Question

Two identical planets are orbiting around a star in elliptical paths having their semi-major axes in the ratio of $1:9.$ If life of man on $1^{s t}$ planet is $80$ years then what will be his life on $2^{n d}$ planet in terms of that planet's year? (Approximate the answer to the nearest integer)

Answer 1

Life years $=\frac{\text { Total time to live }}{\text { One planet year }}$
$ n=\frac{t}{T} $
$\frac{n_{1}}{n_{2}}=\frac{T_{2}}{T_{1}}=\left(\frac{9}{1}\right)^{3 / 2}=27$
$n_{2}=\frac{n_{1}}{27}=\frac{80}{27}=2.96$