Self consistent mean field (SCF) theory is used to investigate the structure of and interactions between layers of polymer chains tethered to a spherical. interface. Traditional methods have combined flat geometry results with the Derjaguin approximation to calculate the interaction potentials between curved surfaces, leading to a great overestimation of both the range and steepness of the pair interaction potential. We have improved upon this approach by utilizing the chain configurational statistics from the curved geometry with a modified Derjaguin approximation to calculate pair interaction potentials. By varying the core radius, the degree of polymerization, and the tethering density in an athermal solvent, the tethered layer assumes structures ranging from those in star polymer systems to planar polymer blushes. The interaction potentials are found to be strictly repulsive with varying degrees of range and steepness. These changes in the interaction potential are related to changes in the tethered layer structure. The results are also compared with those from scaling theories. The range of the interaction potential generally correlates with the layer thickness predicted from scaling theory. The functional form of the interaction potentials does not follow previously proposed forms.