Final Answer:
The U.S.'s first space station launched by NASA on May 14 1973 and which decayed in orbit falling apart in 1979 was called Skylab.
Step-by-step explanation:
Skylab the United States' inaugural space station was launched by NASA on May 14 1973. Its mission was to serve as a platform for scientific research and experiments in the unique microgravity environment of space. Unfortunately Skylab's orbit decayed over time leading to its re-entry into Earth's atmosphere in 1979.
The decay of Skylab's orbit was influenced by various factors, including atmospheric drag and gravitational perturbations from the Earth and the Moon. The station's altitude gradually decreased and as it approached the denser layers of the atmosphere friction increased causing a further decrease in altitude. Eventually Skylab met its demise as it burned up during re-entry.
The calculations involved in predicting orbital decay are complex taking into account factors such as the mass of the object atmospheric density and its initial orbital parameters. Engineers use mathematical models to simulate the orbital decay process. Atmospheric drag, in particular plays a significant role; as Skylab descended the increasing atmospheric density contributed to the acceleration of its decay.
Skylab's operational life was relatively short but it laid the groundwork for subsequent space stations and contributed valuable data to our understanding of living and working in space. Despite its eventual demise Skylab remains an important chapter in the history of space exploration.