A binary star has period T = 2 Earth years and component separation L = 4 astronomical units. If M₁ = Mₛ, where Mₛ is the Sun's mass, find M₂/(5Mₛ).
Physics · Gravitation · Satellites, Orbital Motion & Kepler’s Laws
JEE Mains

Question

A binary star has period T = 2 Earth years and component separation L = 4 astronomical units. If M₁ = Mₛ, where Mₛ is the Sun's mass, find M₂/(5Mₛ).

G1 Physics · Accepted Answer

Step 1: Treat the two-star system as circular motion about the common centre of mass. The separation d obeys ω² = G(M₁+M₂)/d³. Step 2: Use r₁:r₂ = M₂:M₁ for the individual orbital radii; energy and angular momentum follow from v=ωr. Step 3: Apply the stated mass/radius change and simplify. Final: 3.