Orbital Periods of Planets vs Comets

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The discussion focuses on the differences in orbital periods between planets and comets, highlighting Kepler's second law, which states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. It emphasizes that planets typically have circular orbits, while comets have highly elliptical orbits, affecting their orbital periods. The conversation also touches on the distinction between maximum radius (aphelion) and the semi-major axis in orbital mechanics. Understanding these concepts is crucial for grasping the dynamics of celestial bodies. Overall, the thread seeks clarification on these fundamental principles of orbital mechanics.
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Homework Statement
Uranus has an orbit of 19AU and the maximum radius for a comet's orbit is 19AU, so why are the periods different?
Relevant Equations
Uranus orbits 19AU and the comet orbits 19AU
Could someone please tell me if I'm on the right track with understanding this.

The periods of the comet and Uranus is different because of Kepler's second law? Is it because planets orbit the sun in a circular path whereas for comets it's a highly elliptical orbit?

Thank you.
 
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You may want to think about this:
- Which of Kepler's laws is about the orbital period?
- Does this law say anything about the eccentricity of the orbit?

Finally, I think you may be confusing "maximum radius" (aphelion) with semi major axis.
 

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