Answer:
Sun and Earth Star & new planet \[{{R}_{1}}=R\] \[{{R}_{2}}=2R\] \[{{T}_{1}}=T\] \[{{T}_{2}}=?\]
Average life span = 70 years Average life span = ? We know \[\frac{{{T}^{2}}}{{{R}^{3}}}=const\] \[\Rightarrow {{T}_{2}}={{T}_{1}}{{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{\frac{3}{2}}}\Rightarrow {{T}_{2}}=T{{\left( \frac{2R}{R} \right)}^{\frac{3}{2}}}=2\sqrt{2}T\] It means\[2\sqrt{2}\]years of earth are equal to 1 natural year of that planet. \[\therefore \]1 year of earth\[=\frac{1}{2\sqrt{2}}\]planet year Average life span of human on new planet \[=\frac{70}{2\sqrt{2}}=24.75\]planet year
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