My question is how does it get up to that speed? Perhaps the delivery vehicle delivers that also, then vacuum does the rest plus onboard propulsion does the tweaking?
I think you've answered your own question here.
Yes the delivery vehicle gives it to the proper height and the required speed. Inertia then keeps the vehicle in the proper orbit with some tweaking required cause of the near vacuum. The orbit needs tweaking primarily because of gravity perturbations from moon and sun, maybe also some effect from the solar wind and the earth not being a perfect sphere. I think only a few tweaks per year are needed to keep satellites in a proper orbit.
To first order though, the moon's gravitational perturbations are cyclic and cancel out over monthly cycles. I just wanted to make it clear that there wasn't any special earth/moon/sun gravity thing that helped out. You can calculate the orbital distance and the required speed for a circular orbit from the mass of the earth alone.
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