The Girth of the Earth
Geo Resource 1
A practical mathematics activity using some modern technology and a little straight
forward circle geometry to measure the circumference of our planet Earth.
A 14/15 year old student problem. (NZ Year 10/11).
If you just want the problem and no help here it is.
Task
Measure the circumference of the Earth.
Background Information and a few hints…
The Earth is nearly spherical and a cross section through the North and South poles is
a near perfect circular shape. By walking along this “great circle” or line of longitude a
little way we are measuring the length of a small arc which is part of the big circle. A
GPS unit, or an iPhone/Smart phone app such as “GPS Tracker” measures latitude
and longitude. A GPS measures to 1/1000 of a minute of arc. The app GPS Tracker
measures to 0.1 of a second. By working out how far one minute of arc is and then
multiplying by 360 we calculate the circumference.
http://en.wikipedia.org/wiki/Global_Positioning_System
Just Google “gps system”
Knowledge to remember
1 degree = 60 minutes of arc and 1 minute of arc = 60 second of arc.
The Global Positioning System (GPS) comprises 24 satellites (and a few spares), and
allows you to find your position with astounding accuracy and reliability. The US
military operate the system...see
http://www.colorado.edu/geography/gcraft/notes/gps/gps.html
You will need:
• a handheld GPS unit or the iPhone and GPS Tracker app.
• a measuring wheel or tape (see math dept)
• a flat area about 200m N-S long (playing field)
What to do:
• Turn on the GPS unit and let it establish an accurate 3D position of where you are.
This normally takes about 10 minutes. On a Garmin unit a row of black bars indicate a
solid and reliable reading. Or use your Smart Phone app.
• Work out which way North
• Position yourself at the South end of the field
• Let the GPS establish a reliable reading of your position and record the
latitude reading. (eg S 38 42.899)
• Walk North and using the measuring wheel at the same time measure
out 200m or so. More better!
• At the Northern end of your path let the GPS establish a reliable reading and record
your new latitude reading.(eg 39 42.996S)
DONE....Now for some maths.
Draw a picture of what you have done. This will help you understand what you are
measuring. A picture is worth a thousand words!
RECORD AND CALCULATION SHEET (Calculations use GPS data)
Name _______________________ Date ___________________
Place ________________________________________
GPS Reading at beginning ________________________(eg 38 42.889S)
GPS Reading at end ________________________(eg 39 42.996S)
Distance recorded ________________________ ( 200m)
Subtract the two GPS readings? ______________ AnsA (eg 0.107 minutes)
Divide the distance recorded by this answer to find how far in metres one minute
of latitude is ___________________ (1869.159m or 1.869km)
Multiply by 60 to see how far 1 degree of arc is_____________ (112.14km)
Multiply by 360 to measure the girth of the Earth is_____________ (40,370km)
How does this work?
Google “Earths circumference” to check your answer.
More questions! You might others as well.
Is the polar circumference longer or shorter than the equatorial circumference?
Should it be any different?
How can we get an answer using a Smart Phone?
Why are planets spherical?
The rocks at the center of the Earth are heavier. Why?
What makes the heat that makes volcanoes? [Te Papa Museum]
http://www.tepapa.govt.nz/SiteCollectionDocuments/Education/Programmes/Awesome_Forces_Years_3-8.pdf
Is gravity constant?
Does the magnetic field move?
Is True North the same a Magnetic North?
What is True North?
Why is the the Earth round? Is the Earth round?
What is latitude and longitude? What is a great circle?
What has Greenwich, England got to do with all this?
The formula for the circumference of a circle uses π. What is π?
What is the radius of the earth?
How far above the Earth’s surface are the GPS satellites?
What radio frequencies do they use?
What is the mass of the Earth? (Hint...use your mass)
Use and enjoy mathematics. If you wait for an eclipse you can also estimate the
radius of the moon and a few other things once you know a bit of physics.
http://www.astro.washington.edu/courses/astro211/CoursePack/cp03a_distance_sun.pdf
Resource by Jim Hogan 2013, http://schools.reap.org.nz/advisor/ , email jimhogan@clear.net.nz