Part of the answer is planets are not just orbiting the sun, but they’re orbiting each other, but that’s not the whole story.
Think of it as the planet is actually falling into the sun, it just doesn’t hit the sun because it’s moving in a direction that is not towards the sun as well (perpendicular to the line between the planet and the sun).
If you drop a planet from standstill, it will hit the sun. If you push a planet a little bit, it will fall towards the sun, but some of that push will be enough to cause it to miss the sun, even if by a little bit. If it misses the e sun, it will slingshot around and come back to its starting position (an elliptical orbit).
Now if you push a planet with the exact perfect force, it will orbit in a perfect circle. Anything more, or less than that, will form an ellipse.
Because a perfectly circular orbit is not only very hard to occur by chance but even if it was it would not remain as such unless there were zero perturbations from other bodies acting on the orbiting bodies which is impossible. In fact the orbits of the planets in our solar system being as close to circular as they are is pretty impressive.
Like some others have said, for most star systems that have multiple planets orbiting a sun one planet or another may have some substantial gravitational force that will pull another planet slightly put of orbit. This will most likely permanently alter the planets orbit. If you want something that will blow your mind, the sun and Jupiter orbit a point called the Barycenter which is just outside the sun’s surface.
A circle is an ellipse and a very specific one. Just like how a square is a rectangle, but not all rectangles are squares. There’s many different conditions that will form an ellipse but only one perfect condition to make a circle. Since there are more ways to make an ellipse that is non-circular, that is what will happen the vast majority of the time.
If you idealise orbits to two body problem, they are conic sections. That is hyperbola, parabola, ellipse or circle. Circle is a very exact thing, it really only has one degree of freedom whereas ellipse has two. You could say there is only one circle, but many ellipses. In nature you don’t really get such precise perfect things as a circle, so planets have elliptical orbits, that are really quite close to circular, just not exactly.
Imagine you’ve got a pencil on a table. There are a lot of orientations it can be sat in – point to the left, point to the right, point facing you, a million different ways it can be laying flat on the table. But standing up on its point or on the eraser is also totally valid and doesn’t contradict any physical laws (it’s not very stable, but it doesn’t have to be).
In the same way, when you look at planetary orbits you check the physical laws and look at the possible solutions, and you see a huge range of ellipses and also circular. You would expect to see a million planets in elliptical orbits and only occasional circles, and if you look at cometary orbits that’s exactly what you see – lots and lots of very eccentric ellipses and few closer to circular.
So the real question you should be asking is given that, why are so many of the planetary orbits so very close to circular?
The main reason I can think of, and I’m happy to have more pointed out – the gas that formed the planets wasn’t a uniform cloud, it was thrown from the dust that became the sun as it was collapsing down, and it turns out if you model that spinning dust blob collapse, you get circular rings thrown off every so often from the equator of the big spinning dust blob. Those dust rings coalesced into most of the planets, so they were left with pretty circular orbits. You do get less circular orbits – Pluto and Mercury are pretty elliptical for planetish things.
Short answer is, its really hard to naturally settle into a perfectly circular orbit. Imagine the process of going from zero planets, to multiple ones. Our sun starts by itself, surrounded by gas, dust, etc. That material is not evenly distributed, and slowly, one of the more dense regions coalesce to form a planet. For the sake of simplicity, let’s call that planet Ploopiter. Ploopiter has time to gobble up a lot of stuff and gets real big. So big, it’s gravitational influence pulls on the Sun, hard. Ploopiter is also going too fast for how big and close to the Sun it is and begins to move away from the Sun, where it eventually settles to a stable orbit. While that’s happening, Ploopiter gobbles up more stuff and gets even bigger. It’s so big now, the center of gravity between it and the Sun is a point in space slightly outside the Sun’s surface. Let’s call this point, Barry. Ploopiter and the Sun both now orbit Barry. Because this all happened while Ploopiter was moving out to a stable orbit, the Sun and Ploopiter have slightly non-circular orbits around Barry. Non circular = ellipse.
Now other planets form with whatever material is left. There isn’t much so they don’t get that big. They pull less on the Sun, so the center of gravity between our smaller planet and the Sun is nearly at the center of the Sun. But the sun is moving around Barry. Our small planet (let’s call it Erf) is also being pulled on by Ploopiter whenever they’re close. Erf can’t orbit the Sun in a perfect circle if both the Sun wobbles around Barry, and Ploopiter gives it a tug sometimes.
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