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Question: Answered & Verified by Expert
A planet revolves about the sun in an elliptical orbit of semi-major axis 2×1012 m. The areal velocity of the planet when it is nearest to the sun is 4.4×1016 m2 s-1. If the least distance between the planet and the sun is 1.8×1012 m, then the minimum speed of the planet is
PhysicsGravitationJEE Main
Options:
  • A vmin=40 km s-1
  • B vmin=30 km s-1
  • C vmin=10 km s-1
  • D vmin=20 km s-1
Solution:
1022 Upvotes Verified Answer
The correct answer is: vmin=40 km s-1

The areal velocity of a planet around the sun is

dAdt=L2m, where L is the angular momentum of the planet around the sun and m is its mass.

4.4×1016=mvminrmax2m

2×4.4×1016=vmin4×1012-1.8×1012

vmin=40 km s-1

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