Problem 29 - A Complete Resource Book in Physics for JEE Main

Question

As observed from the earth, the sum appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from the earth, this would (A) be similarly true. (B) not be true because the force between the earth and mercury is not inverse square law. (C) not be true because the major gravitational force on mercury is due to the sun. (D) not be true because mercury is influenced by forces other than gravitational forces.

Step-by-Step Solution

Answer

The correct answer is (C), which states that Mercury's motion, as observed from Earth, is not an approximate circular orbit because the major gravitational force influencing it is due to the Sun.

Step 1: Analyze Each Option

Let's go through each option and check if it is true or false. (A) be similarly true: This suggests that Mercury's motion, as observed from Earth, would also appear to be an approximate circular orbit. (B) not be true because the force between the Earth and Mercury is not an inverse square law: This option implies that the behavior of Mercury's motion would be different because the gravitational force between Mercury and Earth is not an inverse square law. However, we must take into consideration the gravitational force between Mercury and the Sun. (C) not be true because the major gravitational force on Mercury is due to the Sun: This option suggests that the motion of Mercury should not appear to follow a circular orbit as observed from Earth, given that the major force acting on it is the gravitational force from the Sun. (D) not be true because Mercury is influenced by forces other than gravitational forces: This implies that other forces, besides gravity, affect Mercury's motion.

Step 2: Choose the Correct Option using Knowledge of Planetary Motion

Now, we'll analyze which of these options make the most sense based on our understanding of planetary motion, gravitational forces, and Kepler's laws. Option (A) could be true because, in general, the orbits of planets around the Sun are approximately circular when viewed from Earth (ignoring eccentricities). Option (B) is not the right explanation because, although it is true that Earth and Mercury's forces are not an inverse square law, the force between Mercury and the Sun is, and that is the primary force acting on Mercury. Option (C) is correct. The major gravitational force on Mercury is due to the Sun, and so its motion should be affected primarily by the Sun's gravity. Therefore, Mercury's motion as observed from Earth should be determined mainly by the Sun's gravity (which is a more influential factor in this scenario than the force between the Earth and Mercury). Option (D) is not true as far as planetary motion in the solar system is concerned. The principal force affecting planetary motion, including Mercury, in the solar system is the gravitational force. So, the most appropriate choice is option (C).

Step 3: Conclusion

Based on our understanding of planetary motion, gravitational forces, and Kepler's laws, we can conclude that the correct answer is option (C), which states that Mercury's motion, as observed from Earth, is not an approximate circular orbit because the major gravitational force influencing it is due to the Sun.