Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to R–5/2a)T2 is proportional to R3b)T2 is proportional to R7/2c)T2 is proportional to R3/2d)T2 is proportional to R3/73Correct answer is option 'B'. Can you explain this answer?

Question

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to R&ndash;5/2a)T2 is proportional to R3b)T2 is proportional to R7/2c)T2 is proportional to R3/2d)T2 is proportional to R3/73Correct answer is option 'B'. Can you explain this answer?

Answer

If the gravitational force of attraction between the planet and the star is proportional to R, it means that the strength of the gravitational force increases as the distance between the planet and the star increases. This is contrary to the inverse square law of gravity, where the force of attraction decreases as the distance increases.

In this scenario, the planet would experience a stronger gravitational force when it is farther from the star and a weaker gravitational force when it is closer to the star. This would result in a peculiar orbit for the planet.

During its orbit, the planet would experience a greater gravitational pull from the star when it is farthest away, causing it to accelerate and move faster. As it moves closer to the star, the gravitational force weakens, causing the planet to decelerate and slow down. This would result in an uneven orbital speed throughout its revolution.

The planet would spend less time in the closer regions of its orbit, where the gravitational force is weaker, and more time in the farther regions, where the gravitational force is stronger. This would lead to an eccentric orbit, where the planet's distance from the star varies significantly during its revolution.

Furthermore, the period of revolution T would be affected by this unusual gravitational force. Since the planet would be moving faster when it is farther from the star, it would cover more distance in less time. Conversely, when the planet is closer to the star, it would cover less distance in more time. As a result, the period of revolution T would not remain constant but would vary throughout the orbit.

Overall, the planet's orbit around the massive star would be irregular, with varying distances and speeds. It would experience a stronger gravitational force when farther from the star and a weaker gravitational force when closer, leading to an eccentric orbit and a non-constant period of revolution.

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