A rocket is launched normally from Earth's surface, away from the Sun, along the Sun-Earth line. The Sun is 3 × 10⁵ times as massive as Earth and is at a distance 2.5 × 10⁴ Earth radii. Earth's escape speed is vₑ = 11.2 km s⁻¹. Find the minimum initial speed vₛ needed to leave the Sun-Earth system.
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Question

A rocket is launched normally from Earth's surface, away from the Sun, along the Sun-Earth line. The Sun is 3 × 10⁵ times as massive as Earth and is at a distance 2.5 × 10⁴ Earth radii. Earth's escape speed is vₑ = 11.2 km s⁻¹. Find the minimum initial speed vₛ needed to leave the Sun-Earth system.

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G1 Physics · Accepted Answer

Step 1: Escape requires zero total mechanical energy at infinity: (1/2)mve² = GMm/R, so ve = √(2GM/R). Step 2: Express GM/R through surface gravity/density/radius when needed. Step 3: Take the required ratio or percentage change. Final: C: vs = 42 km s⁻¹.