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Starfleet2222

Asimov calculates a ratio of the force a planet (primary) is exerting over the force the sun is exerting. His equation is an aplication of Issac Newtons gravitational attraction equation. Using his equation, Asimov can calculate a band around a planet in which a satillite can truly exist. He sets the ratio to be equal to 30, or the planet having a 30x stronger grip on the satillite than the sun. He then defines a interior limit based upon the roche limit. My question is... Are his equations right? If they are, then, the moon is not a true sattilite of earth, and would fall into the planet catagory, or atleast something between a planet and a satillite. If his equations are correct, the sun is "winning" the "tug of war" between the earth and the sun by a factor of over 2. Is he right and everyone else has been wrong about the moon all these years, or am I missing something?? Thanks