Planetary Orbits and Gravitational Force
Question: Every planet revolves around the sun in an elliptical orbit (assuming the sun and the planet are point-like masses compared to the distance between them). Consider the following statements:
Detailed Step-by-Step Explanation
Statement A: The gravitational force between two masses is given by Newton's law of gravitation: \[ F = G\frac{m_1 m_2}{r^2}. \] Thus the force is inversely proportional to the square of the distance. Statement A is true.
Statement B: Newton's law of gravitation shows that the force is directly proportional to the product of the masses (i.e., \(m_1 m_2\)), not inversely. So Statement B is false.
Statement C: The gravitational forces between two point masses act along the line joining the centers of the masses. Therefore, these forces are central forces. Statement C is true.
Statement D: Since the gravitational force is a central force (directed along the line joining the masses), the torque about the sun on the planet (with respect to the sun) is zero: \[ \vec{\tau} = \vec{r} \times \vec{F} = 0. \] Statement D is true.
Conclusion: The correct statements are A, C, and D, which corresponds to option (3) A, C, D.
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