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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.

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NASA NTRS2010

High-Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

It has been known for some time that Taylor series (TS) integration is among the most efficient and accurate numerical methods in solving differential equations. However, the full benefit of the method has yet to be realized in calculating spacecraft trajectories, for two main reasons. First, most applications of Taylor series to trajectory propagation have focused on relatively simple problems of orbital motion or on specific problems and have not provided general applicability. Second, applications that have been more general have required use of a preprocessor, which inevitably imposes constraints on computational efficiency. The latter approach includes the work of Berryman et al., who solved the planetary n-body problem with relativistic effects. Their work specifically noted the computational inefficiencies arising from use of a preprocessor and pointed out the potential benefit of manually coding derivative routines. In this Engineering Note, we report on a systematic effort to directly implement Taylor series integration in an operational trajectory propagation code: the Spacecraft N-Body Analysis Program (SNAP). The present Taylor series implementation is unique in that it applies to spacecraft virtually anywhere in the solar system and can be used interchangeably with another integration method. SNAP is a high-fidelity trajectory propagator that includes force models for central body gravitation with N X N harmonics, other body gravitation with N X N harmonics, solar radiation pressure, atmospheric drag (for Earth orbits), and spacecraft thrusting (including shadowing). The governing equations are solved using an eighth-order Runge-Kutta Fehlberg (RKF) single-step method with variable step size control. In the present effort, TS is implemented by way of highly integrated subroutines that can be used interchangeably with RKF. This makes it possible to turn TS on or off during various phases of a mission. Current TS force models include central body gravitation with the J2 spherical harmonic, other body gravitation, thrust, constant atmospheric drag from Earth's atmosphere, and solar radiation pressure for a sphere under constant illumination. The purpose of this Engineering Note is to demonstrate the performance of TS integration in an operational trajectory analysis code and to compare it with a standard method, eighth-order RKF. Results show that TS is 16.6 times faster on average and is more accurate in 87.5% of the cases presented.

Scott, James R.↗
NASA NTRS2009

Small Earth Observing Satellites Flying with Large Satellites in the A-Train

This paper/poster presents a real-life example of the benefits of flying small satellites with other satellites, large or small, and vice versa. Typically, most small satellites fly payloads consisting of one or two instruments and fly in orbits that are independent from that of other satellites. The science data from these satellites are either used in isolation or correlated with instrument data from other satellites. Data correlation with other satellites is greatly improved when the measurements of the same point or air mass are taken at approximately the same time. Scientists worldwide are beginning to take advantage of the opportunities for improved data correlation, or coincidental science, offered by the international Earth Observing Constellation known as the A-Train (sometimes referred to as the Afternoon Constellation). Most of the A-Train satellites are small - the A-Train is anchored by two large NASA satellites (EOS-Aqua and EOS-Aura), but consists also of 5 small satellites (CloudSat, CALIPSO, PARASOL, OCO and Glory these last two will join in 2009). By flying in a constellation, each mission benefits from coincidental observations from instruments on the other satellites in the constellation. Essentially, from a data point of view, the A-Train can be envisioned as a single, virtual science platform with multiple instruments. Satellites in the A-Train fly at 705 km in sun-synchronous orbits. Their mean local times at the equator are within seconds to a few minutes of each other. This paper describes the challenges of operating an international constellation of independent satellites from the U.S. and Europe to maximize the coincidental science opportunities while at the same time minimizing the level of operational interactions required between team members. The A-Train mission teams have been able to demonstrate that flying as members of an international constellation does not take away the flexibility to accommodate new requirements. Specific examples will be cited, including CloudSat's relocation (to accommodate a new viewing angle for the CALIPSO satellite), Glory's replan to move closer to PARASOL, and OCO's long term plans to minimize on-orbit operations costs while maintaining safety. In all cases, safety is ensured, science returns are enhanced, and operational flexibility is retained to the maximum extent possible.

