As you know the earth has an orbital period of 1 year at an orbital radius of 1.

Question

As you know the earth has an orbital period of 1 year at an orbital radius of 1.0 AU ( astronomical unit, the avg distance between the earth and sun) . If a new "minor planet" we're to be found in a circular orbit with radius of 13 AU, what would its orbital period be? As you know the earth has an orbital period of 1 year at an orbital radius of 1.0 AU ( astronomical unit, the avg distance between the earth and sun) . If a new "minor planet" we're to be found in a circular orbit with radius of 13 AU, what would its orbital period be?

Explanation / Answer

T1= 1 year , r1= 1 AU , r2= 13 AU

Use Kepler’s third law

T^2 = (4^2/GM)*r^3

We can write,

T2^2/T1^2 = r2^3/r1^3

T2^2 = T1^2*(r2^3/r1^3)

Plugging values,

T2^2 = 1^2*(13^2/1^2)   => T2 = 46.87 years = 47 years

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