of measurements, calculations, and plotting, you'll know that half an hour ago, you were within 5 miles or so of where the GPS told you you were.

Thanks, we wanted to try and find the angle as exact as possible.

Ba said:
Can somebody explain how to calculate the sun's angle in the sky at a certain time of day? It is wanted to calculate the length of an object by it's shadow.

There are two components to the suns angle in the sky.

One of them varies with a 24 hour period, you can correct for this component by making your measurements at local noon. This component is due to the rotation of the earth.

The other component will vary with the season, it will have a 1 year period, and it will depend on the latitude of the observer.

If you ignore the axial tilt of the earth, you can probably see if you think aobut it a lot that the sun would be always on the horizon at the poles, and it would pass directly overhead on the equator.

Because of the axial tilt of the earth, this actually happens only on the equniox.

## 1. How do you calculate the sun angle for an object's shadow?

The sun angle for an object's shadow can be calculated by using the length of the object's shadow and the height of the object. You can use the formula tan(θ) = shadow length/ object height, where θ is the sun angle.

## 2. What is the purpose of calculating the sun angle for an object's shadow?

Calculating the sun angle for an object's shadow can help determine the time of day and the position of the sun in the sky. It can also be used for navigation and tracking the movement of the sun over time.

## 3. What units are used for measuring the length of an object's shadow?

The length of an object's shadow is usually measured in feet or meters. However, any unit of length can be used as long as it is consistent with the unit of measurement used for the object's height.

## 4. How accurate is the sun angle calculation for an object's shadow?

The accuracy of the sun angle calculation depends on the accuracy of the measurements taken for the object's shadow and height. The more precise the measurements, the more accurate the calculation will be.

## 5. Are there any online tools or apps that can calculate the sun angle for an object's shadow?

Yes, there are many online tools and apps available that can calculate the sun angle for an object's shadow. These tools use your location and the current date and time to accurately calculate the sun angle. Some popular examples include SunCalc, Sun Position, and Sun Surveyor.

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