# Where is the center of mass of the solar system?

Nov 18, 2015

#### Explanation:

Our solar system consists of the sun, eight planets and their moons, and a bunch of asteroids and comets. By far the majority of the mass in our solar system lies inside of the sun, around 99.8%. We should therefore expect the center of mass, or center of mass, to be especially close to the sun.

The planets themselves move though, so the center of mass moves with them. That means we cannot get an exact answer for where the center of mass is, but we can get an idea of its maximum distance from the center of the sun.

If all of the planets were to line up, each planet would pull the center of mass a little bit farther toward itself, and a little bit farther away from the center of the sun. The center of mass formula tells us that the center of mass location, ${x}_{c}$, for a series of $n$ objects can be found by;

${x}_{c} = \frac{{m}_{1} {x}_{1} + {m}_{2} {x}_{2} + {m}_{3} {x}_{3} + \ldots + {m}_{n} {x}_{n}}{{m}_{1} + {m}_{2} + {m}_{3} + \ldots + {m}_{n}} = \frac{{\sum}_{1}^{n} {m}_{i} {x}_{i}}{{\sum}_{1}^{n} {m}_{i}}$

If we set the sun at $x = 0$ and use the average distance of the planets from the sun, we can approximate the center of mass of the solar system if all of the planets were to align. This would be the farthest the center of mass would move. Plugging in the masses of the sun and planets, found here , and their average distance to the sun, found here , we get a center of mass of a little over twice the radius of the sun.

The planets will never actually align like this however, and most of the time they are scattered around the sun, with their gravity working against each other, so the center of mass should typically be found inside the sun.