# Accession Number:

## AD0855389

# Title:

## Minimum-Fuel Thrust-Limited Transfer Trajectories Between Coplanar Elliptic Orbits.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING

# Personal Author(s):

# Report Date:

## 1968-12-01

# Pagination or Media Count:

## 175.0

# Abstract:

A method is developed for the efficient computation of minimum-fuel transfer trajectories between coplanar elliptic orbits with a thrust-limited variable-mass rocket moving in a central gravitation force field. Each orbit is defined through the eccentricity, semi-latus rectum, and argument of pericenter. Transfer time is left open. The minimum-fuel trajectory is assumed to consist of two thrusting phases separated by a coasting phase. Computation of the minimum-fuel transfer trajectory is accomplished by a direct integration of the rocket equations of motion and the associated adjoint equations which are developed from variational calculus techniques. This direct approach is made possible by a unique transformation of the adjoint equations into a set of equations which provide a much better understanding of the general behavior of minimum-fuel transfer trajectories. Reasonable estimates of the thrusting interval durations, initial thrust angle, and initial true anomaly are derived from the corresponding minimum-fuel, two-impulse transfer trajectory. The initial value of a newly discovered variable is used in conjunction with the initial thrust angle to obtain the thrusting interval durations specified by the two-impulse transfer. Author

# Descriptors:

# Subject Categories:

- Unmanned Spacecraft
- Spacecraft Trajectories and Reentry