已知地球的半径为R，地面的重力加速度为g，引力常量为G，如果不考虑地球自转的影响，那么地球的质量表达式为，地球平均密度的表达式为．

Question

已知地球的半径为R，地面的重力加速度为g，引力常量为G，如果不考虑地球自转的影响，那么地球的质量表达式为 ___ ，地球平均密度的表达式为 ___ ．

Answer 1

由地球表面万有引力等于重力，
可得：G(Mm)/(R2)=mg
解得：M=(gR2)/(G)
地球体积为：V=(4)/(3)πR3
故地球密度为：ρ=(M)/(V)=((gR2)/(G))/((4)/(3)πR3)=(3g)/(4πGR)
故答案为：(gR2)/(G)，(3g)/(4πGR) G(Mm)/(R2)MmMmMmR2R2R22=mg
解得：M=(gR2)/(G)
地球体积为：V=(4)/(3)πR3
故地球密度为：ρ=(M)/(V)=((gR2)/(G))/((4)/(3)πR3)=(3g)/(4πGR)
故答案为：(gR2)/(G)，(3g)/(4πGR) M=(gR2)/(G)gR2gR2gR22GGG
地球体积为：V=(4)/(3)πR3
故地球密度为：ρ=(M)/(V)=((gR2)/(G))/((4)/(3)πR3)=(3g)/(4πGR)
故答案为：(gR2)/(G)，(3g)/(4πGR) V=(4)/(3)444333πR3
故地球密度为：ρ=(M)/(V)=((gR2)/(G))/((4)/(3)πR3)=(3g)/(4πGR)
故答案为：(gR2)/(G)，(3g)/(4πGR) 3
故地球密度为：ρ=(M)/(V)=((gR2)/(G))/((4)/(3)πR3)=(3g)/(4πGR)
故答案为：(gR2)/(G)，(3g)/(4πGR) ρ=(M)/(V)MMMVVV=((gR2)/(G))/((4)/(3)πR3)=(3g)/(4πGR)
故答案为：(gR2)/(G)，(3g)/(4πGR) ((gR2)/(G))/((4)/(3)πR3)(gR2)/(G)(gR2)/(G)(gR2)/(G)gR2gR2gR22GGG(4)/(3)πR3(4)/(3)πR3(4)/(3)444333πR33=(3g)/(4πGR)
故答案为：(gR2)/(G)，(3g)/(4πGR) (3g)/(4πGR)3g3g3g4πGR4πGR4πGR
故答案为：(gR2)/(G)，(3g)/(4πGR) (gR2)/(G)gR2gR2gR22GGG，(3g)/(4πGR) (3g)/(4πGR)3g3g3g4πGR4πGR4πGR