00:05
We're asked to answer questions relating to the world geodetic system in 1984's ellipsoid model of the earth's surface.
00:19
So we're told that this place is the center of the earth at the origin and the north pole on the positive z axis.
00:26
The distance from the center to the poles is 6356 .523 kilometers and the distance to a point on the equator is 6 ,378.
00:37
178 and 137 ,000 kilometers.
00:46
In part a, we're asked to find an equation of the earth's surface as used by the wgs 84.
00:57
Well, to do this one, you mean an equation for an ellipsoid centered at the origin, so ellipsoid which is centered at the origin, which has intercepts x equals plus or minus a, y equals plus or minus b and z equals plus or minus c well this is the equation x squared over a squared plus y squared over b squared plus z squared over c squared equals one now the poles of the model intersect the x axis at z equals plus or minus 63 56 .523 and the equator intersects the x and y axes at x equals plus or minus 6 ,378 .137 and y equals plus or minus 6378 .137 and therefore an equation for the earth's surface is x squared over 6378 and 137 squared and 137 squared plus y squared divided by 6 ,378, and 137th squared plus z squared divided by 6 ,356, and 5233 ,000 squared equals 1.
03:35
In part b, we're told that curves of equal latitude are traces in planes z equals k.
03:53
And we're asked to find the shape of these curves.
04:02
Well, traces in z equals k, well, these are circles with equation x squared over 6378 .137 squared plus y squared.
04:24
Over 6378 .137 squared equals 1 minus k squared over 6356 .523 squared...