I want to know why the Earth rotates around the sun. Why doesn't it rotate around the moon or a different star?

# [Physics] Why does the earth revolve around the sun?

earth

#### Related Solutions

I think I might understand another facet of your question besides what is addressed in the comments. Let me demonstrate a result in classical mechanics which I think might alleviate your concern.

The result is that

*Given a system of particles, the center of mass of the system moves is though it were a point mass acted on by the net external force on the system.*

So if you think of the Earth-Moon system as being acted on by a net external force which is simply the gravitational attraction to the Sun (to good approximation), then what's happening is that this entire system is orbiting (essentially freely falling) around the sun. The details of what's happening in the Earth-Moon system itself are described by the first link in the original comments, but for purposes of what's happening to the entire system consisting of the Earth+Moon when it orbits the Sun, the details of the internal interactions don't really matter.

Here is a proof of the statement above:

Consider a system of particles with masses $m_i$ and positions $\mathbf x_i$ as viewed in an inertial frame. Newton's second law tells us that the net force $\mathbf F_i$ on each particle is equal to its mass times its acceleration; $$ \mathbf F_i = m_i \mathbf a_i, \qquad \mathbf a_i = \ddot{\mathbf x}_i $$ Let $\mathbf f_{ij}$ denote the force of particle $j$ on particle $i$, and let us break up the force $\mathbf F_i$ on each particle into the sum of the force $\mathbf F^e_i$ due to interactions external to the system and the net force $\sum_j \mathbf f_{ij}$ due to interactions with all other particles in the system; $$ \mathbf F_i = \mathbf F_i^e + \sum_j \mathbf f_{ij} $$ Combining these two facts, we find that $$ \sum_i m_i\mathbf a_i = \sum_i \mathbf F_i^e + \sum_{ij} \mathbf f_{ij} $$ The last term vanishes by Newton's third law $\mathbf f_{ij} = -\mathbf f_{ji}$. The term on the left of the equality is just $M\ddot {\mathbf R}$ where $M$ is the total mass and $\mathbf R$ is the position of the center of mass of the system. Combining these facts gives $$ M\ddot{\mathbf R} = \sum_i \mathbf F_i^e $$

The dominant hypothesis regarding the formation of the Moon is that a Mars-sized object collided with the proto-Earth 4.5 billion years ago. The Earth is rotating now because of that collision 4.5 billion years ago.

As the linked question shows, angular momentum is a conserved quantity. Just as something has to happen to make a moving object change its linear momentum, something has to happen to make a rotating object change its angular momentum. That "something" is called force in the case of linear momentum, torque in the case of angular momentum.

External torques do act on the Earth. Tidal forces transfer angular momentum from the Earth's rotation to the Moon's orbit. The Moon formed fairly close to the Earth shortly after that giant impact 4.5 billion years ago, and a day was probably only four to six hours long back then. By a billion years ago, the Moon had retreated significantly and the Earth had slowed down so that a day was 18 to 21 hours long. The Earth has continued slowing down, and will continue to do so.

If those external torques didn't exist we would still have a fast spinning Earth.

## Best Answer

It doesn't. All the planets and the Sun, along with asteroids and comets and multiple other objects all revolve around an effective center of mass known as the barycenter of the solar system. Because the mass of the Sun is so much larger than everything else, that barycenter is close to the Sun.

If you cconsider an isolated Earth-Sun system, the revolution would be around a point about 450 km from the center of the Sun. The Sun itself is about 696000 km in radius, so the Sun would be "wobbling" around, but the Earth is taking a very long trip around that point, from 150 Gm away. So, the primary appearance is that the Earth is travelling around the Sun. In reality, the Sun is moving, too, but due to the other planets, it's not a purely elliptical motion.

For the Earth-Moon system, the barycenter is about 4600 km from the center of the Earth, which is 6380 km in diameter. That's a much bigger "wobble" but the Moon is still a long distance away, 384000 km.

The Sun's mass is so larger that the Earth-Moon revolutionary system orbits the Sun together, but the Earth is

alsorevolving around the Earth-Moon barycenter.