We present, in this paper, numerical simulations of bubble sloshing in a spherical tank, resulting from a tank rotation around a fixed axis in microgravity conditions. This configuration is of great interest in space applications where sloshing can have harmful effects on the stability of satellites. Depending on the dimensionless numbers characterising this phenomenon, our study is focused on the motion and the deformation of a bubble, initially at rest, which is set in motion when the manoeuvre is starting until it reaches a constant rotation speed around the axis. It is shown in this article that, during the first stage of the manoeuvre, the motion of the bubble is essentially driven by the inertial force that depends on the angular acceleration. Next, when the angular velocity is increasing, the centrifugal force being dominant, the trajectory of the bubble is pushed towards the direction between the centre of the tank and the axis of rotation. Finally, when the angular velocity becomes constant, the bubble, reaching a quasi-steady position, is deformed and pressed against the solid boundary of the tank. A quantified description of these phenomena is proposed through a parametric study varying the essential dimensionless numbers, i.e. the Bond number based on the angular velocity, and another Bond number based on the angular acceleration. As the temporal evolution of the forces acting on the satellite wall is of utmost importance for designing satellites and manoeuvres, we also present an analysis characterising the latter. We also detail the first comparisons between the numerical simulations and the Fluidics experiment performed in the International Space Station (ISS) in microgravity conditions. Thanks to these comparisons, we can validate the simulations in configurations of interest.