Engineering topics

Graf, O. F., Jr.

Publications and source records attributed to Graf, O. F., Jr..

8 records

NASA NTRS1980

Mission analysis data for inclined geosynchronous orbits, part 1

Data needed for preliminary design of inclined geosynchronous missions are provided. The inertial and Earth fixed coordinate systems are described, as well as orbit parameters and elements. The complete family of geosynchronous orbits is discussed. It is shown that circular inclined geosynchronous orbits comprise only one set in this family. The major orbit perturbation and their separate effects on the geosynchronous orbit are discussed. Detailed information on the orbit perturbation of inclined circular geosynchronous orbits is given, with emphasis on time history data of certain orbital elements. Orbit maintenance delta velocity (V) requirements to counteract the major orbit perturbations are determined in order to provide order of magnitude estimates and to show the effects of orbit inclination on delta V. Some of the considerations in mission design for a multisatellite system, such as a halo orbit constellation, are discussed.

Graf, O. F., Jr.↗

NASA NTRS1980

A study of the lifetimes of geosynchronous transfer orbits

The study concerns the orbit lifetimes of spent upper stages that are used to boost NASA Space Transportation System payloads into geosynchronous transfer orbits. A semi-analytical method of trajectory computation was developed and applied to these particular orbits. It was found that gravitational perturbations of the sun, moon and oblate earth cause large changes in the perigee altitude. The following parameters have a strong influence on orbit lifetimes: Time of year of launch; Inertial orientation of orbital plane; Inclination of orbital plane.

Graf, O. F., Jr.↗

NASA NTRS1979

Orbit decay analysis of STS upper stage boosters

An orbit decay analysis of the space transportation system upper stage boosters is presented. An overview of the computer trajectory programs, DSTROB, algorithm is presented. Atmospheric drag and perturbation models are described. The development of launch windows, such that the transfer orbit will decay within two years, is discussed. A study of the lifetimes of geosynchronous transfer orbits is presented.

Graf, O. F., Jr.↗

NASA NTRS1977

The method of averages applied to the KS differential equations

A new approach for the solution of artificial satellite trajectory problems is proposed. The basic idea is to apply an analytical solution method (the method of averages) to an appropriate formulation of the orbital mechanics equations of motion (the KS-element differential equations). The result is a set of transformed equations of motion that are more amenable to numerical solution.

Graf, O. F., Jr.↗

NASA NTRS1977

Effects of solar radiation pressure on the orbit of the Solar Power Satellite

The surface area-to-weight ratio of the Solar Power Satellite (SPS) is of the order of sq m/kg. Therefore, solar radiation pressure will be an important perturbation on the orbit, causing large variations in eccentricity. An analytical solution is developed for the motion of eccentricity and the line of apsides. Included is a secular term due to the earth's orbital eccentricity. Several initial conditions are considered. For some cases, the eccentricity is nearly constant over a few years. General characteristics of the motion are discussed. Long-term (30 years) effects of gravity are investigated by using a numerical integration method. Eccentricities of approximately 0.08 can be expected for uncorrected SPS orbits.

Graf, O. F., Jr.↗

NASA NTRS1977

Orbital motion of the solar power satellite

A study on the effects of solar radiation pressure on the SPS orbit is documented. It was shown that the eccentricity of the orbit can increase from initially being zero. The SPS configuration is primarily considered but the results are applicable to any geosynchronous satellite that resembles a flat surface continually facing the sun. The orbital evolution of the SPS was investigated over its expected 30 year lifetime and the satellite was assumed to be in free flight. The satellite's motion was described with analytical formulae which could be used to develop an orbit control theory in order to minimize station keeping costs.

Graf, O. F., Jr.↗

NASA NTRS1976

The elimination of short and intermediate period terms from the problem of a high altitude earth satellite

The Delaunay-Similar elements of Scheifele (1976) are applied to the problem of an earth satellite that is perturbed by the sun, moon, and J2. All three effects are assumed to be the same order of magnitude. Since the external body terms depend explicitly on time, the time element appears as an additional angle variable. Also, the eccentric anomaly is used as a noncanonical auxiliary variable. A solution to the first Von Zeipel equation allows simultaneous elimination of short- and intermediate-period terms. The canonical transformation to mean elements is defined by a generating function that is a series involving Bessel coefficients.

Graf, O. F., Jr.↗

NASA NTRS1975

Lunar and solar perturbations on the orbit of a geosynchronous satellite

The luni-solar effects cause a large amplitude, long-period perturbation of the orbital plane. Canonical differential equations associated with this motion contain a singular point, and are expanded about this point to third order. A solution is given that is valid for long times and is not restricted to small inclinations. Higher order terms are investigated. Expressions are given for the inclination (I) and node as a function of time. Comparisons with a numerically integrated solution show a disagreement in inclination of only .03 deg after 11 years.

Graf, O. F., Jr.↗