A point due east of me is closer to the equator? [duplicate]

Question

This footnote:

East-west directions can be misleading. Point B, which appears due East from A, will be closer to the equator than A. Thus the curvature found this way is smaller than the curvature of a circle of constant latitude, except at the equator. West can exchanged for east in this discussion.

appears on the Wiki page regarding Earth radius. This does not correspond to my understanding of the geometry for an ellipsoidal Earth: if I move due east, I'll stay at the same latitude, and thus I'll still be the same distance way from the equator.

I what sense is a point B that is due east from A "closer to the equator"?

In fact, how can this make sense? nothing in the problem setup differentiates point A from point B, so neither can be closer to the equator than the other since the problem is symmetric.

In response to duplicate question comments: whether I move from A to B via a great circle or via a rhumb line, it shouldn't affect whether one of the two points is closer to the equator than the other.

Answer 1

You need to define exactly what you mean by "move due east"!

If you follow a rhumb line (aka a loxodrome) you will

• always be travelling east
• be following a parallel of latitude
• not be going in a straight line (ie, not the shortest path)
• stay at the same latitude

If you follow a great circle (aka a geodesic or orthodrome), one that is initially heading east, you will

• be changing your azimuth as you go
• be moving away from east (how quickly you do this depends on how great is your initial latitude) as you go
• be going in a straight line (taking the shortest route)
• be moving closer to the equator and eventually cross it

Depending which route you take, you will end up at different points B.