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   John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Wednesday, 18-Sep-2024 01:33:01 JST John Carlos Baez

   When you jump off a chair, the Earth pulls you down with gravity and you accelerate downwards: your downwards velocity increases by 9.8 meters/second each second.

   But as you sit in your chair you are also accelerating! The Earth is turning, so you are moving around in a circle, so your velocity is changing. How fast is it changing?

   I had no idea until I looked it up. If you're sitting near the equator, the turning of the Earth is changing your velocity by 0.03 meters/second every second. Near the north or south pole, it's much less. So this is a small effect.

   But even at the north pole you are also accelerating! After all, the Earth is going around the Sun! This effect is even smaller: you're accelerating at about 0.006 meters/second each second.

   This acceleration is small, but the mass of the earth is incredibly huge, and F = ma, so the force of the Sun on the Earth must be large. How large? It's

   35000000000000000000000

   newtons, or 3.5 × 10²² newtons.

   But what's a newton? Newton, as you know, discovered the force of gravity when an apple landed on his head. The force he felt when the apple hit him was exactly one newton.

   Just kidding. A 'newton' is actually the amount of force it takes to make one kilogram change velocity by one meter per second each second. For example, the Earth's gravity pulls a one-kilogram mass downward by a force of 9.8 newtons.

   So we're back where we started. But we're not done! The Sun is going around the Milky Way, so it's accelerating too. How much?

   We could calculate it - but amazingly, people have actually measured it! Its velocity is changing by 0.0000000023 meters/second each second.

   https://sci.esa.int/web/gaia/-/measuring-the-acceleration-of-the-solar-system-with-gaia