The ratio of the earth's orbital angular momentum (about the Sun) to its mass is `4.4 xx 10^(15) m^(2) s^(-1)`. The area enclosed by the earth's orbit is approximately-___________m^(2).

Options

A. `6.94xx10^(22)`
B. `6.94xx10^(23)`
C. `7.94xx10^(22)`
D. `7.94xx10^(23)`

Answer

A

Explanation

(a) Let L=Angular momentum of earth about sun.
M= Mass of earth
`:.` By Kepler's law, `(dA)/(dt)=(L)/(2M) or dA=(L)/(2M) dt`
The earth completes its orbital journey in 365 days.
`:. "Area" A=(L)/(2M)xxT=(1)/(2)((L)/(M))T`, where T=365 days.
` or A=((4.4xx10^(15))xx365xx24xx60xx60)/(2)m^(2)`
` or "Area" =6.94xx10^(22)m^(2)`
`:.` Area enclosed by earth's orbit `=6.94xx10^(22)m^(2)`