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As I understand, in a balloon/air balloon, a gas burner is used to heat air or using some lighter atom like helium. Since helium or hot air is lighter and less dense than the cool air around the balloon, the heated air or helium causes the whole balloon to rise. And as I understand, vacuum is a space where there are no atoms inside. So no atom inside means it's lighter than to have atom an inside? Isn't it? So why we can't make something fly by giving it a vacuum container?

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If you have helium gas (one of the only gas with escape velocity [wiki source-Helium]) inside the balloon, it will be light. So, the gas inside pushes the balloon upside. Here if you have nothing inside the balloon, the balloon will be lighter than the helium balloon, but the problem is, what will you give you pushing force in the upward direction by maintaining its shape. –  Godparticle May 10 at 9:40

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I assume you are asking why we are not drawing air out of a balloon like container so as to create the lower density that helium or hot air gives us.

The answer is that it is hard to maintain a vacuum with a thin enough, so as to be almost weightless, rigid contaning surface. A balloon with gas inside equalizing the atmospheric pressure with the gas pressure is easy to make air tight and stable. A vacuum in a thin enough walled container would be liable to collapse, due to the atmospheric pressure, and would be hard to make air tight.

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A cool video to illustrate Anna's point: youtube.com/watch?v=Zz95_VvTxZM –  DavePhD May 10 at 10:25
    
@DavePhD Great video! –  LDC3 May 10 at 15:24

Yes, creating a vacuum container and flying it is possible. But the efficiency would't be any greater than helium balloon. When a vacuum is created, a low pressure tending to zero is created. There will be high pressure outside the container or balloon. This pressure will start squeezing the container. The container must be strong enough to sustain such high amounts pressure. This would be like building a submarine. The vacuum container would have to lift itself (which would be several times heavier than a balloon) along with a pay load.

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