# 072 Laboratory 07: Latitude, Longitude, and Metric Measures

## Questions

How many meters per minute of latitude (or longitude)? What is the circumference of the earth in kilometers?

## Purpose and goals

1. To find a mathematical relationship between metric system meters and minutes of longitude or latitude.
2. To continue to develop the concepts of latitude and longitude and their orientation on campus.
3. To use the relationships between meters and minutes to calculate the circumference of the earth at the latitude at which the class is held.

Along a line of latitude, the longitude values increase or decrease.
Along a line of longitude, the latitude values increase or decrease.

Latitude and longitude are measured in degrees and minutes. There are 60 minutes in one degree. There are 360 degrees in one circle. Note that minutes of latitude and longitude are effectively measures of distance not duration, of space not time.

On Earth the equator is 0 degrees latitude. The north pole is north 90 degrees, +90°. The south pole is south 90 degrees, -90°. The equator is half-way between the north and south pole. Pohnpei is located about six degrees north of the equator, almost seven degrees. A global positioning satellite receiver (GPS) will display N 6° 54.580'. The 54.580 are the minutes, the apostrophe is the symbol for minutes.

On Earth the prime meridian is 0 degrees longitude. Pohnpei is located 158 degrees to the east of the prime meridian. The furthest east is 180 degrees. At 180 degrees east one is also 180 degrees west of the prime meridian. East longitude is positive, west longitude is negative. The GPS will display a number near 158° 09.350' minutes at the start of the laboratory.

In part one we will work outside. While outside we will use global positioning satellite (GPS) receivers to walk along either a line of latitude or a line of longitude. Lines of latitude run east - west. Lines of longitude run north - south. We will either walk along a line latitude heading due west, or walk along a line of longitude heading due north. Walking west along the line of latitude will cause the longitude value to decrease. Walking north on a line longitude will cause the latitude to increase.

The start and end longitude or latitude will be recorded using a GPS unit. We will also use the GPS to keep track of the number of meters we walk. A surveyor's wheel will be used to provide a second measure of the distance in meters. If we have more than one GPS, then we will use the extra GPS units to provide additional distance in meter measurements.

## Data gathering [d] [t]

Use the following tables to gather data. There may be changes in the equipment used on the day of the laboratory.

The following presumes that one is walking along a line of latitude.

Walking along a line of latitude from east to west
Line of latitude walked [d] Starting longitude [d] Ending longitude [d] Difference in minutes of longitude along the line of latitude [a]

An alternate table for walking along a line of longitude. Use this table if we walk along a line of longitude.

Walking along a line of longitude
Line of longitude walked [d] Starting latitude [d] Ending latitude [d] Difference in minutes of latitude along the line of longitude [a]

Measures in meters from the field and the computer laboratory

Meter measures
InstrumentDistance/meters
GPS #1 [d]
GPS #2 [d]
GPS #3 [d]
GPS #4 [d]
GPS #5 [d]
GPS #6 [d]
Surveyors wheel [d]
Google Earth ruler (part two) [d]
Mean distance in meters: [a]

In part two, power and Internet permitting, we will learn to use Google Earth to measure the same distance we walked. Google Earth has a ruler feature that can measure in meters.

When you first open Google Earth there may be display problems on Ubuntu Linux. The problem is with Google Earth and not Ubuntu Linux. The instructor will have to demonstrate how to work around the display glitches which cause Google Earth to incorrectly layer dialog boxes such as the ruler on the Google Earth main viewport window and ruler window.

Turn off the "atmosphere" option from the View menu. This will decrease the risk of a program termination due to insufficient memory.

Choose the Options item on the Tools menu.

On the Options menu, in the Show Lat/Long section, click on the radio button to select Degrees, Decimal minutes. This will display latitude and longitude in decimal minutes in Google Earth, which will concur with the set up of the GPS units.

Above the image seen in Google Earth is a blue ruler button, seen above on the right. Click on the ruler button. In the ruler dialog box changes the units to meters. Uncheck the Mouse Navigation box to make it easier to position your ruler.

In order to use the ruler, your instructor will show you how to drag the "invisible" ruler dialog box off the Google Earth screen. The layout that works best is seen below.

Note that the layout seen below may not be possible due to the display issues for Google Earth on Ubuntu Linux. DO NOT MAXIMIZE Google Earth nor resize the window - the program may quit abruptly (crash).

Drag the ruler from the start latitude/longitude to the end latitude/longitude based on the data from the GPS units. Write down the distance in meters from the ruler.

An alternative that would lead to the circumference of the Earth would be to walk a line of longitude such as E 158° 09.573'

## Data analysis [a]

1. Report the difference in minutes of latitude or longitude.
2. Report the mean distance in meters based on the GPS receivers, the surveyor's wheel, and Google Earth.
3. Calculate the number of meters per minute of latitude or longitude by dividing the mean distance in meters by the difference in minutes.

The following is done as a guided class lecture-discussion generating the experimental Earth circumference in class. This is done in a computer laboratory, providing the opportunity to introduce WolframAlpha as a way to obtain the answers to quantitative questions such as the circumference of the Earth

There are 60 minutes in one degree and 360 degrees in a circle. Multiplying those yields 21,600 minutes all the around the Earth. Multiply 21,600 minutes by the meters per minute calculation from above to determine the distance around the earth. Use this value to run an error analysis against the actual circumference of the Earth. The actual circumference for the equator is different from the circumpolar distance. Use the appropriate distance - equatorial or circumpolar - for your error analysis.

## Conclusion [c]

Wrap up with a discussion of the conclusions of this laboratory including answering the questions posed at the start of the laboratory. Consider what errors might be affecting the experimental circumference of the Earth. For example, did the class walk along a straight line? If not, would this affect the measurement? For a discussion of GPS position errors, see also the Kowoma site.

Also marked: [f] [GVOC]