The largest and the shortest distance of the earth from the sun are ${r_1}$ and ${r_2}$, its distance from the sun when it is at the perpendicular to the major axis of the orbit drawn from the sun
The largest and the shortest distance of the earth from the sun are ${r_1}$ and ${r_2}$, its distance from the sun when it is at the perpendicular to the major axis of the orbit drawn from the sun
$\frac{{{r_1} + {r_2}}}{4}$
$\frac{{{r_1}{r_2}}}{{{r_1} + {r_2}}}$
$\frac{{2{r_1}{r_2}}}{{{r_1} + {r_2}}}$
$\frac{{{r_1} + {r_2}}}{3}$
The largest and the shortest distance of the earth from the sun are ${r_1}$ and ${r_2}$, its distance from the sun when it is at the perpendicular to the major axis of the orbit drawn from the sun
The earth moves around the sun is elliptical path. so by using the properties of ellipse
${r_1} = (1 + e)\,a$ and ${r_2} = (1 - e)\,a$
$ \Rightarrow \,a = \frac{{{r_1} + {r_2}}}{2}$ and ${r_1}{r_2} = (1 - {e^2})\,{a^2}$
where $a = $ semi major axis
$b =$ semi minor axis
$e =$ eccentricity
Now required distance = semi latusrectum $ = \frac{{{b^2}}}{a}$
$ = \frac{{{a^2}(1 - {e^2})}}{a} = \frac{{({r_1}{r_2})}}{{({r_1} + {r_2})/2}} = \frac{{2{r_1}{r_2}}}{{{r_1} + {r_2}}}$
Other Language