Orbital mechanics, or rather dynamics – the objects are moving – is very simple at least in our part of the Universe. Just look at the Moon. There must be both an attractive force and a repulsive force acting between us on Earth and the Moon. The strength of each one is maybe dependent on gravity and the distance between the Earth and the Moon. It seems the Moon orbits Earth elliptically in space. Don't ask me to prove it. Just look up!
On Wikipedia it says the perigee of the Moon is ~362 000 km and the apogee is ~405 000km with the midpoint of this elliptical orbit being ~384 000km from Earth.
Let’s start out at this midpoint with the moon having momentum leading it away from Earth in its orbit. As the Moon gets farther away from Earth beyond 384 000km, the attractive force comes to dominate the repulsive force. Meaning the Moon begins to be net pulled towards the Earth. First the momentum away from the Earth is decelerated until the Moon no longer has any momentum moving away from the Earth at the apogee ~405 000km.
As the attractive force is still dominant at this distance, the Moon begins gaining momentum moving towards Earth in its orbit. Until it builds up some good momentum and passes through the midpoint distance of 384 000km once again, but this time going the other way. You can see it yourself by looking up on the Moon. Use your eyes.
As the Moon travels closer to Earth, now the repulsive force begins to dominate. And gradually the repulsive force chips away at the Moon's momentum towards Earth. Until at ~362 000km the repulsive force has brought the Moon's momentum towards Earth to 0. And now the Moon begins to gain momentum moving away from Earth again. It is a simple example or orbital dynamics!
With this the Moon can remain in orbit of Earth for millions or billions of years. Kepler has explained it. One question remains; wouldn't this going back and forth between repulsive and attractive locations of force in orbit, eventually center the Moon at the midpoint distance. For this, I think the rotation of Earth, and the movement of Earth away from its own midpoint away from the Moon, will keep the Moon from achieving a resting midpoint. Another possibility is the action of other bodies like the Sun on the Earth-Moon system, will keep the system from rest distances. Yet another possibility is the idea of a tendency towards stability is based on observing things on Earth, where there is resistance like air resistance, which that tendency might not be true in space.
Anyway, the easiest way to understand orbital mechanics is to look out of the window and watch the Moon.
Our Solar System was, if you believe what you are told at school or by Wikipedia, formed 4.6 billion years ago from the gravitational collapse of a giant interstellar molecular cloud. Imagine that! It was long before I was born and I am sorry I cannot prove it.
However, if you today, 4.6 billion years later, look further away from the tip of your nose and our Universe or Solar System and study other solar systems or galaxies in the sky above, you will find that they do not orbit anything and pop up and disappear into nothing at regular intervals not following any rules of gravity and orbital dynamics.
Don't blame me for it.