Kelly, Angelita C.↗
NASA NTRS2015

Tidal Friction in the Earth-Moon System and Laplace Planes: Darwin Redux

The dynamical evolution of the Earth-Moon system due to tidal friction is treated here. George H. Darwin used Laplace planes (also called proper planes) in his study of tidal evolution. The Laplace plane approach is adapted here to the formalisms of W.M. Kaula and P. Goldreich. Like Darwin, the approach assumes a three-body problem: Earth, Moon, and Sun, where the Moon and Sun are point-masses. The tidal potential is written in terms of the Laplace plane angles. The resulting secular equations of motion can be easily integrated numerically assuming the Moon is in a circular orbit about the Earth and the Earth is in a circular orbit about the Sun. For Earth-Moon distances greater than ∼10 Earth radii, the Earth's approximate tidal response can be characterized with a single parameter, which is a ratio: a Love number times the sine of a lag angle divided by another such product. For low parameter values it can be shown that Darwin's low-viscosity molten Earth, M. Ross's and G. Schubert's model of an Earth near melting, and Goldreich's equal tidal lag angles must all give similar histories. For higher parameter values, as perhaps has been the case at times with the ocean tides, the Earth's obliquity may have decreased slightly instead of increased once the Moon's orbit evolved further than 50 Earth radii from the Earth, with possible implications for climate. This is contrast to the other tidal friction models mentioned, which have the obliquity always increasing with time. As for the Moon, its orbit is presently tilted to its Laplace plane by 5.2deg. The equations do not allow the Moon to evolve out of its Laplace plane by tidal friction alone, so that if it was originally in its Laplace plane, the tilt arose with the addition of other mechanisms, such as resonance passages.

Darwin Redux↗
NASA NTRS2004

A-B-Cs of sun-synchronous orbit mission design

The paper will develop the background and information necessary to explain what a sun-synchronous orbit is how it works. Handy back of the envelope equations will be provided to enable the mission analyst and system engineer to do quick and simple calculations for the orbit parameters selection and to compute mission parameters important to satellite design without having to resort to sophisticated computer programs.

Boain, Ronald J.↗
NASA NTRS1979

The dynamics and control of large flexible space structures, 2. Part A: Shape and orientation control using point actuators

The equations of planar motion for a flexible beam in orbit which includes the effects of gravity gradient torques and control torques from point actuators located along the beam was developed. Two classes of theorems are applied to the linearized form of these equations to establish necessary conditions for controlability for preselected actuator configurations. The feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping, and (2) by applying the linear regulator problem to the individual model coordinates separately. The linear control laws obtained using both techniques were evaluated by numerical integration of the nonlinear system equations. Numerical examples considering pitch and various number of modes with different combination of actuator numbers and locations are presented. The independent model control concept used earlier with a discretized model of the thin beam in orbit was reviewed for the case where the number of actuators is less than the number of modes. Results indicate that although the system is controllable it is not stable about the nominal (local vertical) orientation when the control is based on modal decoupling. An alternate control law not based on modal decoupling ensures stability of all the modes.

Bainum, P. M.↗
NASA NTRS1991

GN/C translation and rotation control parameters for AR/C (category 2)

Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 n.; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm; and (3) close proximity motion, the nearfield motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. This paper defines the reference coordinate frames and control parameters necessary to model the relative motion and attitude of spacecraft in the close proximity of another space system (Region 2 and 3) during the Automatic Rendezvous and Capture phase of an orbit operation.

Henderson, David M.↗
NASA NTRS2008

Short- and Long-Term Propagation of Spacecraft Orbits

The Planetary Observer Planning Software (POPS) comprises four computer programs for use in designing orbits of spacecraft about planets. These programs are the Planetary Observer High Precision Orbit Propagator (POHOP), the Planetary Observer Long-Term Orbit Predictor (POLOP), the Planetary Observer Post Processor (POPP), and the Planetary Observer Plotting (POPLOT) program. POHOP and POLOP integrate the equations of motion to propagate an initial set of classical orbit elements to a future epoch. POHOP models shortterm (one revolution) orbital motion; POLOP averages out the short-term behavior but requires far less processing time than do older programs that perform long-term orbit propagations. POPP postprocesses the spacecraft ephemeris created by POHOP or POLOP (or optionally can use a less accurate internal ephemeris) to search for trajectory-related geometric events including, for example, rising or setting of a spacecraft as observed from a ground site. For each such event, POPP puts out such user-specified data as the time, elevation, and azimuth. POPLOT is a graphics program that plots data generated by POPP. POPLOT can plot orbit ground tracks on a world map and can produce a variety of summaries and generic ordinate-vs.-abscissa plots of any POPP data.

