Question

取离地球无限远处为重力势能的零点,设地球的质量为M,半径为R,引力常量为G,距地面高为h,质量为m的人造卫星的势能为-G

Answer 1

受到的地球引力=向心力

GMm/(R+h)^2=mV^2/(R+h)

Ek=(1/2)mV^2=GMm/[2(R+h)]

机械能E=Ek+Ep=GMm/[2(R+h)]-GMm/(R+h)=-GMm/[2(R+h)]