Assignment Task: Kepler's Laws were transformative. They broke multiple millennia of entrenched thought about the nature of planetary orbits. We covered Kepler's Laws in Lecture 2.
(a) Please write down and clearly label Kepler's laws. You may transcribe them from, or use your own words.
(b) Qualitatively, what does Kepler's Second Law imply about the relative orbital speed of a comet at perihelion compared against aphelion.
(c) According to Kepler's Laws: Earth, like all planets, orbits the Sun on an ellipse. Accordingly, this implies that during parts of the year Earth is closer to the Sun (e.g., at perihelion) than other parts of the year (e.g., at aphelion). Is this the right explanation for the seasons? Please carefully explain and justify your answer.
(d) If Earth's orbit was twice as large (i.e. its semi-major axis was two times its current size), how much longer would a year be (i.e. how much longer would it take for Earth to orbit the Sun).
(e) Mars' orbital period is 687 days (1.88 years). Use Kepler's Third Law to solve for its semi-major axis. Compare this against Earth's semi-major axis.