3 ms·
I think about this sometimes, so I like the idea, but how do you define “straight” on an oblate spheroid? Great circle, constant direction (e.g. “due east”), or
by munchler 1y ago
I think about this sometimes, so I like the idea, but how do you define “straight” on an oblate spheroid? Great circle, constant direction (e.g. “due east”), or something else?
- diggan 1y agoProbably not scientifically accurate or anything, but if you point somewhere, then "straight" is in that direction. I guess it'll loose accuracy as you get further and further in the distance of the direction, but probably for most people would be good enough for "straight in that direction" :)
- brgross 1y agoI went with great circles since that feels like the most “natural” straight line on a sphere — the path you’d walk if you just kept going forward without steering. You could define "straight" as a constant compass direction (I think it's called a "rhumb") -- that would look straight on a Mercator map but would actually require regular steering adjustments to maintain the bearing.
- munchler 1y agoThat makes sense, but I think constant latitude, in particular, is a special case that people often have in mind.
- deleted 1y ago[deleted]
- zamadatix 1y agoThe other methods are about defining different meanings of what "going around" actually is while constant latitude is a special case of many such methods, e.g. great circle, not a new definition of what going that way means.
- lqr 1y agoThe mathematical field of Differential Geometry can answer this question precisely: https://en.wikipedia.org/wiki/Geodesic#Affine_geodesics https://en.wikipedia.org/wiki/Geodesic#Affine_geodesics An oblate spheroid is an example of a Riemannian manifold: a smooth object that looks like a plane (or, in general, any ℝ^n) locally, and has a way to measure angles between vectors in that local plane. All Riemannian manifolds have an object called the Levi-Cevita connection, which defines how vectors in the local plane (tangent space) most naturally map to vectors in other tangent spaces in the immediate neighborhood. Standing at a point on the Earth and looking in a certain direction gives us 1) a point on the manifold, and 2) a direction in that point's tangent space. We then take an infinitesimally small step forward, and apply the Levi-Cevita connection to get from the old tangent space to the (infinitesimally nearby) new tangent space, and repeat. This defines an ordinary differential equation. Integrating the differential equation gives us a curve through the manifold. Within some neighborhood of the initial point, this curve is a geodesic, i.e. the shortest path between the initial point and all subsequent points on the curve. This matches our typical intuition of "straight". (Disclaimer: I am currently learning about this topic, but am not an expert.) edit: https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid goes into some interesting specifics about the results of this process on ellipsoids.