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Orbits with the same period

Orbital period only depends on an orbit's semi-major axis and the mass of the more massive body, which means that different orbits around a planet or moon have the same period as long as the orbits have the same width at their widest point.

Here are a few orbits with different eccentricities but the same semi-major axis, aligned to have their periapses on the same side:

A series of elliptical orbits with the same period but different eccentricities.

Drawing more eccentricities makes it harder to distinguish one orbit from another, but it does produce a memorable teardrop shape:

Drawing more ellipses with the same period creates a teardrop shape.