Two stars of masses 3Mₛ and 6Mₛ are separated by 9R, where R is the mean Earth-Sun distance and Mₛ is the Sun's mass. They orbit their common centre of mass in circular orbits with period nT, where T is Earth's orbital period. Find n.
Physics · Gravitation · Satellites, Orbital Motion & Kepler’s Laws
JEE Advanced 2021

Question

Two stars of masses 3Mₛ and 6Mₛ are separated by 9R, where R is the mean Earth-Sun distance and Mₛ is the Sun's mass. They orbit their common centre of mass in circular orbits with period nT, where T is Earth's orbital period. Find n.

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

JEE Advanced 2021

G1 Physics · Accepted Answer

Step 1: For a circular orbit, v = √(GM/r), L = m√(GMr), K = GMm/(2r), U = -GMm/r, E = -GMm/(2r), and T = 2π√(r³/GM). Step 2: Form the ratio or energy change using the given radii/masses. Step 3: Simplify to the requested value. Final: 9. In this specific setup, apply the calculation to: The distance between two stars of masses 3Mₛ and 6Mₛ is 9R. Here R is the mean distance between the cente.