86.4 The gravitational field and Gauss's law for the the gravitational field Solution: For three vertical surfaces dm=「gds=0 aS For the inclined surface inct=g ds= -gj dS(sin 6f+ cos 6) gdS cos=-gScos0 For the bottom surface ∫g:dsy=∫、-g)(-s分 gds=gs=gS cos 6 86.4 The gravitational field and Gausss law for thethe gravitational field 5. Gauss's law for the gravitational field Solid angle d dAds· r dS cos p ds cos=dA de ② Gauss’slaw M The flux of the gravitational field of M through a closed surface ①us=5gdS 1919 §6.4 The gravitational field and Gauss’s law for the the gravitational field Solution: For three vertical surfaces ver = ⋅d = 0 ∫ g S r r Φ For the inclined surface θ θ Φ θ θ d cos cos )ˆ cos ˆ d ( sin ˆ incl d g S gS g S gj S i j S S = − = − = ⋅ = − ⋅ − + ∫ ∫ ∫ r r For the bottom surface d cosθ )ˆ ) ( d ˆ d ( btm g S gS gS g S gj S j S S = ′ = ′ = Φ = ⋅ ′ = − ⋅ − ′ ∫ ∫ ∫ r r x y θ S r d g r §6.4 The gravitational field and Gauss’s law for the the gravitational field 5. Gauss’s law for the gravitational field 1solid angle 2 2 2 d d ˆ d cos d r S r S r r A φ Ω = ⋅ = = r 2 Gauss’s law The flux of the gravitational field of M through a closed surface ∫ = ⋅ S clsd g dS r r Φ S r d dS cosφ = dA rˆ r r M dΩ φ