A planet moving along an elliptical orbit is closest to the sun at a distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are the linear velocities at these points respectively, then the ratio v₁/v₂ is

Question

Dr. Abubacker · Accepted Answer

[Solution from source] Gravity exerts no torque about the sun, so angular momentum is conserved; at perihelion and aphelion the velocity is perpendicular to the radius, so mv₁r₁ = mv₂r₂ and v₁/v₂ = r₂/r₁. The planet moves faster when closer, so the ratio must exceed 1, which rules out r₁/r₂. Answer (3).

Q. A planet moving along an elliptical orbit is closest to the sun at a distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are the linear velocities at these points respectively, then the ratio v₁/v₂ is

Explanation

Reviewed by Dr. Abubacker

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