If the areal velocity of one planet is 2 times the areal velocity of other planet, then find the ratio of their radii of circular motion around the sun.
Physics · Gravitation · Satellites, Orbital Motion & Kepler’s Laws
JEE Mains

Question

If the areal velocity of one planet is 2 times the areal velocity of other planet, then find the ratio of their radii of circular motion around the sun.

G1 Physics · Accepted Answer

Step 1: Kepler's second law givₑ constant areal velocity dA/dt = (1/2)rvₜ. At perihelion the velocity is transverse and maximum. Step 2: Hence vₘₐₓ = 2(dA/dt)/rₘᵢₙ. Step 3: Substitute the values and convert m s⁻¹ to km s⁻¹. Final: 4.