I'm using a tool I've found online (https://planetcalc.com/713/), which allows calculating the distance between two points on loxodrome using a formula that considers the WGS 84 ellipsoid model. In particular, I want to know the distance only along a meridian, thus the longitude is constant to zero. I set then the starting latitude point to 0°0'00'' and I adjust the end latitude point to specific values which allow returning specific distance values, i.e. multiples of 500 metres. The goal is to extract the latitude values for multiples of a given distance and export them to an Excel spreadsheet.
The formula used to calculate the distance on loxodrome is as follows:
$$S = a * sec \alpha \Biggl[\left(1-\frac14e^2\right)\Delta\phi - \frac38e^2(sin2\phi_{2}-sin2\phi_{1})\Biggl]$$
Where:
- a: semi-major axis of the ellipsoid
- α: course angle (which is zero, considering the longitude Δλ = 0)
- e: eccentricity of the ellipsoid
- ϕ1: starting latitude point
- ϕ2: end latitude point
- Δϕ: difference between ϕ2 and ϕ1
I thought I could automate this process by reversing this formula and isolating ϕ2, but I have no idea how to do it.
I've tried to use the SOLVER.XLAM add-in on Excel by forcing the distance (S) to exact values and find the latitude which returns that distance, but it is not as precise as I'd need.