Manned orbital spacecraft and a host of unmanned remote sensing, imaging and navigation satellites occupy nominally circular,low earth orbits (LEOs). A low earth orbit (LEO) is one whose altitude lies between about 150 km and about 1000 km. An LEO is well above the nominal outer limits of the drag-producing atmosphere (about 80 km), and well below the hazardous Van Allen radiation belts, the innermost of which begins at about 2400 km. Nearly all of our applications of the orbital equations will be to the analysis of man-made spacecraft, all of which have a mass that is insignificant compared to the sun and planets. For example, since the earth is nearly twenty orders of magnitude more massive than the largest conceivable artificial satellite, the center of mass of the two-body system lies at the center of the earth, and the constant µ becomes 395600 km^3/s^2.