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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 NTRS1990

Collision probability at low altitudes resulting from elliptical orbits

The probability of collision between a spacecraft and another object is calculated for various altitude and orbit conditions, and factors affecting the probability are discussed. It is shown that a collision can only occur when the spacecraft is located at an altitude which is between the perigee and apogee altitudes of the object and that the probability per unit time is largest when the orbit of the object is nearly circular. However, at low altitudes, the atmospheric drag causes changes with time of the perigee and the apogee, such that circular orbits have a much shorter lifetime than many of the elliptical orbits. Thus, when the collision probability is integrated over the lifetime of the orbiting object, some elliptical orbits are found to have much higher total collision probability than circular orbits. Rocket bodies used to boost payloads from low earth orbit to geosynchronous orbit are an example of objects in these elliptical orbits.

Kessler, Donald J.↗
NASA NTRS2016

Orbital Eccentricity and the Stability of Planets in the Alpha Centauri System

Planets on initially circular orbits are typically more dynamically stable than planets initially having nonzero eccentricities. However, the presence of a major perturber that forces periodic oscillations of planetary eccentricity can alter this situation. We investigate the dependance of system lifetime on initial eccentricity for planets orbiting one star within the alpha Centauri system. Our results show that initial conditions chosen to minimize free eccentricity can substantially increase stability compared to planets on circular orbits.

Alpha Centauri System↗
NASA NTRS1989

An analytic development of orbit determination for a distant, planetary orbiter

With the advent of the Mariner '71 Mission, NASA has been sending spacecraft to orbit various distant bodies within the solar system. At present, there is still no adequate theory describing the inherent state estimation accuracy, based on two-way, coherent range-rate data. It is the purpose of this article to lay the groundwork for a general elliptic theory, and in addition to provide an analytic solution for the special case of circular orbits. It is shown that circular orbits about distant planets may suffer singularities in over-all position error estimation. These singularities are due to orbit inclination, placement of the line-of-nodes, and insignificant cross-velocity at the start and end of retrograde motion when orbiting a superior planet. Even though these conclusions appear to yield poor state estimation, one should not be unduly alarmed inasmuch as the stated conditions for singularity are not maintained for extended periods during typical mission scenarios. However, mission analysts should be aware of these potential pitfalls and realize that spuriously large results for circular orbiters can be obtained and are not the result of incorrect assumptions or faulty software. The general elliptic problem appears so involved that analytic inversion at this time is just not feasible, and in any case the resulting expression for the position error would likely be so lengthy that any understanding would be lost in the maze.

Russell, R. K.↗
NASA NTRS1987

Experimental measurement of the dynamic pressure distribution in a squeeze film bearing damper executing circular centered orbits

A review of previous experimental measurements of squeeze film damper (SFD) forces is given. Measurements by the authors of SFD pressure fields and force coefficients, for circular centered orbits with epsilon = 0.5, are described and compared with computer predictions. For Reynolds numbers over the range 2-6, the effect of fluid inertia on the pressure fields and forces is found to be significant.

Sanandres, L. A.↗
NASA NTRS1958

Three-Dimensional Orbits of Earth Satellites, Including Effects of Earth Oblateness and Atmospheric Rotation

