It is within the body of the earth itself, because the mass of earth is so much greater than the mass of the moon. It is called the "Barycenter" or "Barycentre". It is a moving point, because of the orbital and rotational movements of the two bodies.
A barycentre is the point at the centre of a system - weighted according to mass or some other attribute - a term used in astronomy for the centre of mass about which a system rotates.
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An apoapsis is the point of a body's elliptical orbit around the system's centre of mass where the distance between the body and the centre of mass is at its maximum.
The sun is the mass centre of the solar system.
An apocentre is another name for an apoapsis, the point of a body's elliptical orbit around its system's centre of mass where the distance between the body and the centre of mass is at its maximum.
It is. Any pair of objects in space orbit their common centre of mass. It gets considerably more complicated with more bodies, but this is a decent general rule. If we consider the earth-sun sytem in isolation, ignoring any other forces, then the system as a whole orbits its centre of mass, which lies within the sun. If you consider the Jupiter-Sun system, that centre of mass lies on the edge of the sun.
Because it was the centre of coalescence/mass round which the solar nebular condensed.
The centre of mass of any solid single oject cannot lie outside its absolute outline, because there is no mass to balance out that contained within it. The centre of a multiple body system can be outside all bodies, such as a binary star or planetary system (e.g. Pluto and Charon).
The term is "binary star system".
All planets orbit around the greatest centre of mass. In our solar system, that is our Sun.
No, many objects have no mass (at least no mass that is part of the body concerned) at their centre of mass. Not ,necessarily. Center of mass is an imaginary point.(at least no mass that is part of the body concerned)
The rest of the solar system orbits a star (the Sun) which stays at the centre. To be precise, the whole solar system revolves around its center of mass. The Sun has about 99.85% of the entire mass of the solar system. So, its not surprising that the center of mass of the solar system is close to the surface of the Sun and that the Sun more or less stays at the center.