For a planet, Earth's mass M e = 8 M p M_e=8M_p M e = 8 M p and Earth's radius R e = 2 R p . R_e=2R_p. R e = 2 R p . If Earth's escape speed is 11.2 km/s, the planet's escape speed is:
Physics · Gravitation · acceleration due to gravity and escape velocity
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Question

For a planet, Earth's mass M e = 8 M p M_e=8M_p M e ​ = 8 M p ​ and Earth's radius R e = 2 R p . R_e=2R_p. R e ​ = 2 R p ​ . If Earth's escape speed is 11.2 km/s, the planet's escape speed is:

G1 Physics · Accepted Answer

v e = √ ( 2 G M / R ) . v_e=√(2GM/R). v e ​ = √ ( 2 GM / R ) . Thus v p / v e = √ [ ( M p / R p ) / ( M e / R e ) ] = √ [ ( M e / 8 ) / ( R e / 2 ) ⋅ ( R e / M e ) ] = √ ( 1 / 4 ) = 1 / 2. v_p/v_e=√[(M_p/R_p)/(M_e/R_e)]=√[(M_e/8)/(R_e/2)·(R_e/M_e)]=√(1/4)=1/2. v p ​ / v e ​ = √ [( M p ​ / R p ​ ) / ( M e ​ / R e ​ )] = √ [( M e ​ /8 ) / ( R e ​ /2 ) ⋅ ( R e ​ / M e ​ )] = √ ( 1/4 ) = 1/2. Hence v p = 5.6 v_p=5.6 v p ​ = 5.6 km/s.

For a planet, Earth's mass M e = 8 M p M_e=8M_p M e ​ = 8 M p ​ and Earth's radius R e = 2 R p . R_e=2R_p. R e ​ = 2 R p ​ . If Earth's escape speed is 11.2 km/s, the planet's escape speed is:

For a planet, Earth's mass M e = 8 M p M_e=8M_p M e = 8 M p and Earth's radius R e = 2 R p . R_e=2R_p. R e = 2 R p . If Earth's escape speed is 11.2 km/s, the planet's escape speed is: