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I know in the lower levels of the stratosphere we can still have 100 mph winds albeit low density winds. Could I possibly go high enough in a balloon or imaginary vertical craft that I would go above the atmosphere and remain relatively stationary at that altitude and the earth rotates away underneath me? IOW, 24 hours would go by and I can return (descend vertically) to around same lat long I launched from just one day later. What altitude would that be? Or would earth's gravity always tug me along to some degree as it rotates?

What are the physics that describe this?

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    $\begingroup$ That won't happen. Air is a viscous fluid and the atmosphere tends to rotate along with the Earth. If you stopped the atmosphere from rotating, it would start rotating again very quickly due to what you could loosely call "friction" with the Earth. $\endgroup$ – uhoh Jul 21 '17 at 4:48
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    $\begingroup$ If you want to be above all winds, you have to be above all atmosphere. But you can't get above all atmosphere with a ballon. There is no ballon lighter than a vacuum. $\endgroup$ – Uwe Jul 22 '17 at 14:27
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The question contains a misconception - wind is the movement of the atmosphere relative to the surface. So if you are at an altitude with no wind, you'll be stationary relative to the surface - the earth won't be rotating underneath you.

However, if the objective is to go up, move around the world and come back close to where you started, you might be interested in the circumpolar vortices. These are regularly used by (unpiloted) scientific high altitude balloon missions such as BLAST, about which an enjoyable documentary was made.

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A balloon cannot ascend above the entire atmosphere. The balloon's buoyancy decreases with height until you're at an equilibrium. The current record is 53 km. At that altitude, you still get wind:

enter image description here

The wind speeds at 50 km are low, indicating that at that altitude, the atmosphere still corotates with the surface. This means your balloon will stay near your takeoff site, drifting slowly due to wind.

You'd need a craft that can fly fast enough to cancel out Earth's rotation speed. Depending on your latitude, an aircraft can do this. A famous example is Concorde, which did London-New York while flying faster than Earth's rotation, so that it would land "before it took off" (local time of landing was before local time of takeoff).

You can also launch a spacecraft into an orbit that cancels out Earth's rotation. This class of orbits is called a polar orbit. Polar orbits are in common use for Earth observation satellites.

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Well the Earth is rotating around 1000 mph. (A rough estimate) You, in your balloon are moving with it.

As you rise into almost no atmosphere you are still moving East at 1000 mph.

An object set in motion stays in motion unless acted upon by some opposite force.

Since there are very few molecules to slow you down and these few molecules are moving East with you, you would continue eastward with the Earth.

After reaching altitude, you would have to use some type of propulsion to slow yourself in the westward direction by 1000 mph.

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