Question

The ratio of earth's orbital angular momentum (about the sun) to its mass is $4.4\times {10}^{15}{m}^2/s$. The area enclosed by earth's orbit approximately is $n\times {10}^{22}$ $m^2$. Then $n$ is
(Answer upto two decimal places)

Answer 1

Let L = Angular momentum of each about sun.
M = Mass of earth
$\therefore$ By Kepler's law, $\frac{dA}{dt}=\frac{L}{2M}$
or $dA=\frac{L}{2M}dt$

The earth completes its orbital journey in 365 days
$\therefore$ Area $A=\frac{L}{2M}\times T=\frac{1}{2}\left(\frac{L}{M}\right)T$,
where T = 365 days
or $A=\frac{(4.4\times {10}^{15})\times 365\times 24\times 60\times 60}{2}{m}^2$
or Area $=6.94\times {10}^{22}{m}^2$
$\therefore$ Area enclosed by earth's orbit $=6.94\times {10}^{22}{m}^2$
$⟹n=6.94$