Magnetosphere is a region of space surrounding Earth magnetic field, the formation of magnetosphere depends on many parameters such as; surface magnetic field of the planet, an ionized plasma stream (solar wind) and the ionization of the planetary upper atmosphere (ionosphere). The main objective of this research is to find the behavior of Earth's magnetosphere radius (Rmp) with respect to the effect of solar wind kinetic energy density (Usw), Earth surface magnetic field (Bo), and the electron density (Ne) of Earth's ionosphere for three years 2016, 2017 and 2018. Also the study provides the effect of solar activity for the same period during strong geomagnetic storms on the behavior of Rmp. From results we found that there are nonlinear relations between the (Rmp) and the three variables (Usw), (Bo) and (Ne). Also we found that during the strong geomagnetic storms there is a reduction in the radius of magnetosphere.