4. What is the flux of the total gravitational field of the Earth and moon through a closed surface that encloses the Moon? If another surface encloses both the earth and Moon, by how much is the flux of the gravitational field changed? The surfaces are shown in figure (a)The flux of the total gravitational field of the Earth and Moon through a closed surface S, that encloses the Moon is =+8ds=-47GMM (b) The flux of the total gravitational field of the Earth and Moon through a closed surface S2 encloses both the earth and moon 02=5g:d=-x(M+ME) The flux of the gravitational field changed ④=中2-1=-4mGMg4. What is the flux of the total gravitational field of the Earth and Moon through a closed surface that encloses the Moon? If another surface encloses both the earth and Moon, by how much is the flux of the gravitational field changed? Solution: The surfaces are shown in figure. (a) The flux of the total gravitational field of the Earth and Moon through a closed surface S1 that encloses the Moon is M S Φ g ds 4πGM 1 1 = ⋅ = − ∫ v v (b) The flux of the total gravitational field of the Earth and Moon through a closed surface S2 encloses both the earth and Moon is d 4 ( ) 2 2 M E S Φ = ∫ g ⋅ s = − πG M + M v v The flux of the gravitational field changed is Φ Φ Φ πGM E 4 ∆ = 2 − 1 = − MM ME S2 S1