Question

A planet revolves around the sun in an elliptical orbit of eccentricity e. if T is the time period of the planet, then the time spent by the planet between the ends of the minor axis and major axis close to the sum is.

• A.
• B. $\mathrm { T } \left( \frac { 2 \mathrm { e } } { \pi } - 1 \right)$
• C. $\frac { \mathrm { Te } } { 2 \pi }$
• D.

Answer 1

Answer: (D)

Answer 2

As areal velocity of a planet around the sun is constant. Therefore, the desired time is

If a = semi-major axis and b = semi-minor axis of ellipse, then, area of ellipse =

Area ABS $= \frac { 1 } { 4 }$(area of ellipse) – Area of triangle ASO