Hacker News Reader

Comment by rwmj | Hacker News Reader

I don't have a globe handy, but can't you sail indefinitely round and round Antarctica? Or doesn't following a line of lattitude count as a "straight line".

View on HN

that would certainly not be a geodesic (the only sensible defintion of "straight line" on a sphere), more like a circle. It would be just like running circles around your house.

You would have to keep turning slightly South to maintain a bearing parallel to the lines of latitude - the only one that's "straight" (it curves downward, but not North or South) is the Equator.

Source? My gut tells me this is not true, but I'm willing to be convinced.

Get a ball and a piece of string. Put the string on any two points of the ball and pull it tight. You'll observe that the path the string follows is part of an "equator" of the ball.

The problem is that the proposed solution doesn't "count" for the purposes of this experiment, which uses a great circle definition of "straight". The easiest way to visualise a great circle, is to place a piece of string over a globe between your origin and destination and pull it tight, that will track a great circle route between the two (and how a flight flying straight between Europe and the US west coast will take off on an pretty northern bearing, and land on a ditto southern, despite not actually going over the north pole and Europe and the US being located east/west of each other).

If you tried to place the string around Antarctica and pull it tight, it'd slip off in the southern direction, which represents the parent's explanation that you'd be steering south (from a great circle course) to keep straight along a latitude.

>> larkeith: You would have to keep turning slightly South to maintain a bearing parallel to the lines of latitude - the only one that's "straight" (it curves downward, but not North or South) is the Equator.

> dbatten: Source? My gut tells me this is not true, but I'm willing to be convinced.

Consider any point on a sphere, pick a direction (which might be along a line of latitude) and visualise the plan defined by that vector and the centre of the sphere. The intersection of the plane with the surface of the sphere is a Great Circle, and that is where you would go if you didn't apply turn to the rudder.

The parallel of latitude defines a plane that does not go through the centre of the sphere (unless it's the equator) and so isn't a "straight line". If you want to stay on the parallel of latitude then you will deviant from the Great Circle, and that's why you need to apply rudder to stay on the parallel instead of the Great Circle.

Does that help?

This is all pretty obvious once you've done some spherical geometry, but can be completely opaque to anyone who hasn't.

It’s confusing because the latitude line 66° south looks like a straight line on a globe. But to sail in a “straight line”, which means keep your steering centered forever, you will travel in a great circle.

All great circles lie on a plane that intersects the sphere (earth) through the center of the sphere. You can see that the only latitude line that’s on a plane intersecting the center of the earth is the equator, and that 66° south doesn’t. This also means that all straight line paths on earth touch the equator at 2 opposing points. Or said another way, you can start with the equator, pick any one point on the equator and rotate it around that point to get a new great circle.

So in order to stay sailing along 66° south, you’d have to have your steering turned constantly just a little bit south.

> It’s confusing because the latitude line 66° south looks like a straight line on a globe.

On the contrary, latitude 66° on a globe looks to me like a fairly tight circle.

http://wordpress.mrreid.org/wp-content/uploads/2011/07/antar...

It sure does, you’re right. So does any “straight line” great circle too, so that isn’t super helpful. The equator has the same circle projection that 66° does.

Look at it from the side and it looks straight. If you’re sitting in the plane of 66°, the projection is straight.

I was trying to be supportive of @dbatten while explaining. It’s easy to get confused about what straight means on a sphere, since nothing is actually straight.

May apologies if I sounded knee-jerky. The intention was to show that a picture was a better answer to @dbatten's very legitimate comment.

The idea is to demonstrate that a "straight" line on a surface needs to be viewed along a normal to that surface at the point of the line you are concerned with, assuming the definition of "straight" is "don't have to turn when travelling along line on the surface". That makes great circles look straight, and non-great circles not.

No line of latitude is straight, except arguably the equator.

Think about the line of latitude at 89.9999°. It will trace a circle around the pole of a few meters radius. 60° south is the same such circle, only bigger.

Reply on news.ycombinator.com