Silly question: balloon floating above vs with the Earth

[wildetudor]

Hi everyone

I had this very silly question pop up that unfortunately I cannot find an answer to myself. If an object - say, a hot-air balloon - flies at a low altitude above the Earth, it will of course remain above the same spot; you could I guess say that it rotates together with the Earth.

However, if the balloon were to rise at a much higher altitude, I'd think that, at some point it will stop being "connected" to the mass of air rotating together with the planet, and it is conceivable that, watching from up there straight down, one would not see the same spot but whatever part of the Earth happens to be immediately underneath at that time, due to the rotation. This reasoning has got to be false, though, since no helicopter that wants to go from A to B could simply climb to a certain altitude and just 'wait' until they're above B - or could they?

Is Earth's athmosphere the reason why air-borne objects are always (or at least up to a certain altitude) "engaged" to the planet's rotation?

I've probably even phrased the problem in too simplistic terms, that maybe ignore the real phenomena at play, however any reply that might help clarify my question will be appreciated!

 

[A.T.]

it will of course remain above the same spot

Only if there is no wind.

However, if the balloon were to rise at a much higher altitude,

How high?

I'd think that, at some point it will stop being "connected" to the mass of air rotating together with the planet,

A hot air baloon leaving the atmosphere?

and it is conceivable that, watching from up there straight down, one would not see the same spot

Sure. Even if there is no wind, the Coriolis acceleration would shift it during the rise.

 

[wildetudor]

Oh, of course, should have mentioned that I was assuming the absence of wind in the balloon thought experiment.

So the force making any flying object rotate with the Earth is not from a body of air (the athmosphere) but is instead the Coriolis force?

And there is no altitude high enough that a flying object could rise to escape being rotated together with the earth?

 

[A.T.]

So the force making any flying object rotate with the Earth is not from a body of air (the athmosphere) but is instead the Coriolis force?

No, the Coriolis force will prevent the balloon from rotating exactly with the Earth.

And there is no altitude high enough that a flying object could rise to escape being rotated together with the earth?

You don't need any altitude to escape being rotated together with the earth. Just stand on the North Pole and rotate opposite to the Earth.

 

[wildetudor]

Thanks, although I'm still not fully clear on all forces that are at play in these hypothetical situations, and exactly how much of what is above the Earth rotates together with it :)

 

[SteamKing]

What about the moon?

 

[TumblingDice]

Thanks, although I'm still not fully clear on all forces that are at play in these hypothetical situations, and exactly how much of what is above the Earth rotates together with it :)

Perhaps reworking your thought experiment is in order. What A.T. pointed out is you're using a hot air balloon which is bound and limited by the atmosphere. The balloon will always be affected by the atmosphere, and it's impossible for it to rise above the atmosphere. Ergo, there's no way to use this thought experiment to measure it not being connected with the atmosphere.

Edit: Perhaps it's clearer to suggest that, by using a balloon, you're really just measuring the motion and influence of the atmosphere. Once it reaches equilibrium temperature and density and stops rising, it could be said it becomes just another part of the atmosphere. So to answer your OP, the atmosphere is influenced by many things, and in this experiment the answer would be, yes, the atmosphere controls the bearing of your balloon.

Are you actually interested in atmospheric effects, or in orbits? For example, if the Earth had no atmosphere...

 

[wildetudor]

Yes, my question was really just about the phenomenon that allows flying objects to rotate together with the Earth, and at what point (presumably, when they are far enough) objects become independent of that. Factors such as wind or the mechanism by which the object stays airborne (as you pointed out, the balloon would *need* the athmosphere to even stay airborne) I was not concerned with, and perhaps I should have made that clear in the OP :)

The orbit I guess would be a different question, since it would imply the flying object being on an elliptical/circular trajectory around the Earth, and the centrifuge would in that case be what's keeping it in orbit (equal magnitude & opposite direction from the gravitational force).

 

[Drakkith]

Remember that you are already moving when you lift off from the Earth. Without a way to counter this, you will keep moving in the same direction no matter how high you get. Combined with the Earth's gravity, this means that there is no height that you can reach with a balloon to get away from this.

 

[voko]

Flying objects rotating with the Earth would be exceptional. Atmospheric circulation ensures that air is almost nowhere co-moving with the Earth.

 

[wildetudor]

So then why is a flying object hovering at any altitude above the ground always rotating at the same angular frequency as the Earth, i.e. staying above the same spot?

 

[voko]

I cannot answer the "why" question because its premise is false. A flying object hovering at any altitude does not stay above the same spot unless it is made to stay above the same spot, which may or may not possible.

The first (in Europe, anyway) balloon ever launched was a hydrogen balloon launched on August 27, 1783 (less than a month before the first hot-air balloon). It stayed in the air for 45 minutes, and landed 21 km away. Not at the same spot by any measure. Modern helicopters need constant input to stay at the same spot, some use automatic stabilizers for that.

 

[wildetudor]

But surely the wind is, in those cases, largely responsible for such an object not remaining above the same spot (as well as, probably, difficulty in controlling the aircraft itself). Probably not easy to answer, but assuming the wind and aircraft control issues stay negligible for the entire duration of the 'hovering', is there any reason to believe the object will not remain above the same spot after a vertical climb? And if so, then is the reason for that likely to be related to the planet's rotation?

 

[voko]

Wind is what atmospheric circulation is. The atmospheric circulation is caused by the rotation of the Earth. One cannot happen without the other. You cannot neglect it because it is not negligible. If you neglect it, then you have to neglect the atmosphere entirely. What is your question about, really?

 

[wildetudor]

I thought it'd have been clear by now what my question was, as I rephrased in at least three different ways. It was simply to know exactly what is the primary force that makes an object that is hovering above the Earth stay above the same vertical spot - in the absence of winds with horizontal components, imperfections of the aircraft's ability to remain stationary in mid-air, or any other practical factor that would obviously impede such a "vertical hovering" experiment in the real world.

But I think you are right, perhaps it does make little sense to ask this question, since you'd be ignoring too many factors. This is simply a question that came into my mind as I was flying in a jet airplane across the Atlantic, and was wondering whether the planet's rotation makes any differece in the flying time when flying east-west as opposed to west-east. This ultimately boils down to whether it would be a (theoretically) conceivable mode of transport to just go high up with a balloon-like object and "wait" for the desired spot of the planet to be rotated until it's immediately underneath you.

 

[voko]

I am sure you noticed that the East-bound flight was a good hour shorter than the West-bound flight. That was not an accident, because it was in the timetable! That is because of the so-called westerlies, a stable pattern of air moving North-Eastward with respect to the rotating Earth.

And the westerlies are caused by the Coriolis force, which is due to the rotation. So you may say that rotation is responsible for the timetable. I should add that rotation is not solely responsible for that, though.

 

[wildetudor]

Alright, I guess I am a bit clearer on all of this now. Thanks a lot to everyone who responded :)

 

[rcgldr]

Perhaps a better thought experiment would be what is the path of an object shot (short impulse) straight up from the surface of a atmosphereless planet, where the objects initial "horizontal" speed is the same as the surface speed of the rotating planet.