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The distance of a planet from the sun is $16 times$ that of the earth. The time period of the revolution of the planet around the sun is [[1]] $years$ .

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Detailed Solution

The distance of a planet from the sun is

16 times

that of the earth. The time period of the revolution of the planet around the sun is

64 years

.
Given: distance of planet from sun is forty times the distance of the earth or

r_{p} = 16 r_{e}

and the revolution time of earth

T_{e} = 1 year

.
According to Kepler’s third law,

T = k {r^{\frac{3}{2}}}^{}

Therefore, it can be said that

\frac{T_{p}}{T_{e}} = \frac{k {r_{p}}^{\frac{3}{2}}^{}}{k {r_{e}}^{\frac{3}{2}}^{}}

On substituting the given values, we get

\Rightarrow T_{p} = {16^{\frac{3}{2}}}^{}

\Rightarrow T_{p} = 64

Hence, the time period of the revolution of the planet around the sun is

64 years

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