This paper presents a comparison between an analytical approximation to a spacecraft transfer from a low Earth orbit to a highly elliptical Molniya orbit with an optimal solution. In this paper, a spacecraft is transferred from low Earth orbit to the final mission orbit by using various initial thrust accelerations ranging from 10-1 to 10-2 m/sec2. An approximate analytical method using a blended control that satisfy some basic physical constraints on the orbit transfer and comparing these results to the exact optimal case found using a well known trajectory optimization software. The comparison between the analytical data and the numerical data showed that the percent error between the two is small, there is about a 13% percent difference in propellant usage for the initial thrust acceleration of 10-1 m/sec2 and 10-2 m/sec2. The factor that affected the results of both solutions is that in the analytical method, the radius of perigee was held constant while with the numerical solution the radius of perigee was free. This difference indicates that while the analytical solution was closely related to numerical solution, it can be improved by doing another analytical analysis with the radius of perigee free.