Why astronauts float in space, even though gravity is still there

Look up on a clear night, and you may see a bright dot cross the sky in a few minutes. It is the space station, and the people inside it float. Most people think gravity stops up there. It does not: the Earth still pulls on the crew almost as hard as on you. Here is the real reason, step by step: how strong gravity is 400 km up, why falling feels like floating, what an orbit is (Isaac Newton saw it with a cannon), and why the Moon falls around us too.