Smith, John C., Jr.↗
NASA NTRS1979

New space initiatives through large generic structures

New possibilities in satellite communications, surveillance, and orbital experimentation provided by the capability to construct and deploy Large Space Structures (LSS) are presented. The advent of the Shuttle will allow deployment of larger antennas with much larger gain sizes, noting new applications in communications, radiometry, and radar in frequencies from 0.24 to 14 GHz. Applications in multi-beam communication which can hold spot sizes on the ground down to 30 miles in diameter, new applications of the large aperture radar antenna, and estimates of soil moisture by the microwave radiometer are discussed. The Solar Power Satellite consisting of a large solar collector orbiting the earth at geosynchronous altitude over the equator which requires ability to construct LSS in space is described, noting the design of solar cells and materials of construction, including graphite composites and aluminum alloys. Space construction procedures and equipment are considered, noting that the most likely procedure would deliver the subsystems to orbit separately, and then construct the spacecraft on-orbit and assemble the satellite.

Johnson, R. W.↗
NASA NTRS2009

Projectile Density Effects on Shield Performance

In the past, the orbital debris environment was modeled as consisting entirely of aluminum particles. As a consequence, most of the impact test database on spacecraft micro-meteoroid and orbital debris (MMOD) shields, and the resulting ballistic limit equations used to predict shielding performance, has been based on using aluminum projectiles. Recently, data has been collected from returned spacecraft materials and other sources that indicate higher and lower density components of orbital debris also exist. New orbital debris environment models such as ORDEM2008 provide predictions of the fraction of orbital debris in various density bins (high = 7.9 g/cu cm, medium = 2.8 g/cu cm, and low = 0.9-1.1 g/cu cm). This paper describes impact tests to assess the effects of projectile density on the performance capabilities of typical MMOD shields. Updates to shield ballistic limit equations are provided based on results of tests and analysis.

Christiansen, Eric L.↗
NASA NTRS1982

Optimal two-impulse transfer between specified terminal states of Keplerian orbits

The integrals of motion for an inverse-square force field and a necessary condition for optimality are used in a transfer orbit co-ordinate system to formulate the solution of the optimal two-impulse transfer between fixed position and velocity vectors on Keplerian orbits. In this co-ordinate system, the equations reveal two asymptotes that are useful in analysing the solution. It is shown that there are only two real extremals (both minimums) which are separated by an asymptote. An approximate analytic solution is also obtained by ignoring a quadratic term whose coefficient is approximately zero for a large class of orbit transfer problems.

Jezewski, D. J.↗
NASA NTRS1995

The Duffin-Kemmer-Petiau oscillator

In view of current interest in relativistic spin-one systems and the recent work on the Dirac Oscillator, we introduce the Duffin-Kemmer-Petiau (DKP) equation obtained by using an external potential linear in r. Since, in the non-relativistic limit, the spin 1 representation leads to a harmonic oscillator with a spin-orbit coupling of the Thomas form, we call the equation the DKP oscillator. This oscillator is a relativistic generalization of the quantum harmonic oscillator for scalar and vector bosons. We show that it conserves total angular momentum and that it is exactly solvable. We calculate and discuss the eigenspectrum of the DKP oscillator in the spin 1 representation.

Nedjadi, Youcef↗
NASA NTRS1994

Relativistic Effects on the Motion of Asteroids and Comets

We study the effects arising from relativistic perturbations on the motion of asteroids and comets and show that for a number of such objects, inclusion of relativistic contributions in the equations of motion gives rise to significant improvements in the orbital solutions.

relativistic↗
NASA NTRS1971

The application of generalized, cyclic, and modified numerical integration algorithms to problems of satellite orbit computation

Generalized, cyclic, and modified multistep numerical integration methods are developed and evaluated for application to problems of satellite orbit computation. Generalized methods are compared with the presently utilized Cowell methods; new cyclic methods are developed for special second-order differential equations; and several modified methods are developed and applied to orbit computation problems. Special computer programs were written to generate coefficients for these methods, and subroutines were written which allow use of these methods with NASA's GEOSTAR computer program.

Chesler, L.↗
NASA NTRS1993

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Vaughan, William W.↗