Every planet revolves around the sun in an elliptical orbit:-
A. The force acting on a planet is inversely proportional to square of distance from sun
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun
C. The Centripetal force acting on the planet is directed away from the sun
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit
Choose the correct answer from the options given below:

Question

Correct formula for height of a satellite from earths surface is :

Answer 1

The question pertains to the fundamental concepts of celestial mechanics, specifically those governing the movement of planets around the sun. The principles inherent in this question are primarily based on Kepler's Laws of Planetary Motion and Newton's Law of Universal Gravitation.

Understanding Kepler's Laws:
- Kepler's First Law states that each planet moves in an elliptical orbit with the sun at one focus. This underlines the elliptical nature of the orbits.
- Kepler's Third Law (Law of Periods) is relevant here: The square of the period of revolution of a planet is directly proportional to the cube of the semi-major axis of its elliptical orbit. This matches with statement D.
Newton's Law of Universal Gravitation:
- According to this law, the force acting on a planet is inversely proportional to the square of the distance from the sun, which is consistent with statement A.
- This law specifically states that the gravitational force is directly proportional to the product of the masses of the two bodies — the sun and the planet — and not inversely, thereby refuting statement B.
Evaluating Incorrect Statements:
- C: The centripetal force acting on the planet is towards the sun, not away from it, ruling out this statement as it contradicts the nature of centripetal forces.

Therefore, the correct answer based on the explanations above is A and D only, which aligns with the principles and the known laws of planetary motion.

Answer 2

The question pertains to the fundamental concepts of celestial mechanics, specifically those governing the movement of planets around the sun. The principles inherent in this question are primarily based on Kepler's Laws of Planetary Motion and Newton's Law of Universal Gravitation.

Understanding Kepler's Laws:
- Kepler's First Law states that each planet moves in an elliptical orbit with the sun at one focus. This underlines the elliptical nature of the orbits.
- Kepler's Third Law (Law of Periods) is relevant here: The square of the period of revolution of a planet is directly proportional to the cube of the semi-major axis of its elliptical orbit. This matches with statement D.
Newton's Law of Universal Gravitation:
- According to this law, the force acting on a planet is inversely proportional to the square of the distance from the sun, which is consistent with statement A.
- This law specifically states that the gravitational force is directly proportional to the product of the masses of the two bodies — the sun and the planet — and not inversely, thereby refuting statement B.
Evaluating Incorrect Statements:
- C: The centripetal force acting on the planet is towards the sun, not away from it, ruling out this statement as it contradicts the nature of centripetal forces.

Therefore, the correct answer based on the explanations above is A and D only, which aligns with the principles and the known laws of planetary motion.

The Correct Option is A

Solution and Explanation

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