Question

The orbital radius of mercury around the sun is 0.38 A U. Determine the angle of maximum elogation for mercury and its distance from earth, where elognation is maximum,

Answer 1

Correct Answer - `22.3^@ ; 1.384xx10^8km`
Here, `r_(ps) =0.38A U , r_(es)= 1A U`
The angle of maximum elongation `"in"`is given
by
`sin "in" = (r_(ps))/(r_(es)) = (0.38)/(1)`
Now,`r_(pe) =r_(es)xxcos "in"`
`1.496xx10^(11) cos (22.3^@)`
`=1.496xx10^(11)xx0.9252 = 1.384xx10^(11)m`
`=1.384xx10^8km`