Question Number 104299 by aurpeyz last updated on 20/Jul/20

an astraonaut weighs 3200N on a planet whose mass is the same as that of the earth but whose radius is half that of the earth. the astronsut weight on the earth is what?

Answered by OlafThorendsen last updated on 20/Jul/20

g_(planet)  = ((M_(planet) G)/R_(planet) ^2 )  g_(earth)  = ((M_(earth) G)/R_(earth) ^2 )  (g_(earth) /g_(planet) ) = (M_(earth) /M_(planet) )×((R_(planet) /R_(earth) ))^2   but M_(planet)  = M_(earth)   ⇒(g_(earth) /g_(planet) ) = ((R_(planet) /R_(earth) ))^2   ⇒(g_(earth) /g_(planet) ) = ((1/2))^2 = (1/4)  ⇒ Weight on earth =  Weight on the planet×(1/4)  = ((3200)/4) = 800 N  (≈ 80 kg : correct for a  human being)

Answered by Dwaipayan Shikari last updated on 20/Jul/20

(g/(g′))=(((R+H)^2 )/R^2 )  ((mg)/(mg′))=((((R/2))^2 )/R^2 )  ((mg)/(mg′))=(1/4)  ((mg)/(3200))=(1/4)  mg=800 N