A comet is in elliptical orbit around the sun. In this orbit the comet's smallest distance from the sun is 72 × 10⁶ m and its largest distance from the sun is 144 × 10⁶ m. The ratio of comet's maximum speed to the minimum speed in the orbit is : (Neglect the presence of all bodies other than the sun and comet).
Physics · Gravitation · Satellites, Orbital Motion & Kepler’s Laws
JEE Mains Advanced

Question

A comet is in elliptical orbit around the sun. In this orbit the comet's smallest distance from the sun is 72 × 10⁶ m and its largest distance from the sun is 144 × 10⁶ m. The ratio of comet's maximum speed to the minimum speed in the orbit is : (Neglect the presence of all bodies other than the sun and comet).

Physics · Gravitation · Satellites, Orbital Motion & Kepler’s Laws

G1 Physics · Accepted Answer

Step 1: Use conservation of specific mechanical energy ε = v²/2 - GM/r and angular momentum h = rvₜ. Step 2: For an ellipse, h² = GMa(1-e²) and ε = -GM/(2a); at a grazing point the radial distance equals the Earth/planet radius. Step 3: Apply the initial geometry and solve for e or the required speed. Final: 2. In this specific setup, apply the calculation to: A comet is in elliptical orbit around the sun. In this orbit the comet's smallest distance from the sun i.