<Dd> − ∇ ⋅ g = ∇ 2 Φ = 4 π G ρ (\ displaystyle - \ nabla \ cdot \ mathbf (g) = \ nabla ^ (2) \ Phi = 4 \ pi G \ rho) </Dd> <P> which contains Gauss's law for gravity, and Poisson's equation for gravity . Newton's and Gauss's law are mathematically equivalent, and are related by the divergence theorem . Poisson's equation is obtained by taking the divergence of both sides of the previous equation . These classical equations are differential equations of motion for a test particle in the presence of a gravitational field, i.e. setting up and solving these equations allows the motion of a test mass to be determined and described . </P> <P> The field around multiple particles is simply the vector sum of the fields around each individual particle . An object in such a field will experience a force that equals the vector sum of the forces it would experience in these individual fields . This is mathematically </P> <Dl> <Dd> g j (net) = ∑ i ≠ j g i = 1 m j ∑ i ≠ j F i = − G ∑ i ≠ j m i R ^ i j R i − R j 2 = − ∑ i ≠ j ∇ Φ i (\ displaystyle \ mathbf (g) _ (j) ^ (\ text ((net))) = \ sum _ (i \ neq j) \ mathbf (g) _ (i) = (\ frac (1) (m_ (j))) \ sum _ (i \ neq j) \ mathbf (F) _ (i) = - G \ sum _ (i \ neq j) m_ (i) (\ frac (\ mathbf (\ hat (R)) _ (ij)) (\ left \ mathbf (R) _ (i) - \ mathbf (R) _ (j) \ right ^ (2))) = - \ sum _ (i \ neq j) \ nabla \ Phi _ (i)) </Dd> </Dl>

Any object that moves in the earth's gravitational field is called a