Had this question come up the other day, thought I knew the answer, but the more I thought about it the less I was sure.

Will an aircraft flying from east to west cover a trip of equal distance faster than the return west to east trip because of the Earth's rotation under the flight path? (Leaving out the effect of any jetstream or tailwind.)

My first inclination was to say yes... not by much, but a slight advantage would be present with the effect being more pronounced the longer the trip. But the more I thought about it the more I wasn't sure. Since any plane would take-off with a speed relative to that same rotation what would the difference really be? And if there was one is it independent of the speed of the aircraft? So, now I'm leaning towards no (even though I still really think yes deep inside).

I'm sure I could figure this out by doing a little math (hahahaha - yeah right) or bothering to get a few books off the shelf. But why not share with the folks at BA to teach and amuse a larger group? So, come on all you rocket scientists - give me a hand here.

Edited: Because after all this I got the initial question backwards anyway... duh!

Errrrp... I guess this really belongs in the General Astronomy forums - sorry. Chalk it up to exhaustion.

no.

Actually, this depends on which hemisphere you're in. The rotation of the Earth causes the winds to have a prevailing direction. In the north, it's west-to-east, and in the south it's east-to-west. Flying into these winds will slow you down, while flying with them will speed you up. This is really only terribly significant when flying into/agains the jet streams, though, as the prevailing winds to not necessarily dominate at any given time, or in any given place.

Note where he said:
I think he's talking about relativistic effects, however minor those may be.

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Oops. I completely missed that bit...
YOU'RE ALL CIA MISINFORMATION AGENTS!

Oh, wait. Wrong forum.

Yep.

Kenneth, you gotta give more than just "No" Why not?

Ok, I'm going to guess yes. And here's why.

When the plane is sitting still on the ground, it is moving with the speed of the ground. To hover over that position, it has to move a little faster in the same direction the earth spins.

v = (omega)*r for circular motion, right? To maintain the same (omega), or angular velocity, it has to increase its tangential velocity. If it doesn't do that, then it moves relative to the earth's surface. The higher it goes, the more pronounced this is. So, even if it does not change its speed at all, if it lifts off the ground, it will eventually end up over some other location.

That's just a guess, though.


Actually, I suppose that's an argument for the opposite, isn't it? Since the earth rotates from west to east (it does, right? Please tell me I'm not completely insane), you'd actually move west while hovering.

Hush, I'm tired, and had too much cola too late in the evening.

Hehehe... I knew this would be fun. How long before Jay, Glom or someone comes in and ruins my fun with a definitive answer? I suppose it will be at first light... Heh, who knew working the vampire shift has its advantages?

I like your response though Ut... makes sense to me. So, now I say "Yes" again (even though I'm secretly thinking "No", while deep down inside I think the answer really is "Yes").

Edit: Because I can't spell anyway let alone at 3am.

Three hours? One can of Coke says it's three hours.

Oh sweet Elvis, I have to stop drinking these...

As far as I can tell, it shouldn't make any difference at all...

Take for example, when you walk around on a train. Do you walk faster when going against the direction in which the train is traveling? Obviously not (unless you're doing it on purpose). To expand this example, think of a blimp... Should one take off and hover above the ground without any addtional propulsion, would the blimp travel at 30km/s (earth's rotational speed?) the instant it lifts off? The answer is no.

The illusion of "traveling faster when going against Earth" is only relative from a viewer far away, not influenced by Earth's gravitational pulls. In which case, the aircraft would either be way too small to be registered on any known device or way to slowly compared to Earth's own movements.

In practice, it is three hours. However, thats because planes flying from the US to Europe get to ride the Jet Stream, and so have a big helpful tailwind, rather than a headwind.

There are a couple of relativity effects usually attributed to Einstein, the time dilation due to motion, and the time dilation due to gravity. On the Earth, we have a varying motion (because of rotation and latitude) and varying gravity (because the poles are closer to the center of the Earth). However, the Earth's surface is an equipotential surface, which means that the two effects compensate, and cancel each other, on the surface of the Earth.

The geoid is an equipotential, not the surface. You still have altitude-dependent shifts. Time runs slower at sea level than it does on the top of Everest. Only ~100 ns a day slower (assuming my quick calculation was correct), but slower nonetheless.

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For most of the surface of the Earth, the geoid is the surface. But the point is the same as far as the OP--the rotation of the Earth is compensated for, so that eastward travel should not be different from westward travel.

Are you asking whether an observer who is staying put will measure a difference in travel time, or whether the people on the plane will measure a different travel time?

If you want to know about this from the perspective of the people on the airplane, then Hafele and Keating's results should apply. In that case, travelling eastward they lost time, and they gained time during the westward trip, so the trip east was indeed covered in less time.

From the point of view of the people on the ground, however, I think that there would not be any difference in travel time.

Wouldn't there only be a difference measured from a frame of reference not on Earth? Since the distance traveled is measured on the surface of Earth, not absolute distance though space.

Well, my first response would be to say "no" to the question.

However, consider this: looking down on the North Pole, Earth rotates in anti-clockwise direction on it's axis. Hence, we might argue that a plane traveling over the equator from East to West will take less time compared to the same journey backwards because the Earth is moving as well as we are in the air.

On the other hand, the plane moving from West to East over the equator (on our return journey) may get the aid of jetstream or whatever, however, that will not make the plane go any faster or reach our destination any quicker. Maybe, we will save some fuel.

Just some thoughts.

I would say that, (in a magical world where the speed of your trip is not effected by prevailing winds or jet stream of course) that the higher you go, the harder it would be to go east and the easier it would be to go west. Just as the bad astronomer said about space elevators here http://www.badastronomy.com/mad/1996/elevator.html altitude would definitely cause an advantage. It makes sense to me, therefore it must be true, right?

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And it was tens or hundreds of nanoseconds.

That was in regards to how long it would be until someone came along to ruin Rich's fun.


I still haven't seen anything said that says my idea is wrong. Ignoring general relativity, if you lift off from the planet, your angular velocity will decrease. Your linear velocity will remain the same, but your angular velocity will decrease.

omega = v/r

So, as r gets larger, omega gets smaller. If you're travelling at constant v, then, you'll see the Earth rotate beneath you.


Oh, but the answer is yes. It is already travelling at Earth's rotational speed even before it takes off. If it weren't, it would slide over the Earth's surface, right?


The relativity discussion taking place is really quite interesting. From the view of GR, does it matter which direction the plane is flying? The gravitational field can be considered constant at any given altitude, right? So, so long as you fly in either direction at the same altitude, there shouldn't be a difference. I haven't done GR in school yet, though, so this is over my head.

In the train example the person running to the front of the train would appear to be going faster than a person running to the back... to an outside observer. Just as a ball dropped on that train would appear to take a curved path to the outside observer, even while seemingly falling straight down to those on the train.

So to an outside observer would an westbound aircraft appear to go any slower as the planet turns in the same direction beneath it? Once again, ignoring the effects of any winds.

Ut, the fun continues!

I guess I owe you a Coke.

Does the atmosphere at high altitude rotate the same speed as Earth, or slower? Assuming impossible ideal conditions with no prevailing wind or jet streams, etc.

If it did, I'd call that a wind. At least, for my purposes (which deal mostly with hitting baseballs, and blowing bubbles )

30km/s is approximately Earth's orbital speed. Rotational speed is only about 465 m/s at the equator, less as you approach the poles.

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If the atmosphere rotates at the same speed as the Earth it wouldn't be wind because you are rotating along with it.

That depends on how you define speed. Tangential, or angular?

Angular.

Then I agree. Would you like a Coke, too?