In the picture below the planet orbits around the sun with a period of 40 months and takes 12 months to translate from the point D to point E and 1 month from point B to C. the area of the ellipse is A. mass of the satellite.
Q. The area of the shaded region

Options

A. A/20
B. A/8
C. A/40
D. A/4

Answer

B

Explanation

Angular momentum of stellite `=(2)/(t)`
per unit mass per unit area
`implies(2)/((40xx30xx24xx60xx60))`
Area swept `propt`
`Area_("DES")=((A)/(40))xx12=(3A)/(10)`
`Area_("SEM")=Area_("DES")-Area_("EMD")`
`implies(3A)/(10)-(A)/(4)implies(A)/(20)`
`Area_("SEM")=Area_("SMC")=(A)/(20)`
`Area_("SBC")=((A)/(40))xx1`
Total shaded area `impliesArea_(SEM)+Area_(SMC)+Area_(SBC)`