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Enslaved by Yandere Sister Chapter 45

I’m bored, so will explain the logic needed to solve a basic HS physics problem. See below the chapter link (so it doesn’t get in the way of those who don’t care).

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» Chapter 45 «

Q: “Find the radius of a geostationary satellite orbiting Earth in terms of the Earth’s radius.”

We immediately know a few things from the problem – the orbital period of the satellite is 24 hours (well, close to it), it is circular (geostationary is a special case of geosynchronous that is circular; for HS physics all orbits are circular so even if it was stated to be geosynchronous you would still assume circular), and that we’ll need the Earth’s radius and mass, the latter we guess we need as orbits are defined by the mass of the body they are orbiting, so seems fitting to use here.

We know the force acting on the satellite is gravity, and we’ll use Newton’s law of universal gravitation for that. In this setup, gravity is acting in a “center seeking,” or “centripetal” manner, so we’ll grab the equation for centripetal force and set the equation equal. The satellite’s masses cancel each other (hence even if the problem gave it to you could ignore it), then it’s just some simple algebra to solve for orbital radius. Normalize to Earth’s radius and you’re done.

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