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# Escape speed?

The escape speed from a distant planet is 41 km/s. If the acceleration of gravity on the planet surface is 16.0 m/s2, what is the radius of the planet?

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- billrussell42Lv 72 months agoFavorite Answer
V₀ = √(2GM/R) = 41000 m/s

2GM/R = 41000²

M = 41000²R/2G

g = GM/R² = 16

M = 16R²/G

41000²R/2G = 16R²/G

41000² = 32R

R = 5.25e7 m or 52500 km

g = GM/R²

Escape speedV₀ = √(2GM/r)V₀ = √(2gr) (alternate)G = 6.673e-11 Nm²/kg²where M is mass of body and r is distance from center of bodyg is gravity at the surface

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