To start with: the sun is not the center point of solar system. But the answer is more complicated than that. First, we have to define the center of our solar system, then we need to investigate why people believed the earth was the center instead of the ‘obvious’ answer of the sun, which is also wrong.
So, where is the real center of our solar system if it isn’t the sun?
So, to say that the sun is the center is reasonable, since the barycenter is so close to the sun. But using the sun as the center in calculations will lead to inaccurate results.
When calculating thigs to do with the center, you should always use the barycenter of our solar system since this will yield the correct results.
What is a barycenter?
The term ‘barycenter’ simply means the point where the center of mass is in any system. The center of mass in our solar system is near the sun because the sun is the astronomical object with the greatest mass in our solar system, but in other systems it may be further from any of the objects.
Where is the barycenter?
The barycenter is a point in space that is, for the majority of the time, not located within the sun. It is usually outside of the sun and the sun orbits around it.
The reason that the barycenter is not within the mass of the sun is because of Newton’s third law. This law states that every action has an equal and opposite reaction.
In this case, the way that the sun exerts gravitational force on the earth and the other planets is actually reciprocated to a lesser extent by the planets on the sun.
This is why the center of the sun could never be the center of our solar system.
So, is any astronomical object the center of anything?
If we talk in terms of the science we have just used, this is unlikely. This is because of a few factors. Imagine that there are two planets of exactly the same mass that are in space with nothing else around them. Since they are both the same mass, they will exert the same gravitational force on each other.
Therefore, they will both be put into orbit of the other and thus, the center of orbit would not be either of the planets, but a point of space in the middle of them.
This is because the masses of the two planets are equal so the acceleration must be equal too. They will end up both moving at exactly the same speed.
All of this is only possible if they are orbiting the midpoint in between the two of them, this is how we know that a midpoint is the real answer to the center of our solar system.
What about when the two planets are not the same mass?
If we have the same planets but this time give the second planet more mass than the first, the forces between them will still be equal and opposite according to newton’s third law.
But the equation F = ma shows that because the second planet has a larger mass than the first, the second planet must accelerate less to keep a constant force.
This means the second, larger planet will move less than the first smaller one. Because of this, the larger second planet will end up shifting towards the center of rotation, or the barycenter. Making it closer to the barycenter than the first planet is.
What about when one planet is a lot bigger than the other?
Well, this is similar to what we see with our sun. Bigger that second planet gets, the slower it has to move in order to keep the force a constant between the two planets, and thus the closer it will get to the barycenter or the center of rotation.
But the center of a system cannot be a planet or astronomical object unless the object’s mass is infinite. This means it would not have to move at all. And we have never seen anything like that in the universe.
Back to the sun
Since the sun is far larger in mass than the earth, it follows that the barycenter of our solar system is extremely close to the sun. The center cannot be the center of the sun since the sun does not have infinite mass. Also, there are more planets than just the earth that are exerting their own force on the sun.
And it isn’t just the planets: all planets, asteroids and moons will tug on the sun causing the barycenter to be outside of the sun. Our solar system’s center of mass is sometimes within the sun, but most of the time outside it, this is due to the complicated nature of all of the gravitational forces acting on the sun.
But why did people think the earth was the center?
The main reason for this belief is that people historically have felt that the earth is the center of the solar system due to a lack of knowledge, and mainly because that is how they felt.
We are an arrogant organism here on earth, we tend to think that everything revolves around us, including everything revolving around the earth. Years and years ago, when there were less astronomical advancements with technology, we could not measure that the earth’s path was actually curved and orbiting around the sun.
So, we assumed that the earth stayed still and everything moved around us, since this is what it looks like when we look up to the sky.