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Question

The drawing above is NOT drawn to scale.
The drawing represents a planet orbiting some star. The planet is closer to the star as it moves from point 1 to point 2 than it is when it moves from point 3 to point 4 in its orbit. The dotted line shows the orbital path.
If the time it takes the planet to get from point 1 to point 2 is equal to the time it takes the planet to get from point 3 to point 4 then which of the following statements is true, according to Kepler's laws of planetary motion?

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A
The average speed as the planet travels from 1 to 2 is the same as when it travels from 3 to 4.
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B
Area 1 in the diagram is equal to Area 2.
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C
Area 1 in the diagram is smaller than Area 2.
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D
The planet moves further from 3 to 4 from 1 to 2.
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E
The average speed as the planet moves from 3 to 4 is greater than when the planet moves from 1 to 2.
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Solution

The correct option is B Area 1 in the diagram is equal to Area 2.
Correct answer is option B.
From Kepler's Second Law, an imaginary line joining a planet and the sun sweeps out an equal area of space in equal amounts of time.
The closer the object is,lesser is the gravitational potential energy, large is the kinetic energy and hence the speed.

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