system
Given the following post, respond as if you're commenting on Reddit:
human
Is it possible to fill a football with just enough helium to match the density of air, making it float in place?

It just came across my mind, throwing a football that does not come down. Would it be possible?
gpt
A regulation football has a weight of 410-450 gram and a circumference of 68-70 cm. Lets assume a ball of 410 gram (as light as possible) with a circumference of 70 cm (as large as possible). Furthermore, lets assume that the skin of the ball has negligible thickness.

That leaves us with a sphere with a circumference of 70 cm of helium that has to lift up 410 grams of mass. A circumference of 70 cm means a radius of 11.14 cm and therefore a volume of 5792 cm^(3) or 5.792 l.

The lifting capacity of helium-filled objects is based on the principle of buoyancy and is determined by the difference in mass between an amount of helium and the same volume of air. Note that footballs are pressurized, so they contain more air than normal outside air. A typical football will have about twice the mass of air per liter as its outside environment (meaning it's inflated to 1 atmosphere). The density of air is about 1.225 gr/l at standard atmospheric temperature and pressure. So double that for the inside of a football and you get 2.25 gr/l. Or about 13 gr of air inside a football.

You can take that all out and replace it with helium (0.18 gr / l), hydrogen (0.09 gr / l) or even a vacuum (somehow constructing a ball that doesn't implode) (0 gr / l). However, the most you'll gain is a buoyancy force capable of lifting 13 gr (when using vacuum), which is the amount of air displaced. This is very small compared to the 410 gr that the ball is allowed to weigh.

In fact, the difference in mass is smaller than the total mass range that such a ball is allowed to have according to the regulations. So while the ball will be a bit lighter, the difference will be small enough that it's likely that only advanced players will notice the difference.