Search NASA⌕ Search

SEARCH · Search NASA

Results for “ORBIT EQUATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

A Simplified, Closed-Form Method for Screening Spacecraft Orbital Heating Variations

A closed-form analytical technique has been developed to screen orbital average heating variations as a function of beta angle, altitude, surface area, and surface optical properties. Using planetary view factor equations for surfaces parallel-to and normal-to the local vertical, a cylindrical umbral shadow approximation, and a simplified albedo flux model, heating rate equations are formulated and then integrated to obtain orbital average heating. The results are compared to detailed analytical predictions using Monte Carlo integration and an assessment of error is presented.

Rickman, S. L.↗
NASA NTRS1977

New contributions to the problem of capture

Libration-point capture is analyzed in the framework of the restricted three-body problem in order to obtain general results capable of predicting the major features of an arbitrary postcapture orbit, with specific reference to capture as the presumed mode of origin of Jupiter's outer satellites. Some examples of libration-point capture are computed, the time a body remains captured is estimated, and a long-term numerical integration of orbits is carried out which shows that the equation used to estimate capture lifetimes is quite conservative. An extended capture criterion is proposed and used to demonstrate that direct postcapture orbits lie outside retrograde ones. Mass change involving one or both primaries is evaluated as a means of producing permanent capture, it is found that mass-change effects can produce 'pull-down capture', and consideration is given to the orbital evolution of Jupiter's outer satellites. The effect of drag in the solar nebula or in a nebula around proto-Jupiter on the capture process is briefly investigated. It is concluded that a capture origin for the outer satellites is improbable within the last 4.6 billion years but that either mass change or nebula drag could have been effective in producing capture.

Heppenheimer, T. A.↗
NASA NTRS1985

A homotopy continuation method for general preliminary orbit determination and special application to the Tracking and Data Relay Satellite System

A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The use of this technique, the homotopy continuation method, was motivated by the possible need to perform preliminary orbit determination in the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. In the formulation studied here, a set of six tracking observations is continuously transformed from a set with known solutions to the given set with unknown solutions, and the corresponding orbit state vector is followed from the a priori orbit state to the solution orbit states. A modular numerical algorithm is developed to follow the state vector. The technique is formulated and then tested, using both real and simulated tracking, with positive results. Direct comparisons show that the basic method has a much larger radius of convergence than standard or simply modified Newton-Raphson methods. An extension of the basic method is formulated that is expected to produce a global method.

Smith, R. L.↗
NASA NTRS1988

Evolution of inclined galactic gas disks. I - A cloud-fluid approach

In this paper, numerical models are developed to follow the time-dependent behavior of inclined gas disks in nonspherical galaxies. Differential equations are developed which describe the time rate of change of the orbits of mass elements composing a thin, smoothly warping and twisting gas disk. These equations include multiple moments due to the nonsphericity of the galactic mass distribution, Coriolis effects arising from determination of orbits in a reference frame which tumbles with the surface figure of the galaxy, and viscous forces arising from cloud-cloud collisions. A cloud-fluid approach is used in determining the viscous forces. Physical arguments are used to determine the maximum permissible local value of the coefficient of kinematic viscosity. For small initial inclinations, analytic expressions are obtained for the inclination as a function of time and for the settling time, and the features of the solution are discussed.

Steiman-Cameron, Thomas Y.↗
NASA NTRS1973

The physical librations of the moon, including higher harmonic effects

The equations of the physical libration of the moon are developed using a representation of the earth-moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. The Improved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree is performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10-sec six-yearly (argument omega), 1.2-sec three-yearly, 0.5-sec annual, and 0.1-sec monthly; on pole direction they are on the order of 0.5-sec six-yearly and 1.0-sec monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.

Kaula, W. M.↗
NASA NTRS1979

Finite beta effects on the drift-cyclotron instability

The effects of finite plasma beta and strong plasma inhomogeneities on the microinstability resulting from the unstable coupling of ion-cyclotron oscillations and an ion drift wave are examined. A local electromagnetic, kinetic dispersion equation, which takes into account finite orbit modifications of both ions and electrons as well as the effects of strong inhomogeneities on the ions and permits the continuous tracking of the instability from the weak gradient regime to the strong gradient regime, is derived and solved numerically. Finite beta is shown to increase the frequency and reduce the growth rate of the instability, but not completely stabilize it due to electromagnetic effects. When plasma inhomogeneity is sufficiently strong, finite beta reduces the growth rate of the large k sub y band of a given harmonic more than the small k sub y band; however, the most unstable bands remain the same as in the case of zero beta. Implications of these results for the Tandem Mirror Experiment are discussed.

Gladd, N. T.↗
NASA NTRS1981

Intelsat satellite scheduled for launch

The launch schedule for Intelsat 5-B, the prime Intelsat satellite to provide communications services between the Americas, Europe, the Middle East, and Africa, is presented. The planned placement of the satellite into an elliptical transfer orbit, and circularization of the orbit at geosynchronous altitude over the equator are described. Characteristics of the Atlas Centaur launch vehicle, AC-56, are given. The launch operation is summarized and the launch sequence presented. The Intelsat team and contractors are listed.

Source record↗
NASA NTRS1982

Mass driver reaction engine characteristics and performance in earth orbital transfer missions

Configurations of a typical mass driver reaction engine (MDRE) are presented and its use for delivery of payloads to geosynchronous orbit (GEO) from low earth orbit (LEO) is discussed. Basic rocket equations are developed for LEO to GEO round-trip missions using a single exhaust velocity. It is shown that exhaust velocities in the 5-10 km/sec range (specific impulse of 500-1000 sec) are well suited for mass drivers, minimizing the overall cost of missions. Payload delivery rate fractions show that there is little to be gained by stretching out LEO to GEO transfer times from 90 to 180 days. It therefore pays to use the shorter trip time, approximately doubling the amount of delivered payload during any fixed time of use of the MDRE.

Snow, W. R.↗
NASA NTRS1982

Space transportation

The physical laws governing launch vehicles are reviewed, together with the performance of launch vehicles thus far used and expected developments in space transportation systems. Launches are generally made in the direction of earth rotation to take advantage of the initial velocity in that direction, which can amount to about 0.46 km/sec at the equator. Spacecraft usually attain a parking orbit, where spacecraft conditions are assessed before moving on to final orbit or interplanetary trajectory. Rocket batteries were first used in a battle near Beijing in 1232, and manned space flight began with the Vostok flight in 1961, followed by the Apollo lunar landings in the later 1960s. Rocket thrust performance is analyzed, together with the thrust/mass ratio for ascent and descent. The Shuttle, capable of placing 29.5 t in LEO, will be or is equipped to also carry IUS and PAM engines for transferring payloads from LEO to GEO. Parallel burn boosters may be added to increase the payload capability, and Shuttle-derived launch vehicles may be developed to carry construction materials to space and return to earth for a runway landing. Alternatively, the Shuttle engines may be modularized in order to develop a heavy-lift launch vehicle for unmanned cargo ascents.

Davis, H.↗