It is roughly called the barycentre : when two or more objects rotates with a point that is called as barycentre, the barry centre can be fix with one equation.

mass of the earth = M=6x10rest to power 24kg, distance of barycentre from the centre of the earth=x km, the moons mass= m=7.5x10rest to power 22kg

distance between earth and moon=Y km=384000 km, the equation is MxX=m(Y-X) if we put the above values in this equation :6x10rest to power24x X =7.5x10rest to power 21x(384000-X), therefore X=4740Km and the redius of the earth=6400 it means the barycentre of the earth and moon is on 4740km distance.

the centre of the earth rotates with the barycentre in 27 days, the barycentre of sun and jupiter will be 48000 km,

and in 2130 the barycentre of the solarsystem from the sun's centre will be only 14599 km.

your ideas ! please quote.