Physics

Problem

(a) Show that the sum of the perihelion distance

r_{\min}

and aphelion distance

r_{\max}

of a planet is equal to

2a

, where

a

is the semi-major axis of the orbit. (b) The Earth’s orbital eccentricity is

0.017

and its mean distance from the Sun (taken equal to the semi-major axis) is

1.496\times10^{11}\,\text{m}

. Calculate the difference between the aphelion and perihelion distances of the Earth in kilometres. a. Show that the sum of the perihelion distance

r_{\min}

and aphelion distance

r_{\max}

of a planet is equal to

2a

, where

a

is the semi-major axis of the orbit. b. The Earth’s orbital eccentricity is

0.017

and its mean distance from the Sun (taken equal to the semi-major axis) is

1.496\times10^{11}\,\text{m}

. Calculate the difference between the aphelion and perihelion distances of the Earth in kilometres.