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Let the speed of the planet at the perihelion P be V_(P) and the sun-planet distance SP be r_(p). Relates (r_(p), V_(P)) to the corresponding quantities at the aphelion (r_(A), V_(A)). Will the planet take equal times to tranverse BAC and CPB ?

Answer» <html><body><p></p>Solution :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_DOC_OBJ_PHY_XI_V01_B_C09_SLV_003_S01.png" width="80%"/> <br/> According to law of conservation of angular momentum. Angular of the planet at P = Angular momentum of the planet at A <br/> `<a href="https://interviewquestions.tuteehub.com/tag/rarr-1175461" style="font-weight:bold;" target="_blank" title="Click to know more about RARR">RARR</a> mV_(P)r_(P) = mV_(A)r_(A)` (or) `(V_(P))/(V_(A)) = (r_(A))/(r_(P))` Since `r_(A) <a href="https://interviewquestions.tuteehub.com/tag/gt-1013864" style="font-weight:bold;" target="_blank" title="Click to know more about GT">GT</a> r_(P)` so `V_(P) gt V_(A)` <br/> Here area SBAC is greater than the area SCPB. <br/> According to Kepler.s second law, as the arcal velocity of the planet is contant <a href="https://interviewquestions.tuteehub.com/tag/around-5602275" style="font-weight:bold;" target="_blank" title="Click to know more about AROUND">AROUND</a> the sun , i.e. equal areas are swept on equal times, hence the planet will take longer <a href="https://interviewquestions.tuteehub.com/tag/time-19467" style="font-weight:bold;" target="_blank" title="Click to know more about TIME">TIME</a> to traverse BAC than CPB.</body></html>


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