However, these approximations are close to the actual data, and they allow for the development of a polar equation (5 ‑ 4cosθ) that produces a perfect limaçon. A representation that uses a better approximation of the actual data will not result in such a nice curve.
People used to believe that the Earth was the center of the Universe. Instead of thinking that the Earth was one of several planets that revolved around the Sun, they believed that the Sun and the other planets revolved around the Earth. Relative to the Earth, what would the path of Mars look like?
Now, think about this: What would the path of Mars look like, relative to Earth, if both planets were in motion?
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