Emotional Development
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With reference to Kepler's laws of planetary motion and the universal law of gravitation, consider the following statements:
- 1. Kepler's second law (law of areal velocities) is based on the fact that angular momentum remains conserved while moving under central forces, according to which the line joining a planet and the Sun sweeps out equal areas in equal intervals of time.
- 2. If the present distance between the Earth and the Sun suddenly decreases to half of its original distance, the Earth's year (orbital period) will be reduced to approximately 35.35 percent of the original year.
- 3. The universal law of gravitation is based on the center of mass, and the gravitational force acting between two point masses depends on the nature of the intervening medium and its temperature.
- 4. An astronaut inside an artificial satellite experiences weightlessness because the gravitational force acting on the satellite becomes zero and the satellite is in a state of free fall around the Earth.
Which of the statements given above is/are completely correct?
✓ Correct! Well done.
✗ Not quite — the correct answer is highlighted above.
Detailed Explanation
Explanation
To determine the correct statements regarding Kepler's laws and gravitation, let us analyze each statement:
- Statement 1 is correct: Kepler's second law is a direct consequence of the conservation of angular momentum for central forces.
- Statement 2 is correct: According to Kepler's third law ($T^2 \propto R^3$), if the distance $R$ is halved, the new time period becomes $T' = (1/2)^{3/2} T \approx 0.3535 T$, which is 35.35% of the original.
- Statement 3 is incorrect: The gravitational force between two masses is independent of the nature of the intervening medium or temperature.
- Statement 4 is incorrect: The gravitational force is not zero; rather, weightlessness occurs because the satellite and astronaut are in continuous free fall towards the Earth.
Therefore, only statements 1 and 2 are correct. For advanced preparation, refer to quality study materials.
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