| Overview Over
2000 years ago the Greek astronomer Eratosthenes figured out that the Earth was round, and
set out to measure its circumference (read the inlay Enrichment Focus 2.1 on page 28 of
the text for the full description). You can repeat his measurement of the Earth’s
circumference with the aid of a collaborator who lives at another latitude. This
demonstrates how the ancient Greeks knew the Earth was round, and how they were able to
use some simple math and trigonometry to measure its circumference. Understanding this
method should reinforce in your mind one of the first uses of the scientific method.
Observation
Details
First, you must find a patch of level ground. You
are going to measure the shadow cast by an object of known height, and the ground must be
level to allow an accurate determination of the Sun’s height.
Your
collaborator should be at a latitude at least five degrees different from your own and
preferably no more than six time zones away from yours. Since we all live at about the
same latitude here, I will assign you a collaborator, probably from New York (I am
teaching an astronomy course for a college in New York via the internet, and I am giving
them this same assignment!). I will give you contact information for your partner; it will
be your responsibility to work out the date of your observtion(s).
Both you and your
New York partner will need the following:
- A stick of length between one and two meters (one to two yards).
- If you can drive a stick into the ground, all you will need is the
stick and a measuring device. If you cannot
drive a stick into the ground, it would be easiest if you had a local partner to hold the
stick while you measure its shadow.
- A level to make sure that the stick to be measured is vertical. You can use a weight hanging from a string to determine
this as well.
- A means of measuring length, such as a meter stick or tape measure.
Observation Instructions
Both partners should perform the following steps on the same
day.
- Sometime between 11 AM and 1 PM local time (or in this case,
noon and 2 PM Daylight Saving Time) set up the stick so that it is vertical on level
ground. It is important that each partner take his or her measurements during the above
intervals in their own time zones.
- Measure the above-ground length of the stick and the length of
its shadow.
- Repeat the measurements, if possible, several times. The more
observations you can make, the better will be your estimate of the Earth's circumference
- Calculate the Sun's elevation (the angle that the Sun makes
with the horizon using the following equation:
Use the
program Excel to create a worksheet to complete the calculations. We will cover this in
class.
Using a road map, atlas or internet
source, determine the north - south distance between you and your partner. Do not bother
to measure the east - west distance between your locations, as that is unimportant.
Report your results to your partner.
Calculate the difference in Sun
elevation between the observations made by you and your partner. Then use the folowing
equation to calculate the Earth's diameter.
(the symbol p (pi) represents a number that is roughly equal to 3.14159)
Once you have
determined the Earth's radius, you can go on to find the diameter and circumference:
Earth's diameter = 2 x Earth's radius
Earth's circumference = 2p Earth's radius
Project
Objectives
- Determine the way in which the Earth’s curved surface makes the Sun
appear to be at different angles above the horizon when seen from different latitudes.
- Perform a simple analysis of collected observational data.
- Learn the benefit of combining observations to refine conclusions.
Project Components
You should submit
the following items in a simple lab report format including the information requested in
sections as specified below:
I. Introduction:
In this section you give some brief background information on the subject, and state
the nature and purpose of the observing project. All of the information you need to
complete this section is in the text, but you are welcome to use the internet as a
research tool as well.
II. Observations:
This section describes the details of your observations. You must include the following
information for both you and your partner:
·
State the date(s) and time(s) of
your observations
·
The city, state, latitude and
time zone of each observer
·
A brief description of what you
measured
·
The measurements themselves
III. Results and Discussion:
This is where you write about the results of your observations. This section must
include the following information:
·
The calculated Sun's elevation
for you and your partner
·
The Earth's radius, diameter and
circumference based on your calculations
You must show all of your math for the
calculations.
The answers to the following questions:
a)
How does your calculated value of
the Earth’s diameter compare with reality?
Note:
If your calculated results of the Earth's circumference do not agree to within plus or
minus 10% of the expected value, you and your partner should repeat your observations.
b)
What factors might have caused your
calculation to be in error?
IV. Conclusions:
In this section you summarize the project and
your results.
A simple
lab report such as this one should be about 1 or 2 pages in length.
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