A three-dimensional analytical solution was derived for an incompressible steady potential at an initially uniform velocity flow around a sphere, which translates forward, backward, rotates longitudinally or transversally. The concept of relative velocity was used to analyze the flow around the transitionally moving sphere. To analyze the flow around the longitudinally rotating sphere, A formula of the circumferential velocity of the fluid is found at the equatorial plane of the sphere and then generalized to the whole sphere as an approximation. The superposition principle of velocities was used to analyze the flow around the transversely rotating sphere, the stagnation points were detected and analyzed, the pressure distribution at the equator was calculated and compared with the experimental and CFD results, and the lift coefficient was calculated and compared with the experimental results and a good agreement for C_p and C_L was found at low spin factors, In contrast, at high spin factors the results begin to diverge due to the viscous effects and eddy formation.