How can NASA's Lunar Reconnaissance Orbiter projects verify the existence of the fifth force

The spring constant of the earth is found to be 1.1 × 10−8/s2 which is based on the famous Pound and Rebka gravitational red-shift experimental data. The spring force, or so-called the fifth force of the earth is then known. This paper suggests how can NASA's Lunar Reconnaissance Orbiter (LRO) projects verify the existence of the fifth force by simple free fall experiment without man-mission. Such a force, as we have predicted, should be the type of intermediate range.