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I was thinking last night: for most of my life I’ve been taught that the planets in our solar system orbit the Sun, which insinuates that the Sun is in a fixed point in 3-dimensional space, and that the planets orbit around this star in arcs.
But why is this so? Why does the Sun and the planets orbiting it not “drop” or fall into the space below them? Or is this actually the case, and that the Sun being fixed (and the planets orbiting it doing so on a fixed plane) is an incorrect assumption?
Why does the Sun and the planets orbiting it not “drop” or fall into the space below them?
Believe it or not, your confusion stems from your definition of "below".
So what is "down"? It's not a single direction at all. I think you will immediately see that it's actually "towards the center of the earth". Watch:
So why is "down" always towards the center of the Earth? Gravity. That's how it works, gravity pulls you towards the center of things. This is so fundamental that we have a term for it "center of mass".
Note that's "center of mass" and not "center of Earth". That's because gravity works on everything, which is why Newton called it Universal gravitation. Before Newton so clearly codified it, it was widely believed that motion on Earth was fundamentally different than in the sky - the mundane vs. the heavenly. But he demonstrated nope, it works on everything the exact same way.
Ok, so if the exact same thing works on earth and the planets, let's step back a bit. If you add up all the mass in the solar system, it turns out the sun is around 1000 times all the rest put together. So then if "down" on the earth is the center of the earth, one can see that "down" for the solar system would be the center of the sun. I mean, it's pretty much the solar system all by itself.
So, then, everything falls down toward the sun. And that's exactly what the planets are doing. Things fall down, not up or sideways. And down is towards the sun. So things fall towards the sun.
Now one tiny addition:
the planets in our solar system orbit the Sun
Did you know they do so on a plane? If "down" is simply "towards the sun", then why is Earth's orbit on the same plane as, say, Jupiter? Why isn't it orbiting in some other path?
Well that turns out to be history. Way in the past we didn't have planets, just a big ball of gas and dust. Anyone that wasn't in a stable orbit either hit the sun of was flung off into spaces, so over time you start to see things that are roughly circular. Now that circle could be anywhere, so why are the lined up? Well consider what happens if one bit of rock is circling left and another right. Eventually, giving it a billion years or so, they hit. Now you're left with one larger rock with the sum of their motions. Rinse, repeat. After that same billion years anyone with a non-circular orbit is gone, and what's left is a nice approximation of the total momentum of the original gas cloud, just condenced.
Physics is about measuring observables and making observations, and then finding mathematical models that fit the observations accurately and also can predict future behaviors of the participants accurately.
In ancient times the observations were with eyes and time measurements depended on the rising and setting of the sun. Even then they developed geocentric models: the earth is the center and the sun and stars, the firmament revolving around the earth.
In the Hipparchian and Ptolemaic systems of astronomy, the epicycle (from Ancient Greek: ἐπίκυκλος, literally upon the circle, meaning circle moving on another circle1) was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. In particular it explained the apparent retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from the Earth.
A complicated model fitting the data then observed and being predictive, it still works in the planetaria constructions on the net.
All motions in the earth star system are relative, and the mathematics transforms from one system to the other. The discovery of the Heliocentric system and the preferred usage is because mathematically it is much much simpler and clear , and the introduction of the gravitational force as responsible for the orbits took understanding one level down.
Why does the Sun and the planets orbiting it not “drop” or fall into the space below them?
At this level of forces and attraction of massive bodies, one has a theory which has conservation laws that have to be obeyed, and the orbits of the planets around the sun or the moon around the earth have to obey these absolute laws : conservation of energy, conservation of momentum and conservation of angular momentum.
A body approaching the sun can be caught in a limited number of trajectories, the same as objects thrown on the air, the so called conic sections.: parabbolas, hyperbolas elipses and circles. The last two are closed orbits, and once caught there angular momentum conservation keeps them there, continually falling and continually avoiding the fall.
One has to study the mathematics to really understand physics models. The answer to the title is : angular momentum conservation. (Interactions with other bodies can change the distribution of angular momentum in a system, but it has to be overall conserved.)
See also the answer here for the earth moon system.
The short answer: Gravity!
Under Newton's laws of motion (which are mostly sufficiently accurate to model the solar system), a star and with planets roughly confined to a plane is a reasonable stable configuration. For convenience, you can treat the star as a fixed point at the origin of your coordinate system, but according to Galilean relativity you can add a velocity to the star and its orbiting bodies, without affecting the physics at all.
In other words, if the Sun suddenly started "dropping" in a certain direction at say 1000 km/h, and everything else in the solar system did too, it would make no difference to the dynamics of the solar system.
However, the solar system doesn't exist in a void. The solar system is gravitationally bound to the Milky Way galaxy. We orbit within the galaxy, but it's by no means a simple Keplerian orbit, but it means the solar system is kind of locked into position, relative to our neighbouring stars, although there is a small amount of relative motion. The Milky Way is gravitationally bound to the Local group, which is gravitationally bound to the Virgo supercluster. Etc. The old Atlas of the Universe site has some nice diagrams.
But if we neglect all the stuff outside the solar system, and our motions with respect to it, then it's still not quite right to treat the Sun as a fixed point, since it moves relative to the barycentre of the solar system, as shown in the diagram here.
The sun is not in a fixed position. It is moving 371 km/s relative to the cosmological microwave backround, which rougly corresponds to how fast it is moving relative to the average masses in the universe. Much of this is because of the velocity of the Milky Way, which might be about 627 km/s. Inside the Milky Way it is moving about 200-220 km/s (the velocities are in different directions, so they do not add straight to each other).
Newton figured out that objects will keep moving once in motion, with forces changing their direction. In this case gravity is what is keeping the planets in orbits around the sun, and the sun orbiting around the center of the galaxy. There is nothing "keeping them up" and in a sense they are falling because of gravity, but because of their high velocities they miss their central objects.
There's no such thing as "below" in the Universe. There are observers and respect to the observers there are coordinate systems. And all physics laws are based on these observers and how they measure things around.
Let's take an inertial frame. We can observe and analyze the motion of the solar system with respect to this inertial frame. When we observe the motion of the system we see that everything is bonded to each other. This means that the total energy of the planets is negative.
Negative total energy simply implies that a system is bounded. If the system is bounded then we can observe an orbital motion around the stars (or some other type of motions respect to the energy values).
But what happens if the total energy is positive ? Positive total energy means the particle can escape from the system or in other words, from the gravitational force that is acting on it. Simply it becomes "free".
Sun is also bounded to the Milky Way and Milky Way is also bounded to the SuperCluster called Laniakea, which contains approximately 100,000 galaxies.
The answer to your question is simply everything around you see is bonded to each other in a way that, they don't move randomly/arbitrarily in space.
