When you have two massive objects in space, they both orbit around a point between them that's levied towards the heavier one, something we call a "barycentre".
The more similar the objects are in mass, the more central the barycentre will be relative to their positions, and hence the objects will appear to equally orbit around a single point.
However, as you might expect, there is a huge range of objects in the universe in terms of their mass and, as is the case with a lot of solar systems, you quite often have 1 massive object that has loads of relatively tiny objects orbiting around it.
That's because, as I mentioned earlier, the barycentre is shifted towards the more massive object, and when the difference in mass is so great, the barycentre will essentially reside inside of the more massive object.
The most recognisable example of this would be the sun and Earth.
The sun is approximately 330,000 times more massive than Earth, meaning that it would take almost a third of a million Earths to match the mass of the sun!
Therefore, the barycentre between the two lies inside of the sun, which simplifies to just us orbiting around the sun.
Not only is this the case with Earth, but everything else in the Solar System...
... Apart from Jupiter.
The most massive planet in our solar system
Jupiter is the largest planet by volume in the Solar System, but more importantly, it's the most massive, and by a significant margin.
In fact, Jupiter is so massive that it's more than twice the combined mass of everything, (apart from the sun of course) in the solar system.
Saturn is absolutely huge - how can Jupiter be more than twice the mass of Saturn let alone anything else....
While Saturn is extremely large in terms of volume, coming close to the size of Jupiter, its mass is significantly less.
The reason for that is slightly off-topic and instead covered in one of my other articles which you can give a read here if you're interested.
The relative sizes of the 4 gas giants compared to the Earth! Note that even though Jupiter isn't astronomically larger than, say Saturn, it is far, far heavier in terms of mass...
Jupiter is over 350 times as massive as the Earth, where as Saturn, the 2nd most massive planet, is only 90 times as massive...
Now, because Jupiter is so massive, even though the sun is still 1000 times more massive, that difference is small enough for the barycentre to be shifted just outside of the sun, and hence they both orbit together around this point.
It's still very much one sided though, as this barycentre lies a mere 30,000km away from the sun's surface, but that's enough of a difference to recognise.
See below a couple of screenshots I took in Universe Sandbox that sort of illustrates how it orbits around a barycentre with and because of Jupiter. The lines that you can see are orbital lines of the sun that represent its path.
Hopefully, you can see that the sun is being tugged at with enough "force" (gravity isn't a force per say), such that it shifts to the direction of whatever is tugging it.
The sun appears to reach a point before falling back and completing another half circle. This is because as Jupiter orbits around this barycentre, it tugs at the sun from different directions as time passes.
Therefore, it can be concluded that Jupiter does not actually orbit the sun, despite common belief and instead orbits around a single point that's located just outside of the sun.
Because this barycentre, or centre of gravity as you can also call it, is located outside of the sun, the sun also orbits around this point just like Jupiter does.
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