Gravity exists on other planets too – if something is big enough it will have a gravitational pull. That’s why we’re pulled to this planet, why the Moon is circulating round our planet, and why Earth circles the sun. Our amount of pull is dependent on the size of Earth.
That also means that you have your own gravity that is pulling (ever so slightly) on everything around you including the earth, moon, sun and the entire universe 🙂
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