Let the speed of the planet at the perihelion P in figure be v_(P) and the Sun planet distance SP be r_(P). Relater r_(P), v_(P) to the corresponding quantities at the aphelion (r_(A),v_(A)). Will the planet take equal times to transverse BAC and CPB?

Let the speed of the planet at the perihelion P in figure be v_(P) and

1.	Let the speed of the planet at the perihelion P in figure be v_(P) and the Sun planet distance SP be r_(P). Relater r_(P), v_(P) to the corresponding quantities at the aphelion (r_(A),v_(A)). Will the planet take equal times to transverse BAC and CPB?
Answer» Solution :The magnitude of angular momentum at P is `L_(p)=m_(p)r_(p)v_(p)` Similarly magnitude of angular momentum at A is `L_(A)= m_(A)r_(A)v_(A)` From conservation of angular momentum `m_(p)r_(p)v_(p)= m_(A)r_(A)v_(A)` `(v_p)/(v_A)= (r_A)/(r_p)` `r_(A) gt r_(p) :. v_(p) gt v_(A)` area bound by SB and SC `(SBAC gt SBPC)` By 2nd law equal areas are SWEPT in equal INTERVALS of time. Time taken to TRANSVERSE `BAC gt ` time taken to transverse CPB.