A project about math, education, and math education.
Creating Planet Earth
Although it is a bit simplistic, to start, let’s assume Earth is a perfect sphere with a radius of 6378.1 kilometers. To simplify this, for our work in Geogebra later, simply use 6.378. Longitude is drawn by creating great circles, meaning their center is the origin. Assuming we will add a new line of longitude ever 10 degrees, find the equation for at least three of these great circles.
Making the same assumptions as problem 1, let’s move onto latitude. This is different than longitude because they are not great circles. Once again, see if you can come up with an equation for at least three of the “circles” of latitude.
Geogebra can be a little tough to use for this, thus I have included my planet Earth file here. Take a look and see if you can break down the parametric equations used. Also, feel free to create your own file from scratch and then compare your results to mine.
Turns out that Earth is only approximately a sphere and, when trying to create GPS systems, Earth is actually treated as an ellipsoid with an equatorial radius of 6378 km and a polar radius of 6356 km. Build an equation for this ellipsoid and graph it in Geogebra.
Now, the challenge many of you can probably see is that this messes with our latitude and longitude circles. Find a way to correct your equations and prove that they work with your Geogebra file.