Four exoplanets—A, B, C and D—move around a distant star. Their orbital parameters are:
Planet A: a=0.70AU,e=0.10
Planet B: a=1.20AU,e=0.05
Planet C: a=1.20AU,e=0.30
Planet D: a=2.00AU,e=0.25
Here a is the semi-major axis and e the eccentricity.
(i) Arrange the four planets in the order of increasing orbital period.
(ii) Arrange them in the order of increasing average orbital (mean) speed.
(iii) Arrange them in the order of increasing instantaneous linear speed at perihelion.
(iv) Justify all three orderings clearly, citing the relevant Keplerian considerations in each case. Where planets share the same rank, state this explicitly with reason.