Matching the orbits is not a small task. You don’t just speed up from behind and catch up. When you speed up it changes the orbit, for example speeding up in a circular orbit will change the orbit to an elliptical orbit. A maneuver known as a “transfer orbit maneuver will have to be performed, likely a Hohmann transfer orbit maneuver. This will likely involve at least two motor burns. The first burn will move from a circular orbit into an elliptical orbit. Then with the right time delay a second burn will slow the spacecraft from the elliptical orbit back into a circular orbit, and hopefully right next to the target satellite.
True. Matching orbits is “complex”. Energy heavy and mass heavy (thrusters and fuel and controllers) if you’re going in a short time. Very slow otherwise.
One of the first Gemini astronaut test pilots “invented” the math and methods for his PhD. Then went into orbit and proved his method worked
I hope it works. I believe it will.