##### Difficulty of Project

Hard

##### Grade Level

High School

##### Cost (Approximate Cost)

$5-$50

##### Safety Issues

There is no safety issues related to this project.

##### Material Availability

Materials are readily available at a local supermarket.

##### Approximate Time Required to Complete the Project

1-2 Weeks

### Objective

This project investigates how to determine the speed of earth’s rotation.

Using simple protractors and meter sticks the goal for this experiment is to measure the rate of angular change as the earth rotates around the sun and to extrapolate the data to deduce the speed of earth’s rotation.

### Materials and Equipment

- Protractor
- Meter Stick
- Clipboard
- Timer
- Writing utensil
- Data table

### Introduction

Earth rotates around the sun, the Earth's position changes relative to the sun. The Earth completes 360 degree rotation in 24 hours. The sun appears in different locations in the sky as the earth makes its complete rotation. The sun appears to rise from the horizon at dawn. The sun rises from the easterly side of the sky and appears to be in a position 90 degrees at midday and continues toward the westerly horizon. It is the position of the earth that is changing in relation to the sun while in fact the sun remains at a fixed point in the sky. The angle of the sun in relation to earth can be determined by applying the law of parallelograms and measuring the change in shadow length over time as shadow length changes when position of sun in relation to earth changes.

### Research Questions

- What geometric measurements are used to understand the earth moon sun system?
- How can navigators use geometric tools to study celestial bodies?
- What is the revolutionary path of earth?

### Terms and Concepts

- Geocentric Model
- Heliocentric Model
- Law of parallelograms
- Pythagorean Theorem
- Logarithm
- Rate

The diagram illustrates two views from Earth as it completes one rotation in 24 hours.

### Experimental Procedure

- Using a meter stick and one person, measure the length of the person’s shadow in millimeters for precision.
- Record the time of the measurement and length of the shadow.
- At precisely 5 minutes following the initial measurement, measure the length of the person’s shadow and the time of measurement.
- Repeat the measurements at 5 minute intervals for one hour ensuring the person remains in the same position.
- Measure the height of the individual in millimeters.
- For the shadow length at each time interval, divide the value of the shadow length by the individual’s height thus determining the slope of the line of the triangle formed from the individual’s position and length of shadow.
- Using logarithmic tables, find the value of the slope in the tan column of the logarithmic table to deduce the angle of the sun in relation to earth at that moment.
- For each shadow length, record the angle of the sun in relation to the earth.
- Using a protractor plot the angular change of the earth overtime. On the x-axis, time should be documented. On the Y-axis, the angle change should be documented. A linear correlation should form between the time and the angle change.
- The rate or speed at which earth moved from one point to another, or from one angle to another can be determined from the angular distance travelled divided by the time for the angular change. Using the known distance from Earth to the Sun as 1 astronomical unit and the angle change over time, the speed of the Earth’s revolution can be determined from the speed equals distance/time equation.

### Bibliography

- Office of Naval Research
- “The Earth’s Rotation and Reference Frames for Geodesy and Geodynamics” edited by Alice K. Babcock and George A. Wilkins. Published on behalf of the International Astronomical Unit 1988.

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