The principal purpose of the present paper is to present sets of equations which may be used for calculating complete trajectories of earth satellites from outer space to the ground under the influence of air drag and gravity, including oblateness effects, and to apply these to several examples of entry trajectories starting from a circular orbit. Equations of motion, based on an "instantaneous ellipse" technique, with polar angle as independent variable, were found suitable for automatic computation of orbits in which the trajectory consists of a number of revolutions. This method is suitable as long as the trajectory does not become nearly vertical. In the terminal phase of the trajectories, which are nearly vertical, equations of motion in spherical polar coordinates with time as the independent variable were found to be more suitable. In the first illustrative example the effects of the oblateness component of the earth's gravitational field and of atmospheric rotation were studied for equatorial orbits. The satellites were launched into circular orbits at a height of 120 miles, an altitude sufficiently high that a number of revolutions could be studied. The importance of the oblateness component of the earth's gravitational field is shown by the fact that a satellite launched at circular orbital speed, neglecting oblateness, has a perigee some 67,000 feet lower when oblateness forces are included in the equations of motion than when they are not included. Also, the loss in altitude per revolution is double that of a satellite following an orbit not subject to oblateness. The effect of atmospheric rotation on the loss of altitude per revolution was small. As might be surmised, the regression of the line of nodes as predicted by celestial mechanics is unchanged when drag is included. It is clear that the inclination of the orbital plane to the equator will be relatively unaffected by drag for no atmospheric rotation since the drag lies in the orbital plane in this case. With the inclusion of atmospheric rotation it was found that the inclination of the plane changed about one-millionth of a radian per revolution. Thus the prediction of the position of the orbital plane of an earth satellite is not complicated by the introduction of drag. The line of apsides, which without drag but with oblateness moves slowly in space, tends to move with the satellite when drag is included in the calculations. As a results, the usual linearized solutions based on oblateness alone must be basically altered when drag is included to take into account the rapid movement of the line of apsides. In the second illustrative example the final revolution was calculated to impact for a number of trajectories in an orbital plane inclined at 650 to the equator. Of particular interest is the large effect the oblateness gravitational field and atmospheric rotation can have on the impact point. For a value of CDA/m of unity, and for an initial downward angle at 80 miles altitude of 0.01 radian, such as might be utilized for manned re-entry, oblateness had an influence of about 300 miles in the impact point, and atmospheric rotation had about a 150-mile influence.

Nielsen, Jack N.↗
NASA NTRS2000

An Unsteady Long Bearing Squeeze Film Damper Model: Circular Centered Orbits - Part 1

This paper, the first of a two-part series, presents results of an unsteady rotordynamic analysis of a long-bearing squeeze film damper executing circular centered orbits using a fluid circuit approach. A series of nodes and branches represent the geometry of the flow circuit. The mass and momentum conservation equations are solved to predict the pressure distribution in the squeeze film. The motion of the bearing is simulated by the variation of geometry within the flow path. The modeling methodology is benchmarked against published experimental long-bearing squeeze film damper test results. The model provides good agreement with the experimental damping coefficient.

Schallhorn, P. A.↗
NASA NTRS1992

Generalized probability model for calculation of interference to the Deep Space Network due to circularly Earth-orbiting satellites

The probability of exceeding interference power levels and the duration of interference at the Deep Space Network (DSN) antenna is calculated parametrically when the state vector of an Earth-orbiting satellite over the DSN station view area is not known. A conditional probability distribution function is derived, transformed, and then convolved with the interference signal uncertainties to yield the probability distribution of interference at any given instant during the orbiter's mission period. The analysis is applicable to orbiting satellites having circular orbits with known altitude and inclination angle.

Ruggier, C. J.↗
NASA NTRS1999

Solar Sail Optimal Orbit Transfers to Synchronous Orbits

A constant outward radial thrust acceleration can be used to reduce the radius of a circular orbit of specified period. Heliocentric circular orbits are designed to match the orbital period of Earth or Mars for various radial thrust accelerations and are defined as synchronous orbits. Minimum-time solar sail orbit transfers to these synchronous heliocentric orbits are presented.

Powers, Robert B.↗
NASA NTRS1981

Study of certain launching techniques using long orbiting tethers

A study of the basic equations governing orbital transfers using long orbiting tethers is presented. A very simple approximation to the general transfer equation is derived for the case of short tethers and low eccentricity orbits. Numerical examples are calculated for the case of injection into a circular orbit from a platform in eccentric orbit and injection into eccentric orbit from a platform in circular orbit. For the case of long tethers, a method is derived for reducing tether mass and increasing payload mass by tapering the tether to maintain constant stress per unit of tether cross section. Formulas are presented for calculating the equilibrium orbital parameters taking into account the mass of the platform, tether, and payload.

