What is the escape velocity from the surface of a spherical planet having twice the mass of Earth (2 M_E) and twice the radius of Earth (2 R_E)?
Answer and explanation
Correct answer: D. Equal to the escape velocity from Earth (v_e)
- Step 1: Escape velocity formula: v_e = sqrt(2 G M / R). Step 2. For the new planet: v_e' = sqrt(2 G (2 M_E) / (2 R_E)) = sqrt(2 G M_E / R_E) = v_e. Step 3. The factor of 2 in mass cancels with the factor of 2 in radius under the square root. Answer: Equal to the escape velocity from Earth (v_e). Why not the others: 2 v_e would require an 8-fold mass increase or 4-fold radius decrease.
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