 The loxodrome's whole length as it goes from the south pole to the north pole is fairly routinely seen to be "R" csc "θ" where "R" is the radius of the earth (in particular if the loxodrome goes straight east, it circles the earth infinitely many times without getting closer to either pole, so its length is ∞.Let a loxodrome pass through the point whose longitude and latitude are both 0; call this the "central point".Suppose one starts at the central point and travels a certain distance in a certain direction along this loxodrome and arrives at geographic location .