Colombo, G.↗
NASA NTRS1992

Origin of orbital debris impacts on Long Duration Exposure Facility's (LDEF) trailing surfaces

Orbital debris tracked by the US Space Command is mostly in near circular orbit around the Earth. If small debris were in the same types of orbits, there would be very few orbital debris impacts on the Long Duration Exposure Facility's (LDEF's) trailing surfaces. However, at least 15 percent of the impacts found on the trailing A03 gold surface was found to be orbital debris impacts. This measurement suggests that the orbital distribution of small debris is not the same as that of larger debris. Although this is not a total surprise, since modelling of satellite breakups has predicted different distributions, it does raise questions as to what types of orbits could be responsible for these impacts. A model was developed to explain these LDEF results. The model calculates the expected debris impact crater distribution around LDEF, as a function of debris orbital parameters. The results show that only low inclination and highly elliptical orbits could be responsible for these impacts. The most common object left in this type of orbit is an orbital transfer stage, used by the US and ESA to place objects into geosynchronous orbit, and inclinations near 28 and 7 degrees for the US and ESA, respectively. Even large fragments from satellites, which break up in these types of orbits, are difficult to observe from the ground; consequently, little is known about the number and characteristics of breakups in these orbits. The LDEF data suggest that these objects are breaking up. The LDEF data also suggest that the ratio of the contribution of small debris from this type of orbit to the contribution from circular orbits is about an order of magnitude larger than the same ratio for debris tracked by the US Space Command.

Kessler, Donald J.↗
NASA NTRS1999

Orbit Determination for Mars Global Surveyor During Mapping

The Mars Global Surveyor (MGS) spacecraft reached a low-altitude circular orbit on February 4, 1999, after the termination of the second phase of aerobraking. The MGS spacecraft carries the Mars Orbiter Laser Altimeter (MOLA) whose primary goal is to derive a global, geodetically referenced 0.2 deg x 0.2 deg topographic grid of Mars with a vertical accuracy of better than 30 meters. During the interim science orbits in the' Hiatus mission phase (October - November 1997), and the Science Phasing Orbits (March - April, 1998, and June - July 1998) 208 passes of altimeter data were collected by the MOLA instrument. On March 1, 1999 the first ten orbits of MOLA altimeter data from the near-circular orbit were successfully returned from MGS by the Deep Space Network (DSN). Data will be collected from MOLA throughout the Mapping phase of the MCS mission, or for at least one Mars year (687 days). Whereas the interim orbits of Hiatus and SPO were highly eccentric, and altimeter data were only collected near periapsis when the spacecraft was below 785 km, the Mapping orbit of MGS is near circular, and altimeter data will be collected continuously at a rate of 10 Hz. The proper analysis of the altimeter data requires that the orbit of the MGS spacecraft be known to an accuracy comparable to that of the quality of the altimeter data. The altimeter has an ultimate precision of 30 cm on mostly flat surfaces, so ideally the orbits of the MGS spacecraft should be known to this level. This is a stringent requirement, and more realistic goals of orbit error for MGS are ten to thirty meters. In this paper we will discuss the force and measurement modelling required to achieve this objective. Issues in force modelling include the proper modelling of the gravity field of Mars, and the modelling of non-conservatives forces, including the development of a 'macro-model', in a similar fashion to TOPEX/POSEIDON and TDRSS. During Cruise and Aerobraking, the high gain antenna (HGA) was stowed on the +X face of the spacecraft. On March 29, 1999 the HGA will be deployed on a meter long boom which will remain Earth-pointing while the instrument panel (including the MOLA instrument) remains pointed at nadir. The tracking data must be corrected for the regular motion of the high gain antenna with respect to the center of mass, and the success of the MGS determination during Mapping will depend on correctly accounting for this offset in the measurement model.

