You wrote: “The goal of higher education isn’t to create people who have answers, it’s to create people who can ask good questions and discover answers for themselves.”
OK: My question was: “Has it been proven that the Earth's magnetic field originates within the Earth?”
Is that a good question?
The link that I posted indicates that it has NOT been proven.
Then in that site it continues that: “The rotation of the Earth plays a part in generating the currents which are presumed to be the source of the magnetic field.”
This presumption then simply assumes that the mass of the Earth creates a magnetic field simply by rotating. I find that hard to believe. In the next link that I posted, it indicates that magnetic field is caused by moving electrons.
What would cause electrons to move within the Earth? (Is that a good question?)
In the next link it indicates that there are very energetic electrons moving around the earth.
Conclusion: Moving Electrons going around the Earth create the Earth's magnetic field.
As for orbital mechanics it seems simple. If an object is moving fast enough away from the Earth then it can escape the Earth's gravitational field, if the objects has a certain speed, then it can stay in orbit around the Earth, if the object is moving slow then it can be pulled to the ground by the gravitational field.
Naturally you can explain it with mathematics, such as: \epsilon = \epsilon_k+\epsilon_p\!

\epsilon={v^2\over}}-{/mu\over{r}}= -{1\over{2}}{\mu^2\over{h^2}}\left(1-e^2\right)=-\frac{\mu}{2a}