A planet revolve around the Sun in an elliptical orbit. Its areal velocity dA/dt is 4.0 × 10¹⁶ m² s⁻¹. The least distance between the planet and the Sun is 2 × 10¹² m. Find the maximum speed of the planet in km s⁻¹.
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Question

A planet revolve around the Sun in an elliptical orbit. Its areal velocity dA/dt is 4.0 × 10¹⁶ m² s⁻¹. The least distance between the planet and the Sun is 2 × 10¹² m. Find the maximum speed of the planet in km s⁻¹.

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G1 Physics · Accepted Answer

Step 1: Kepler's second law givₑ areal velocity dA/dt=(1/2)rvₜ. At the nearest point the velocity is perpendicular to the radius and is maximum. Step 2: vₘₐₓ=2(dA/dt)/rₘᵢₙ=2(4.0×10¹⁶)/(2×10¹²)=4×10⁴ m s⁻¹. Step 3: This is 40 km s⁻¹. Final: C.