# Analytic ephemeris generator

**Analytic Ephemeris Generator (AEG): Initial AEG development (Stepping Stone Award)**

In 2019 IEEE Region 5 recognized NASA/JSC with a Stepping Stone Award for the development of the Analytic Ephemeris Generator (AEG) which provided the Primary real-time orbiter predictor for the early space program. Subsequent advancement of the AEG is still used in advanced space orbiter predictions. The following is a brief summary taken from the award nomination.

In the latter part of 1962, during the early development of TQ10 (a NASA computer program for spacecraft trajectory propagation, maneuvers, analyses and documentation), it was recognized that in the computation of rendezvous trajectories, the numerical integration methods for trajectory propagation would be very slow (hours, even days of computer time) and would be extremely expensive in terms of computer resources. An alternative method was urgently required. The work of a well-known Dutch-American astronomer, Dirk Brouwer came to the attention of Alan Moore and Ed Lineberry in the Mission Analysis Branch at the Manned Spacecraft Center in Houston, Texas. Brouwer, a graduate of the University of Leiden, was the Professor of Astronomy at Yale University. Brouwer had formulated the equations for an Analytic Ephemeris Generator (AEG). The Brouwer AEG used an analytic model of the Earth’s gravity field, an analytic model of the Earth’s atmospheric density, and an innovative analytic technique for integrating these force fields in describing the motion of spacecraft. The key to the Brouwer method was in the analytic technique used in the rapid integration of the forces acting on the spacecraft. The advantage of the AEG was that a vehicle state vector could be advanced from its current state to a time in the future (or past) with a single computation pass thru the code. The alternative method for trajectory propagation was a numerical integration technique, such as Runge-Kutta or Enke, that steps the trajectory in small time increments, requiring a complete computation cycle with each step. The AEG made the computations required (and in the case of rendezvous analyses, of two space vehicles simultaneously!) much more rapidly within the capabilities of the computer systems available at the time.

The AEG with its analytic modeling of the Earth gravity field, the Earth’s atmospheric density and drag forces coupled with innovative analytic techniques for the integration of those force fields on the motion of spacecraft was a very key addition to the DKI and to Monster, two rendezvous maneuver computer tools created and used by the Mission Analysis Branch for detailed analyses and planning documentation. It was later claimed that the success of Monster was critically dependent upon the successful implementation of the AEG.

Alan Moore was the key developer in the implementation of the Brouwer AEG formulation into TQ10, with inspiration and guidance from Ed Lineberry. Alan had become familiar with the work of Dirk Brouwer, established a relationship and acquired the formulation for implementation. In the early months of 1963 Alan and William (Bill) Reini worked with Lineberry on implementing the AEG into the dedicated rendezvous analysis tool, the Monster. Other Mission Analysis team members worked with Alan and Bill in testing the implementation and providing software documentation.

In September of ’63 Ed Kenyon joined the Mission Analysis team. He started working with Alan and soon took a lead role in the continued development of the AEG. In 1964 Bill Reini and Alan Moore completed checkout of the AEG software and documented the formulation in the form of an MPAD Internal Note -which was transmitted to IBM for implementation in the RTCC. The original AEG was incorporated into the Trajectory Subsystem of the RTCC (Real Time Computer Complex of the new NASA/MSC Mission Control Center in Houston, Building 30.) The MCC was in development leading up to the time of manned Gemini missions, which began in the Spring of 1965. For several reasons, RTCC AEG implementation was not without its problems; Howard “Bill” Tindall and William A. Sullivan of the now Mission Planning and Analysis Division were key players in overseeing the IBM implementation and final checkout of the RT AEG software. Also, the Real Time AEG proved essential to the rapid trajectory propagation of the Gemini/Agena spacecraft vectors. The AEG was the primary real-time orbit predictor in the RTCC for Gemini and all subsequent manned missions.

In the latter part of 1965 or early 1966, Alan Moore left NASA to work in industry and Ed Kenyon took on the responsibility for the AEG development. In 1966 and 1967, Kenyon was instrumental in the development of an AEG model for incorporation into a lunar version of Monster. He worked with Dr. Baker of UCLA who had developed an analytic model of the lunar gravity field. Kenyon was supported by Doug Ingram, a TRW contractor worker for MPAD, in the coding of the lunar AEG. Bill Reini incorporated the AEG into the “Lunar Monster” for use in all Apollo rendezvous mission planning and analysis. Kenyan MSC Internal Note 68-FM-119, dated May 21, 1968 highlighted the Apollo Real-Time Rendezvous support program.

The lunar AEG was also implemented in the RTCC. Several years later an updated version of Monster & earth-based AEG was developed for use in Skylab and ASTP planning.

In 1974 Ed Lineberry, while on a one-year sabbatical, developed an even more elegant and more accurate formulation for the AEG. Gus Babb worked with Ed implementing a simplified Jacchia atmosphere model into the AEG. The Lineberry AEG formulation was coded up by Reini and became the MPAD and MCC standard. The improved AEG was later incorporated into the Flight Design System (FDS).