This research is motivated by the lack of understanding of students on the sphericalgeometry. The purpose of this study is to analysis Local Instruction Theory (LIT) developedfrom Hypothetical Learning Trajectory (HLT) on the spherical geometry. The Lessons thatinclude LIT are Realistic Mathematics Education (RME) learning. The research method isdesign research that starts from preliminary design, touch experiment and retrospectiveanalysis with two cycles. The population in this study is all students of group IX. There arethree activities to produce LIT to spherical geometry. These activities are: Identify the elementsin the spherical geometry including the tube, cone, and ball, the activity find the concept ofarea and volume of spherical geometry, the activity of solving the problem area and the volumeof spherical geometry, and the activity of applying problems with daily life.