Consider a particle moves in inverse square law central force motion and – Free B10
Consider a particle moves in inverse square law central force motion and choose the correct answer in the following statements:
Answer
Planet’s Orbital Motion Explained – Central Force Mechanics
Question 1: Circular Orbit Condition
In inverse square law central force motion, a particle’s orbit is circular when:
The shape of the orbit is determined by its eccentricity (ε) and total energy (E).
- For a circular orbit: ε = 0 and E = Vmin (minimum bound energy).
- Option a: ε = 0 and E = 0 – Incorrect (circular orbit needs negative energy).
- Option b: ε = 1 and E = 0 – Incorrect (ε = 1 indicates parabolic path).
- Option c: ε = 0 and E = Vmin – Correct.
- Option d: ε = 1 and E = Vmin – Incorrect (contradiction between ε and E).
Final Answer: Option c
Question 2: Speed Comparison at Periapsis and Apoapsis
Given an elliptical orbit, compare speeds at point A (periapsis) and point B (apoapsis).
Using:
- Conservation of Angular Momentum: L = m × r × v⊥
- Kepler’s Second Law: Equal areas in equal time ⇒ faster motion when closer to the center.
Since rA < rB, then vA > vB to conserve angular momentum.
Final Answer: Option c – vA > vB
Question 3: Speed Comparison at Different Orbit Points
In another elliptical orbit diagram, compare speeds at point B (periapsis) and point C (apoapsis).
Applying same principles:
- Point B is closest ⇒ periapsis.
- Point C is farthest ⇒ apoapsis.
- So, vB > vC
Final Answer: Option c – vB > vC
📌 Summary of Final Answers
- Question 1: Option c – ε = 0 and E = Vmin
- Question 2: Option c – vA > vB
- Question 3: Option c – vB > vC