Thread: Which way do I go

1. Originally Posted by fast
Let’s confine the parameters to the continental United States. Pick a point towards the middle such that the point can get no further from the border. Then, draw a circle around the point such that it can be no larger without crossing a border. I don’t know what the radius would be in miles, but i’ll just use a nice round number and call it 500 miles. The distance from the most northern point to the most southern point would be 1000 miles. East to west would be 1000 miles. In fact, every point would be equal distance to its opposite.

Now, let’s say the entire area of the circle was paved and flat and we ran a car race where we both averaged 100 MPH. We would essentially tie every time we raced. What’s most important here is that it wouldn’t matter what direction we raced. We always tie.

Now, you decide to take to the skies while I remain below. We run 360 races (one for each degree of the circle). In fact, it’s like running 180 courses twice—one one way and one the other way. No matter what, we always average 100MPH.*

But, we don’t tie anymore with one exception. You beat me each and every time except for the one time we tie. If I want to run the race again (and not lose) where do I start, and where do I finish? Essentially, what direction do I go? Which of the 180 tracks do I choose and which way do I run it?
It sounds like you are asking, "if you jump straight into the air, how for to the West will you land". Right? You are asking how far the planet moves beneath you in a given amount of time while airborne, versus being in contact with the ground? It also sounds like you are trying to compare two ground-racers.. but why would either beat the other when they are both traveling the same distance on the ground? The question doesn't really make sense to me.

That is just not how it works. Gravity affects the air just as much as the ground beneath it. The air is just a less-dense part of the planet, in a manner of thinking. Just like the water in the oceans.... The air moves with the ground as the planet rotates. Other forces affect the motion of air (wind from weather) which is caused by uneven heating of the surface of the Earth.... The ground itself does not move at different speeds relative to any other piece of ground (they do not move relative to each other, otherwise our planet would have ripped itself in half long ago)

2. Originally Posted by Jokodo
Originally Posted by fast
Maybe it’s the arcs representing flight paths that is giving the illusion that the planes aren’t flying straight. Maps don’t rotate. If the planes fly straight, they’re not flying toward their destination but instead where their destination is gonna be. A map would have to be virtual to capture that. A straight line to represent the plane not turning and a rotating map to capture earths spin.
The "arcs representing flight paths" are not due to the earth's spin or the planes anticipating where their destination will be, they're by and large due to the fact that the shortest route between any two points is never along a parallel (except when the parallel is the equator), but rather along a , plus some following winds.

Also, the shortest route from a point 500 miles to your east to a point 500 miles to your west does *not* cross your position, and that's true for air routes as much as surface routes. Unless, again, you're at the equator - or if by "a point 500 miles to your east" you mean the point you'd reach in a great circle route starting at your position with an initial bearing of 90.
A Great Circle is not a curved path. It is only a curved path when drawn on a flat map... as maps are. It is a correction of the error imposed by drawing the surface of a sphere onto a flat square.
A path "due East" around the equator of the planet is a straight line. It is not curved. Space-time is curved by the gravity of the planet. Your path through space-time is straight. Think of a satellite... Is it constantly turning to stay at constant altitude? nope. It is traveling straight, just like Newton predicted.

3. Originally Posted by Gun Nut
Originally Posted by Jokodo
Originally Posted by fast
Maybe it’s the arcs representing flight paths that is giving the illusion that the planes aren’t flying straight. Maps don’t rotate. If the planes fly straight, they’re not flying toward their destination but instead where their destination is gonna be. A map would have to be virtual to capture that. A straight line to represent the plane not turning and a rotating map to capture earths spin.
The "arcs representing flight paths" are not due to the earth's spin or the planes anticipating where their destination will be, they're by and large due to the fact that the shortest route between any two points is never along a parallel (except when the parallel is the equator), but rather along a , plus some following winds.

Also, the shortest route from a point 500 miles to your east to a point 500 miles to your west does *not* cross your position, and that's true for air routes as much as surface routes. Unless, again, you're at the equator - or if by "a point 500 miles to your east" you mean the point you'd reach in a great circle route starting at your position with an initial bearing of 90.
A Great Circle is not a curved path. It is only a curved path when drawn on a flat map... as maps are. It is a correction of the error imposed by drawing the surface of a sphere onto a flat square.
A path "due East" around the equator of the planet is a straight line. It is not curved. Space-time is curved by the gravity of the planet. Your path through space-time is straight. Think of a satellite... Is it constantly turning to stay at constant altitude? nope. It is traveling straight, just like Newton predicted.
Thanks for asking! Cars and planes are not satellites and great circle routes not orbital trajectories. Next question?

Other than that, I fail to see a Connection between my post and your response.

4. Originally Posted by Jokodo
Originally Posted by Gun Nut

A Great Circle is not a curved path. It is only a curved path when drawn on a flat map... as maps are. It is a correction of the error imposed by drawing the surface of a sphere onto a flat square.
A path "due East" around the equator of the planet is a straight line. It is not curved. Space-time is curved by the gravity of the planet. Your path through space-time is straight. Think of a satellite... Is it constantly turning to stay at constant altitude? nope. It is traveling straight, just like Newton predicted.
Thanks for asking! Cars and planes are not satellites and great circle routes not orbital trajectories. Next question?

Other than that, I fail to see a Connection between my post and your response.
orbital trajectories (which you never mentioned in your post) have nothing to do with great circles. and my response was adding to yours, not opposing it. "you" was the poster you were responding to... sorry that was confusing.

