86.4 The gravitational field and Gauss's law for thethe gravitational field Example 1 M g dg =dg cosa g P dM 8= Gd。8=[ dg cos a= x G花 ds (R2+x2)√R2+ g(x)=-gi 2TRAGx (R2+x2)32 86.4 The gravitational field and Gausss law for the the gravitational field 3. Gravitational field lines A useful alternative geometric representation of the field F GM The properties of the field lines: OThe direction of the gravitational field at any point is tangent to the field line passing through that point and in the direction indicated by arrows on the field line. 1616 §6.4 The gravitational field and Gauss’s law for the the gravitational field Example 1: x O P λ R g r d g r d α dM 2 2 3 2 2 2 2 0 2 2 2 ( ) 2 d ( ) d cos d R x R Gx s R x x R x G s r x r G g g R x + = + + = = = ∫ ∫ ∫ π λ λ λ α π dgx = dg cosα s r G r M g G d d d 2 2 λ = = g r g x g i x ˆ ( ) = − r 3. Gravitational field lines A useful alternative geometric representation of the field. r r GM m F g(r) ˆ 2 = = − r r 1The direction of the gravitational field at any point is tangent to the field line passing through that point and in the direction indicated by arrows on the field line. The properties of the field lines: §6.4 The gravitational field and Gauss’s law for the the gravitational field