Question

The orbit of the planet Mercury around the Sun is in elliptical shape with Sun at a focus. The semi-major axis is of length $36$ million miles and the eccentricity of the orbit is $0.206$. Find:
(i) How close the Mercury gets to sun?
(ii) The greatest possible distance between Mercury and Sun

Answer 1

Given, $e=0.206a=36$ million miles
The closest distance of the mercury from the sun is $F_{1}A$
The greatest distance of the mercury from the sun $F_{1}A$
$C{F}_1=ae=36\times 0.206=7.416$
$F_{1}A=CA-C{F}_1=36-7.46=28.584$ million miles
$F_1{A}^{\prime }=C{A}^{\prime }+C{F}_1=36+(36\times 0.206)$
$=36+7.46=43.416$ million miles.