Two planets are observed going around a star. planet xoron has an orbital period that is twice as long as planet krypton. which planet has a shorter average orbital radius?

Krypton

Explanation:

Kepler's third law states that the cube of the semimajor axis of the orbit of a planet is proportional to the square of the orbital period. Mathematically, we can write:

or

(1)

where

r is the semimajor axis of the orbit

T is the orbital period

In this problem, we are told that Planet xoron has an orbital period twice as long as planet kripton: given relationship (1), this means that Planet xoron will also have a longer orbital radius (so, planet krypton has a shorter orbital radius).

Mathematically, we can write the equation as

where 'x' stands for Xoron and 'k' stands for Krypton. Since

The ratio between the radii will be

So, Krypton will have a shorter average orbital radius.

c. magnitude and direction