The adhesive contact between a nano-scale rigid sphere and an elastic half-space is investigated. By integrating the Lennard-Jones potential, the force by the rigid sphere can be obtained. Then, using the arc-length continuation algorithm, the load-displacement relationship and pressure distribution are obtained. The results are compared with those computed with Derjaguin's approximation. It is found that those computed with Derjaguin's approximation do not predict the adhesive contact precisely for large Tabor's parameter or small spheres. In such circumstances, the method proposed should be used
