Question

Imagine that we detect an exoplanetary system in which the orbital periods of the planets are X: 56 days, Y: 104 days, Z: 230 days. What can we conclude from this information?

a) These planets are in a 1:2:3 orbital resonance.
b) All of these planets are inside the frost line.
c) X must have a much higher mass than Z.
d) X is a hot Jupiter.
e) X is the closest planet to the star and Z is the farthest.

Answer 1

Statement (e) is correct: X is the closest planet to the star and Z is the farthest, as inferred from the orbital periods using Kepler's third law. The other options cannot be confirmed with the given data.

Step-by-step explanation:

Based on the given orbital periods (X: 56 days, Y: 104 days, Z: 230 days), we can conclude that statement (e) is correct: X is the closest planet to the star and Z is the farthest. This determination is made under the application of Kepler's third law, which relates the orbital period of a planet to its average distance from the star. If all planets orbit the same star and the periods are longer for Y and Z, then their average distances or semi-major axes are also larger, placing them further from the star in comparison to X. Statement (a) is incorrect as the planets are not in a simple numerical resonance like 1:2:3. The lack of specific mass or composition data makes it impossible to confirm statements (b), (c), or (d) solely based on orbital period data.