I still think the OP was more about a failure to understand that the air (for the most part) moves with the planet... and momentum keeps things moving that are already being moved by ground's rotation.

5. Originally Posted by Gun Nut
Originally Posted by Jokodo
Originally Posted by fast
Maybe it’s the arcs representing flight paths that is giving the illusion that the planes aren’t flying straight. Maps don’t rotate. If the planes fly straight, they’re not flying toward their destination but instead where their destination is gonna be. A map would have to be virtual to capture that. A straight line to represent the plane not turning and a rotating map to capture earths spin.
The "arcs representing flight paths" are not due to the earth's spin or the planes anticipating where their destination will be, they're by and large due to the fact that the shortest route between any two points is never along a parallel (except when the parallel is the equator), but rather along a , plus some following winds.

Also, the shortest route from a point 500 miles to your east to a point 500 miles to your west does *not* cross your position, and that's true for air routes as much as surface routes. Unless, again, you're at the equator - or if by "a point 500 miles to your east" you mean the point you'd reach in a great circle route starting at your position with an initial bearing of 90.
A Great Circle is not a curved path.
Say that again. Slowly.

Any straight path that starts on the surface of a sphere leaves that surface (either it's a tangent that heads off into space, or a chord that tunnels into the ground).

All paths that are bound to the surface of a sphere are curved.

6. So, if the lines running east and west are misleading, then running a perfectly straight steel ladder from the east coast to the west coast (or let’s say, perfectly east and west with no northern or southern bend), then besides the vertical bend, as it will concave down, a representation of that on a map will not appear straight. I guess.

7. Originally Posted by fast
So, if the lines running east and west are misleading, then running a perfectly straight steel ladder from the east coast to the west coast (or let’s say, perfectly east and west with no northern or southern bend), then besides the vertical bend, as it will concave down, a representation of that on a map will not appear straight. I guess.
A 500 mile long straight object running E/W along a latitude line (following the curvature of the Earth) will look straight on the projected flat map but appear shorter on the map than it actually is (except at the equator). For it to connect two points at the same latitude on the Earth that are 500 miles apart, it will look like an arc on the projected flat map,

ETA:
OOPS, brain fart. If the object is straight (except for following the Earth's curvature) then it can't stay on the same latitude for 500 miles. It has to look like an arc on the flat map with either the center or the ends not on the latitude line. So you are right, a straight ladder will appear curved on the flat map.

8. Other than the equator, a line of latitude cannot have a centre of curvature that coincides with the centre of the Earth. That is, even after accounting for the curvature needed in the plane of the gravitational pull, there must be an additional curvature in the plane normal to the pull of gravity. Only a Great Circle - a circle centred on the centre of the Earth - can curve only in the plane of the gravitational pull. And the shortest distance between two points on a sphere is the shorter of the two segments of a Great Circle that passes through both points. So a line of latitude is not the shortest distance between points of equal latitude. The shortest route will always entail moving closer to the nearer pole than the centre of the latitude line.

(A Rhumb line is a line of constant bearing; All straight lines on a Mercator Projection are Rhumb lines. These were important to navigation in the age of sail, when fuel costs were non-existent, and ships were steered by seamen who had varying degrees of skill or literacy - following a constant bearing is easy, while navigating a Great Circle, using just a compass, is hard).

9. Originally Posted by Gun Nut
Originally Posted by Jokodo
Originally Posted by fast
Maybe it’s the arcs representing flight paths that is giving the illusion that the planes aren’t flying straight. Maps don’t rotate. If the planes fly straight, they’re not flying toward their destination but instead where their destination is gonna be. A map would have to be virtual to capture that. A straight line to represent the plane not turning and a rotating map to capture earths spin.
The "arcs representing flight paths" are not due to the earth's spin or the planes anticipating where their destination will be, they're by and large due to the fact that the shortest route between any two points is never along a parallel (except when the parallel is the equator), but rather along a , plus some following winds.

Also, the shortest route from a point 500 miles to your east to a point 500 miles to your west does *not* cross your position, and that's true for air routes as much as surface routes. Unless, again, you're at the equator - or if by "a point 500 miles to your east" you mean the point you'd reach in a great circle route starting at your position with an initial bearing of 90.
A Great Circle is not a curved path. It is only a curved path when drawn on a flat map... as maps are. It is a correction of the error imposed by drawing the surface of a sphere onto a flat square.
A path "due East" around the equator of the planet is a straight line. It is not curved. Space-time is curved by the gravity of the planet. Your path through space-time is straight. Think of a satellite... Is it constantly turning to stay at constant altitude? nope. It is traveling straight, just like Newton predicted.
Having flown small planes, you fly a circular path above the Earth maintaining constant altitude. In vusual flight you keep the horizon in a fixed position to the aircraft.

If you flew in a straight line you either hit the ground or if ]f you have enough thrust leave the planet.

10. Wow. If I took out a large flat map of the US and placed a pin on the map that marks the point I’m at in South Carolina — and then — place another pin on the map that marks a point 1000 miles west of my location — and then — use a straight edge ruler to draw a straight line between the two pins, then not only would the path marked on the map not reflect the closest path to take to get between the two points, but the actual distance between the points (as the crow flies) would actually be less than 1000 miles. That means walking due west (or due east or due anything) is not a straight walk. The curved line IS the straight path.

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