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Compare Sun's Zenith to Sunrise and Sunset

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Author: Bob Bonnet and Dan Keen

Purpose or Problem

The purpose is to determine if the Sun's highest altitude in the sky during the day is at the time exactly halfway between sunrise and sunset.

Overview

The Sun illuminates half of the Earth all the time. But the length of daylight is not half of a day (12 hours) every day. In fact, the length of daylight changes daily and varies at different locations on the Earth.

From about December 22nd to June 21st, the length of daylight increases daily in the Northern Hemisphere, and it decreases from June 21st to December 22nd. This is because the Earth does not spin on its axis in the same plane as it orbits the Sun. The Earth is tilted toward the orbiting plane at a 23½ degree angle.

This tilt not only accounts for why the length of daylight varies, it also gives us a changing of seasons from spring, summer, fall, and winter.

The Sun rises in the east and sets in the west, but the path it travels across the sky changes as the seasons change. The altitude (its height above the horizon) of the Sun reaches a higher angle during the day in the summer than in the winter.

Does the Sun reach its highest point in the sky (its zenith) during the day at the time that is halfway between sunrise and sunset for that day?

Knowing the position of the Sun at all times during the day throughout the year at a particular location is important to architects who design buildings. They need to know how much sunlight will enter through windows because this will affect their designs for lighting, heating, and air conditioning.

Hypothesis

Hypothesize that the Sun reaches its zenith during the day at the time that is equally between sunrise and sunset.

Materials List

  • 1×1 square piece of plywood
  • Large protractor
  • Pencil
  • Carpenter's level
  • Modeling clay
  • Sunny day
  • Time of sunrise and sunset for that day (available from a daily newspaper, the Farmers' Almanac, your local radio station, or a National Oceanic and Atmospheric Administration (NOAA) weather radio)
  • Possible adult supervision needed

Procedure

First, be sure you never look directly at the sun! Next, find the time of sunrise and sunset for the day you do this project. These times can often be found in a local daily newspaper, from an almanac, from the news on a local radio station, or from a NOAA weather radio.

Then, calculate the total number of minutes between sunrise and sunset. Divide that number by two. Convert the answer to hours and minutes. Add that to the time of sunrise to arrive at a time that is midpoint between sunrise and sunset.

Now, mount a protractor on a small piece of plywood, so it stands perpendicular to the board. Modeling clay can be used to secure the protractor.

Next, set the protractor device outside in an area that receives unobstructed sunlight all day. Lay a carpenter's level lengthwise, and then widthwise, to level the board. Pile a little sand or small stones under the board to level it.

The reference point of zero on the protractor will be held constant (the plywood and protractor will be kept level horizontally with the ground). The movement of the Earth is the variable in this project.

About two hours before midday, begin measuring the angle of the Sun's altitude by placing the point of a pencil by the base at the middle of the protractor, and raising the pencil up or down until no shadow of the pencil is cast. Remember, do not look directly at the sun during this project. Check the angle of the pencil by reading the increments on the protractor.

Make these measurements at ten-minute intervals. Write down the angle of the Sun's height.

Continue making measurements until one hour after the Sun's angle begins to decrease.

Did the Sun's peak height occur at about the time you calculated the midpoint between sunrise and sunset?

Results

Write down the results of your experiment. Document all observations and data collected.

Conclusion

Come to a conclusion as to whether or not your hypothesis was correct.

Something More
  1. Is the Sun always at zenith at 12 o'clock noon?
  2. Determine the azimuth (the angle between sunrise in the east and sunset in the west) of the Sun. Thumbtack a piece of white paper onto a piece of plywood, and slightly hammer a nail in the center through the paper and into the plywood, just deep enough for the nail to hold. At sunrise, draw a line tracing the shadow cast by the nail. Just before sunset, when the shadow cast by the nail is about to disappear, draw a line tracing the shadow. Measure the angle. Repeat this once a week for a month. Does the angle change? Is the angle increasing or decreasing in size? Which season are you headed toward? Does the peak height of the Sun in its path across the sky change from week to week?
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