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Letthe speed of the planet attheperihelion pin be vPand the Sun-planet distance SP be r_(P). Relate {r_(P), v_(P)} to the corresponding quantities at the aphelion {r_(A), v_(A)}. Will the planet take equal times to traverse BAC and CPB ?

Answer» <html><body><p></p>Solution : The <a href="https://interviewquestions.tuteehub.com/tag/magnitude-1083080" style="font-weight:bold;" target="_blank" title="Click to know more about MAGNITUDE">MAGNITUDE</a> of the angular <a href="https://interviewquestions.tuteehub.com/tag/momentum-1100588" style="font-weight:bold;" target="_blank" title="Click to know more about MOMENTUM">MOMENTUM</a> at P is `L_(p)` =`m_(p) r_(p) v_(p)`, since inspection tells us that rp and vp are mutually perpendicular. Similarly,` L_(A) = m_(p) r_(A) v_(A)`. From angular momentum conservation<br/> `m_(p) r_(p) v_(p) = m_(p) r_(A) v_(A)`<br/> or `(v_(p))/(v_(A)) = (r_(A))/(r_(p))`<br/> since `r_(A) gt r_(p), v_(p) gt v_(A).` <br/> the area SBAC bounded by the ellipse and the <a href="https://interviewquestions.tuteehub.com/tag/radius-1176229" style="font-weight:bold;" target="_blank" title="Click to know more about RADIUS">RADIUS</a> vectors SB and SC is larger than SBPC in From Kepler’s second law, equal <a href="https://interviewquestions.tuteehub.com/tag/areas-883934" style="font-weight:bold;" target="_blank" title="Click to know more about AREAS">AREAS</a> are swept in equal times. Hence the planet will take a longer time to traverse BAC than CPB.</body></html>


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