Cool idea! One big problem is that some mounts can do this and others cannot. There was software being developed a long time ago called Satellite Tracker, which I believe was freeware and open source, but it was Windows only. It was supposed to work great with LX200 mounts, but my mount is a Losmandy Gemini. I had tried the program at one point and found that my mount could only use the "leap frog" method of satellite tracking rather than differential tracking rates which the LX200 can do. The frustrating part was that the mount itself is supposed to be capable of custom tracking rates, but the software in the hand paddle only allows goto commands and just a couple of predefined tracking rates. But if you have an LX200 and a PC, you are in luck. I just did a quick google search and this looks like the software I remember:
As a new user I inquired about this as well. I believe that thread is possibly what come up in searches for INDI in regards to satellite tracking.
At the time there was a script that could issue leepfrog commands, but there was not way to make corrections, and the timing, location and fine adjustments are critical.
For satellite tracking the old Alt-Az, LX200 compatible mounts is the way to go. They permit continuously variable tracking rate changes.
The Satellite Tracker on Heavenscape has been around for a long time. The original developer recently ended support, and we lost the forums. But it has since been picked up by new developers.
There is one other independent developer who has created some interesting tools called TeleTrak for satellite tracking that is capable of image feature tracking. Enabling it to follow launching rockets. But again the software was developed for LX200.
Best of luck in your search.
His YouTube channel is called Astronomy Live. User ngchunter on Cloudy Nights.
INDI/KStars on Raspberry Pi 4, 4gb
Raspbian Buster with AstroPi3 script configuration
Skywatcher HEQ5 Pro Mount
Canon 600D Camera
Orion SSAG/ASI120mm @280mm Guide Scope
Adafruit Motor Hat shield
Adafruit GPS Module
Generic Bluetooth Joystick.
Startech 7 port powered USB Hub.