Lemoine, F. G.↗
NASA NTRS1994

The long-term forecast of station view periods

Using dynamical systems theory, a definite integral is obtained that gives the average view period of a ground station for spacecraft in circular orbits. Minor restrictions exist on the class of circular orbits to which this method can be applied. This method avoids the propagation of the orbit, which requires a lot of resources, and simplifies the algorithm used to compute the mean station view period. The integral is used for long-term station load forecast studies. It also provides a quantitative measure of the effectiveness of a ground station as a function of its latitude.

Lo, M. W.↗
NASA NTRS1969

Space Flight Handbooks: Volume III. Planetary Flight Handbook: Part 7 - Direct Trajectories to Jupiter, Saturn, Uranus and Neptune. Supplement B. Tabular Trajectory Data for Direct Trajectories to Uranus and Neptune

The trajectory data are presented chronologically and are organized by holding the arrival date constant while varying the Earth departure date in increments of 10 days. Upon completion of the specified range of Earth departure dates, the arrival date is incremented and the range of departure dates is repeated. For long trip times, where the variation of the trajectory parameters is relatively small, the size of the increment of the arrival date is increased. The range of departure and arrival dates and their corresponding increments are given in Table 5-1 for each launch opportunity. The criterion for the selection of these dates is that they encompass the region in which the Earth departure hyperbolic excess speed is less than or equal to 0.65 EMOS. There are two lines of print for each trajectory (departure-date/arrival date pair). In the first line the two left most columns contain the dates of departure and arrival. The next 18 columns of the first line can be divided into three groups: six columns of data related to departure, six columns pertinent to the heliocentric phase of the mission, and six columns related to arrival at the target planet. The second line of print contains, respectively, the Delta V requirements for departure and arrival, the total Delta V requirement, the heliocentric transfer trajectory type, and four parameters defining conditions at arrival. The value computed for the arrival Delta V is for entry into a circular orbit. The radius selected for this orbit, while necessarily somewhat arbitrary, is representative of the broad range of orbit radii which tend to minimize the arrival Delta V for the range of excess speeds between 0.1 and 0.8 EMOS. The value selected for Uranus and Neptune is 3 planet radii. Significant reductions in the computed Delta V can be realized by assuming entry into an elliptical orbit having a periapsis radius equal to the selected circular-orbit radius. The magnitude of the reduction can be determined from Figures 2-6 and 2-8 i n Section 2.

Source record↗
NASA NTRS2010

Detection of Planetary Emission from the Exoplanet TrES-2 Using Spitzer/IRAC

We present here the results of our observations of TrES-2 using the Infrared Array Camera on Spitzer. We monitored this transiting system during two secondary eclipses, when the planetary emission is blocked by the star. The resulting decrease in flux is 0.127% +/- 0.021%, 0.230% +/- 0.024%, 0.199% +/- 0.054%, and 0.359% +/- 0.060% at 3.6 microns, 4.5 microns, 5.8 microns, and 8.0 microns, respectively. We show that three of these flux contrasts are well fit by a blackbody spectrum with T(sub eff) = 1500 K, as well as by a more detailed model spectrum of a planetary atmosphere. The observed planet-to-star flux ratios in all four lRAC channels can be explained by models with and without a thermal inversion in the atmosphere of TrES-2, although with different atmospheric chemistry. Based on the assumption of thermochemical equilibrium, the chemical composition of the inversion model seems more plausible, making it a more favorable scenario. TrES-2 also falls in the category of highly irradiated planets which have been theoretically predicted to exhibit thermal inversions. However, more observations at infrared and visible wavelengths would be needed to confirm a thermal inversion in this system. Furthermore, we find that the times of the secondary eclipses are consistent with previously published times of transit and the expectation from a circular orbit. This implies that TrES-2 most likely has a circular orbit, and thus does not obtain additional thermal energy from tidal dissipation of a non-zero orbital eccentricity, a proposed explanation for the large radius of this planet. Key words: eclipses - infrared: stars - planetary systems - stars: individual (OSC 03549-02811) - techniques: photometric

Donovan, Francis T.↗
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↗