Now, a given point of coordinates (x, y) within the ellipse should belong to a given ellipse of the same eccentricity as the original ellipse (i.e. of semi-axes a and b) and with a given semi-major axis X, and hence this point should be on the velocity contour of v X , i.e. v(x, y) = v X . So, all we need to identify v(x, y) is to identify its corresponding v X , and this should be easily done by mapping the point (x, y) on the point (X, 0) where we exploit the basic mathematical formulae and relationships of ellipse, that is: