If an initially non-rotating (zero angular momentum) satellite starts moving around a main body, such as the earth,
One could argue for the latter by considering the orbit around earth as a ”straight ahead” in curved space.
In general the satellite will continue to have no rotation. However the satellite can slowly start rotating due to tidal forces, forces from earths magnetic field or from atmospheric drag.
Initially it would still have no rotation, but as it is in a non uniform gravity field the center of gravity would be slightly below the center of mass. This can create a torque on it.
"A body's center of gravity is the point around which the resultant torque due to gravity forces vanishes. Where a gravity field can be considered to be uniform, the mass-center and the center-of-gravity will be the same. However, for satellites in orbit around a planet, in the absence of other torques being applied to a satellite, the slight variation (gradient) in gravitational field between closer-to (stronger) and further-from (weaker) the planet can lead to a torque that will tend to align the satellite such that its long axis is vertical. In such a case, it is important to make the distinction between the center-of-gravity and the mass-center. Any horizontal offset between the two will result in an applied torque." From Wikipedia; https://en.wikipedia.org/wiki/Center_of_mass#Center_of_gravity
Well, the fuel inside the booster tank would slosh around, creating a torque for which the satellite would slowly have to rotate to provide an anti-torque. Of course, other factors like thermal expansion, bombardment from space dust and all are not included.
