Adwarf planet discovered out beyond the orbit of pluto is known to have an orbital period of 619.36 years. what is its average distance from the sun?

Explanation:

Let's begin by explaining that according to Kepler’s Third Law of Planetary motion “The square of the orbital period  of a planet is proportional to the cube of the semi-major axis  of its orbit”:

(1)  

Now, if is measured in years (Earth years), and is measured in astronomical units (equivalent to the distance between the Sun and the Earth: ), equation (1) becomes:  

(2)  

So, knowing and isolating from (2) we have:  

(3)  

(4)  

Finally:

T his is the distance between the dwarf planet and the Sun in astronomical units

Converting this to kilometers, we have:

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