Astronomy Ch03.3: Ranking Task: Kepler's Third Law of Planetary Motion

Part D Each of the following diagrams shows a planet orbiting a star. Each diagram is labeled with the planet's mass (in Earth masses) and its average orbital distance (in AU). Assume that all four stars are identical. Use Kepler's third law to rank the planets from left to right based on their orbital periods, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.) - 2AU: One Earth Mass & Three Earth Mass - 1AU: One Earth Mass & Two Earth Mass

Kepler's third law tells us that the orbital period of the planet is related to its average distance from the star, but not to the planet's mass. This is actually an approximation of Newton's derivation of the Kepler's third law. If the planet's mass is deemed insignificant compared to the mass of the star the planet orbits, then we arrive at Kepler's third law. Since planets' masses are generally many orders of magnitude less than the mass of the stars they orbit, this is a valid approximation in most cases.

Part A The following diagrams all show the same star, but each shows a different planet orbiting the star. The diagrams are all scaled the same. (For example, you can think of the tick marks along the line that passes through the Sun and connects the nearest and farthest points in the orbit as representing distance in astronomical units (AU).) Rank the planets from left to right based on their average orbital distance from the star, from longest to shortest. (Distances are to scale, but planet and star sizes are not.)

Note that the line that passes through the Sun and connects the nearest and farthest points in the orbit is called the major axis, and half this line is the semimajor axis — which is the planet's average distance from the Sun.

Part C The following diagrams are the same as those from Parts A and B. This time, rank the planets from left to right based on their average orbital speed, from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.)

You correctly ranked the planets according to average orbital speed. Note that the pattern is another of the ideas that are part of Kepler's third law: Planets with larger average orbital distances have slower average speeds.

Part B The following diagrams are the same as those from Part A. This time, rank the planets from left to right based on the amount of time it takes each to complete one orbit, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.)

You correctly ranked the planets according to how long they take to complete an orbit, which is what we call the orbital period. Note that the pattern is one of the ideas that are part of Kepler's third law: Planets with larger average orbital distances have longer orbital periods.