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NEET 1988 (AIPMT) · Kepler's Laws & Planetary Motion

Kepler's Laws & Planetary Motion question from NEET 1988 (AIPMT)

Q34NEET 1988 · AIPMTMedium

Kepler's Laws & Planetary Motion

The largest and the shortest distance of the earth from the sun are r1r_1 and r2r_2. Its distance from the sun when it is at perpendicular to the major-axis of the orbit drawn from the sun is

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Answer: (c)

  1. The required distance is the semi-latus rectum ll of the ellipse.
  2. r1=a(1+e)r_1 = a(1+e), r2=a(1−e)r_2 = a(1-e) and l=a(1−e2)l = a(1-e^2).
  3. l=a(1+e) a(1−e)a=r1r2(r1+r2)/2l = \frac{a(1+e)\,a(1-e)}{a} = \frac{r_1 r_2}{(r_1+r_2)/2}
  4. So the answer is (c) 2r1r2r1+r2\frac{2r_1r_2}{r_1+r_2}.
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