The acceleration of Solar System body number i is, according to Newton's laws: r ¨ ¨ i = G ∑ ∑ j ≠ ≠ i m j r i j − − 2 r ^ ^ i j where m j is the mass of body j, r i j is the distance between body i and body j, r ^ ^ i j is the unit vector from body i towards body j, and the vector summation is over all bodies in the Solar System, besides i itself.