Motion of the Sky

Overview

As the Earth spins on its axis, the rotation makes the Sun, Moon, stars, and planets seem to move across the sky from east to west. Near the celestial poles it appears as if objects move in circles around the pole, while at the celestial equator they move in what appears to be a straight line across the sky. Each day all the objects appear to make one full circle of 360° (although for most stars half of this circle is below the horizon). For more about the motion of the stars across the sky, read section 1.1 on page 4 of the text.

By watching one object and measuring its movement in a known amount of time you can measure the Earth's rate of rotation. As a group we can measure these movements and compare them for different objects. Since the motion is caused by the rotation of the Earth and not the individual motions of the objects, we certainly hope that all our measurements will agree!

Measuring Angles in the Sky

This project requires that you measure the position of an object in the sky at two times, using your hand as a measurement tool. To see how this works, make a fist with your hand and extend your arm outward in front of you so that it is fully extended. The width of your fist, from the thumb side to the little finger side, is roughly ten degrees. Now extend your index finger upward. Its width is approximately two degrees; your middle finger is approximately one degree. Finally, take a look at the fingernail on your little finger: it is about a half degree across. For a graphic representation of this measuring technique, refer to Figures 1.2 and 1.3 on page 6 of the text.

Combining these different angular sizes lets you measure the angles between two points in the sky. For example, two stars might be two fists + three thumbs, or roughly 26°, apart. In general it is very difficult to be highly accurate with this method, but it is good enough for our purposes.

Method

Select a planet or a star near the celestial equator from the supplied list. How do you know where the celestial equator is? When looking southward the celestial equator is 90° minus your latitude above the horizon. For example, if you are at 30° north latitude, the celestial equator is 90° minus 30°, or 60°, above the southern horizon.

Choose a location from which to view the object, making sure that there is unobstructed sky to the west of the object (since that is where it is going to move). Make a mental or written note of exactly where you are standing; in a couple of hours you will be returning to within one foot of this spot, perhaps in the dark.

Select a landmark such as a tree or building on the horizon that is beneath the chosen object. Measure how many degrees there are between the landmark and the object.

Allow at least two hours to pass.

Standing in the same place as you were in Part 2, measure how far above the landmark the object is, and how far to the west the object has moved. Record these measurements.

Next, we will use the Pythagorean theorem (a² + b² = c² ) to determine how many degrees the star has moved. For the purposes of this project, we use the following form of the Pythagorean theorem:

The equation above translates to the following statement:

          the number of degrees the object has move equals

          the square root of the number of degrees the object has moved vertically squared

          plus the number of degrees the object has moved horizontally squared

Confused? No problem! Here's an example. Let's say when you make your first observation, the object you are observing is 5 degrees above and 5 degrees to the west of your landmark. Two hours later, the object is 10 degrees above and 32 degrees to the west of your landmark. That means that in two hours, the object traveled 5 degrees vertically and 27 degrees horizontally. Then we plug those figures into the equation:

degrees moved = square root of vertical movement squared plus horizontal movement squared, or

                         So the object moved a total of 27.45 degrees

After completing the calculation above, divide the degrees the object has moved by the number of hours between your observations. This is the number of degrees the object moves each hour. Once again using the example above, we divide 27.45 by 2, giving a result of 13.7. This means that the object you observed moved 13.7 degrees per hour.

Finally, check your observational results against your expected results. How many degrees per hour should an object near the celestial equator move per hour? If you don't know, discuss it with your classmates, or do some research using the internet. (hint: the Earth turns on its axis once every 24 hours, so a given point on the equator moves through 360 degrees in 24 hours). If your results are not within plus or minus 5 degrees the expected amount, there must have been a flaw in your observational techniques. Re-read the instructions carefully, and repeat your observations. If you cannot get the expected value, ask your fellow classmates for help and advice. If no one in the class is able to figure it out, we will cover the subject again as a whole class.

Answer this question: Is the result in the example given above, 13.7 degrees of motion per hour for an object near the celestial equator, within the accepted margin of error? In other words, would this observation need to be repeated, or would you consider it valid?

Project Objectives

• Determine the rate at which the Earth's rotation causes stars and other sky objects to move
• Perform a simple analysis of observational data
• Learn the benefit of combining observations to refine conclusions

Project Components

• Complete the observations (repeat if necessary)
• Record the data
• Complete the calculations
• Submit the lab report in required format (described below)

Lab Report Requirements

You should submit the following items in a simple lab report format:

I.  Introduction:
In this section you give some background information and state the nature and purpose of the observing project. All of the information you need to complete the introduction can be found in this document.

II.  Observations:
This section includes information on your observations. You must include the following information:

·          the date and time of your observations

·          your latitude and longitude, city and state

·          the name of the object you observed

·          the measurements you made at the two (or more) observing times

III.  Results and Discussion:
This is where you give the results of your observations. You must include the following information:

·          How many degrees did the object move per hour? You must show your mathematical calculations. (You can just describe the calculations using words if you do not have the capability of inserting the math symbols.)

·          How does this compare with the expected value for objects located on the celestial equator?

·          Explain how you came up with the expected value for objects on the celestial equator.

·          If your first set of observations did not give you the expected value and you had to repeat your observations, tell how you think your first set of observations went wrong.

·          How does knowing how many degrees an object near the celestial equator moves per hour tell you the spin rate of the Earth?

IV.  Conclusions:
In this section you summarize the project and your results.

A basic lab report such as this one should be about 1 or 2 pages in length.

Happy Observing!!

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