If we put a ball around a piece of atmosphere, will this affect its acceleration while falling to Earth?

Question

Imagine the air inside of a ball is the same as the air in the atmosphere of the Earth. So the ball is not rigid (though the shell is).

What effect has this non-solidness of the inside of the ball (equal to the air surrounding it) on the acceleration of the ball if we let it fall down?

1)Will it have a negative contribution to the acceleration (which thus becomes less)?

2)Will it have no effect at all?

1)The air inside the ball is also accelerated because the ball is accelerated, in contrast to the surrounding air. This will create a tiny force upwards (because of the inertia of the gas?) because the air accumulates at the top of the ball and thus will affect the acceleration in a negative way. Like the air in an accelerating car.

2)If we consider that the surface of the ball is put around a 3-d ball of air, the air inside the ball won't "feel" the difference. The air outside is the same as inside the ball. If this also will be the case while falling you would expect no influence on the acceleration.

A positive contribution to the acceleration I can't imagine.

My instinct tells me that the ball's acceleration becomes a tiny bit less. Less than what? Less than the ball filled with atmospheric air falling with no reduction in the acceleration.

Answer 1

Even though the air inside the ball is not part of the "rigid body" formed by the surface, it is still a very good approximation to treat the entire ball as a rigid body. This is because the mass of the air inside the ball is very small compared to the surface of the ball.

The only way it would deviate from a rigid body is it would not have spherical symmetry. When the ball is accelerating, the air inside it will clump slightly towards the top of the ball (like how a balloon goes forward in an accelerating car).

So the center of mass will be slightly higher than the center of the ball, but you wouldn't see much difference in the velocity of a hollow ball with a vacuum inside (though this ball will go slightly faster).

Answer 2

Two effects will come into play in the difference between a solid ball and a hollow one filled with air.

The first difference is the overall density of the two balls. The solid ball is the same size as the hollow one but weighs more, so is less bouyant and sinks faster through the atmosphere.

The second, much smaller, effect arises because a hollow ball is less rigid than a solid ball. A falling flexible sphere tends to flatten out somewhat in the air, increasing the drag. The more rigid material you replace with air, the more flexible the ball becomes and the more it deforms.

Note that the actual behavior of the air inside the ball is irrelevant. Because gravity works on the air molecules just the same as the ball itself, the pressure is equal in all directions inside a free-falling ball; and if you simply encapsulate a bit of the atmosphere, the pressure is the same inside as out, so only the rigidity and form of the skin matters overall. One exception to this is if you encapsulate low-pressure air high in the atmosphere and drop it, the higher pressures at lower altitude will begin to crush the ball if it is airtight.