F10.7 is the measured solar power flux at 10.7 cm wavelength. It is measured all over the world but primarily from Penticton observatory in Canada.
The largest source of uncertainty in orbit propagation for satellites in Low-Earth Orbit (LEO) is atmospheric drag. Solar activity directly effects the density of the atmosphere. It is an input to many atmospheric models which are used when propagating orbits. Which is central to all conjunction assessments (predicting where objects will be in case they might come too close).
The sun heats the object and causes it to emit vapor, it emits more vapor on the side facing the sun, these emissions have a measurable affect on the orbit.
