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Gravity affects objects proportionally to their mass, and electrostatic forces affect objects proportionally to their electrical charge. We can observe that the attraction of the planet Earth for various objects, which we describe as weight, is proportional to mass, not to electrical charge. Consequently we can confidently infer that the attractive force exerted by the planet Earth is gravitational in nature and not electrostatic. It is also true that if there were some enormous electrical charge on the Earth and the moon, causing them to attract each other, we could expect an enormous electrical discharge to take place by which the extra electrons would leave the negatively charged object (moon or planet as the case may be) and travel to the positively charged object.

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Q: How do you know that electrostatic forces are not the cause for the gravitational attraction between moon and earth?
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