Emotional Development
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Consider the following statements regarding Kepler's laws of planetary motion and the universal law of gravitation:
- 1. Kepler's second law (law of areal velocities) is based on the fact that angular momentum remains conserved under central forces, according to which the line joining a planet to the sun sweeps out equal areas in equal intervals of time.
- 2. According to Newton's universal law of gravitation, the force of attraction between two bodies is inversely proportional to the product of their masses and directly proportional to the square of the distance between them.
- 3. When moving upwards from the surface of the earth or going deep inside the earth, the value of acceleration due to gravity ($g$) decreases, and the value of $g$ becomes zero at the center of the earth.
- 4. The orbital speed ($v_0$) of a satellite depends on the radius of the earth, and if a satellite revolves very close to the earth, its orbital speed is approximately 7.9 km/s.
Which of the above statement(s) is/are completely true?
✓ Correct! Well done.
✗ Not quite — the correct answer is highlighted above.
Detailed Explanation
Statement 1 is true because Kepler's second law is a form of the conservation of angular momentum. Statement 2 is false because, according to Newton's law of gravitation, the force is directly proportional to the product of masses and inversely proportional to the square of the distance between them, whereas it is written in reverse here. Statements 3 and 4 are completely true; $g$ decreases with height or depth and is zero at the center, and the orbital speed of a near-Earth satellite is $7.9\text{ km/s}$.
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