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You may want to use perturbation theory. This only gives you an approximate answer, but allows for analytic treatment. Your force is considered a small perturbation to the Keplerian elliptic orbit and the resulting equations of motion are expanded in powers of $K$. For linear perturbation theory, only terms linear in $K$ are retained. This simply leads to ...


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I'm going to start by going over the Pauli Exclusion Principle. Basically, it says that two fermions (in this case, electrons) can't be in the same quantum state. To expand: No two electrons in an atom can share the same numbers for their four quantum numbers. What are quantum numbers? Well, I'll admit that Wikipedia describes them a lot better than I can, ...


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Earth's gravity is quite weak. It manages to compress air (luckily for us), but that's about it. Since the Earth is not a black hole it can never compress something else to be a black hole. That being said, lets consider some object and assume something compresses it to a black hole. The Schwarzschild radius is defined as $$ R_s = \frac{2GM}{c^2}. $$ Now ...



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