Apollo 11 Reloaded: Optimization-based Trajectory Reconstruction

This paper wants to be a tribute to the Apollo 11 mission, that celebrated its 50th anniversary in 2019. By using modern methods based on numerical optimization we reconstruct critical phases of the original mission, and more specifically the ascent of the Saturn V, the translunar injection maneuver that allowed the crew to leave the Earth’s sphere of influence, and the Moon landing sequence, starting from the powered descent initiation. Results were computed by employing pseudospectral methods, and show good agreement with the original post-flight reports released by NASA after the successful completion of the mission

Essential Nutrients for Bone Health and a Review of their Availability in the Average North American Diet

Osteoporosis and low bone mineral density affect millions of Americans. The majority of adults in North America have insufficient intake of vitamin D and calcium along with inadequate exercise. Physicians are aware that vitamin D, calcium and exercise are essential for maintenance of bone health. Physicians are less likely to be aware that dietary insufficiencies of magnesium, silicon, Vitamin K, and boron are also widely prevalent, and each of these essential nutrients is an important contributor to bone health. In addition, specific nutritional factors may improve calcium metabolism and bone formation. It is the authors’ opinion that nutritional supplements should attempt to provide ample, but not excessive, amounts of factors that are frequently insufficient in the typical American diet