What is the distance between the center of mass of the earth-sun system and center of the sun?

Question

Please explain how this is calculated

Answer 1

The sun's mass is 328,900 times the mass of the earth-moon combination. Divide the distance from the center of the sun to the center of the earth by that, and get about 300 miles from the center of the sun to the barycenter.

Answer 2

This is a way more complicated question than you think it is. The center of the sun moves around the solar system's center of mass as a countermass to the centers of mass of everything else in the solar system.

The motion of the sun's center in this regard is very complicated, but the envelope of those motions is roughly a MacLauren ellipsoid whose two major axes are almost coplaner with Jupiter's orbit. The major axes each are about two solar diameters long and the minor axis is about 5% of a solar diameter long.

Although Jupiter and Saturn have the most influence on the sun's motion, the effect of Uranus becomes apparent with the passage of time. So you can't answer your question with the simple application of two-body mechanics.

The center of mass between the sun and Earth is 279 miles from the center of the sun. But the center of mass that counts is the solar system center of mass.

Answer 3

A simple way to approximate this distance is to assume, as Isaac Newton did, that all of the mass of each body is concentrated at its center. Thus, the problem becomes a teeter-totter equation where DsunXMsun=DearthXMearth where Dsun+Dearth=93,000,000 miles. The actual point of balance is slightly more earthward and requires complex calculus to solve. (Msun= the sun's mass and Mearth= the earth's mass.) P.S. I disagree with David S. The center of mass of two bodies can always be calculated, regardless of the influnce of other bodies. If his argument is carried to its conclusion, we would need to factor in the Andromeda galaxy and everything else in the universe!

Answer 4

450 km

R=1/M (sum mi ri)