Constraint 1 given in section 1.7 can be stated
as...
Putting constraint 2 of section 1.7 into
mathematics gave me some severe headaches. This constraint states that the Y value on the
central meridian is the length of arc from the equator to the point on the earth. As a
mathematician I automatically took the following approach...
Where ds is the differential arc segment and C is the arc line. Using pythagoras's
theorem and noting that we are on the central meridian so y is always 0.
Then parametrizing the arc with t one gets the standard second year calculus result...
Filling in the values of x and z from the parametric equations of the spheroid one
gets...
Or in terms of the eccentricity is...
