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You're explaining to friends why an astronaut feels weightless orbiting in space shuttle & they respond?

that they thought gravity was just a lot weaker up there.

Convince them that it isn't so by calculating how much weaker (in %) gravity is 380 km above the Earth's surface.

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I could do that fairly easily, but I don't think it would be all that convincing. The point would be made much more apparent with a scale drawing, showing how low the orbit is compared to the width of the planet.