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?

Question

Gaurav Shrivastava · Accepted Answer

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.

Categories

Popular topics

Regarding the principles of astrodynamics and gravitation, consider the following statements:

Detailed Explanation & Solution

Related Questions