Emotional Development
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Regarding the principles of astrodynamics and gravitation, consider the following statements:
- 1. According to Kepler's second law of planetary motion (Law of Areal Velocities), the line joining a planet to the sun sweeps out equal areas in equal intervals of time, which is mainly based on the principle of Conservation of Angular Momentum.
- 2. The value of the universal gravitational constant ($G$) depends on mass and distance, and upon going to an infinite distance from the Earth's surface, the value of acceleration due to gravity ($g$) becomes zero, while the value of $G$ remains unchanged.
- 3. The 'escape velocity' ($v_e$) of a body from the Earth's surface depends on its mass, and the escape velocity for heavy bodies is greater than that for light bodies.
- 4. The orbital period of a geostationary satellite is 24 hours and it revolves from west to east in the direction of the Earth's rotation at a height of about 36,000 km from the Earth's surface.
Which of the above statement(s) is/are completely true?
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Detailed Explanation
Statement 1 is true because Kepler's second law is a direct consequence of the conservation of angular momentum. Statement 2 is false because the universal gravitational constant ($G$) is a universal constant and does not depend on the mass of bodies or the distance between them. Statement 3 is false because the formula for escape velocity is $v_e = \sqrt{2gR}$, which does not depend on the mass of the body being projected at all. Statement 4 is true because the period of a geostationary satellite is 24 hours and its orbit is about 36,000 km above the equator.
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