The mean distance of Earth from the Sun is $149.6 \times 10^6$ km and the mean distance of Mercury from the Sun is $57.9 \times10^6$ km. The period of Earth’s revolutions is 1 year, what is the period of Mercury’s revolution?

$\cfrac { { T }_{ 1 }^{ 2 } }{ { r }_{ 1 }^{ 3 } } =\cfrac { { T }_{ 2 }^{ 2 } }{ { r }_{ 2 }^{ 3 } }$

$1=$ Earth; $2=$ Mercury

$\cfrac { { 1 }^{ 2 } }{ { \left( 149.6\times { 10 }^{ 6 } \right) }^{ 3 } } =\cfrac { { T }_{ 2 }^{ 2 } }{ { \left( 57.9\times { 10 }^{ 6 } \right) }_{ }^{ 3 } }$

$\Rightarrow \cfrac { 1 }{ 3348071.936\times { 10 }^{ 18 } } =\cfrac { { T }_{ 2 }^{ 2 } }{ 194104.539\times { 10 }^{ 18 } } \Rightarrow { T }_{ 2 }^{ 2 }=0.057975\Rightarrow { T }_{ 2 }=\sqrt { 0.057975 }$

${T}_{2}=0.24$ year on Earth

$1$ year on Earth $=365$ days