Earth’s orbit may be treated as an ellipse with semi-major axis and eccentricity

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

Earth’s orbit may be treated as an ellipse with semi-major axis

a = 1.496\times10^{8}\,\text{km}

and eccentricity

e = 0.0167

. The orbital period is

365.25\,\text{days}

. Take the area of an ellipse as

A = \pi a b

, where

b = a\sqrt{1-e^{2}}

. Answer the following. (i) Compute the area of Earth’s orbital ellipse in

\text{km}^2

. (ii) Hence find Earth’s areal velocity in

\text{km}^2\,\text{day}^{-1}

. (iii) Estimate the time (in days) required for Earth to sweep

30\%

of its orbital area, starting from any convenient reference position.