86.4 The gravitational field and Gauss's law for the the gravitational field Because 8. ds=dS cos 0=-GAn cos 0ud=8·dS=- gm ds coso -GMd2 @chd d=g dS=-4GM ds cpsφ=d4 ds2 S/ 86.4 The gravitational field and Gausss law for thethe gravitational field The flux through the spherical surface which surrounded the M GM GM =4g dS bas -NGM The flux through the arbitrary surface which surrounded the m D=s8 dS=-47GM20 Because d d cosθ cosφ 2 r GM g ⋅ S = g S = − r r ∫ ∫ ∫ = ⋅ = − = − Ω φ Φ d d cos d 2 S clsd GM r S g S GM r r Φ g dS 4πGM S clsd = ⋅ = − ∫ r r §6.4 The gravitational field and Gauss’s law for the the gravitational field S r d dS cosφ = dA rˆ r r M dΩ φ S θ g r GM S r GM r Sr r GM g S S S S π Φ 4 d ˆ d ˆ d 2 2 = − = ⋅ = − ⋅ = − ∫ ∫ ∫ r r The flux through the spherical surface which surrounded the M The flux through the arbitrary surface which surrounded the M g S GM S Φ = ⋅d = −4π ∫ r r §6.4 The gravitational field and Gauss’s law for the the gravitational field