question_answer

In an imaginary planetary system, the central star has the same mass as our sun, but is much brighter so that only planet twice the distance between the earth and sun can support life. What would be the average life span of a human on that planet in terms of its natural life? The average life span of a human on the earth may be taken to be 70 years.

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