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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Photospheric faculae and the solar oblateness - A reply to 'Faculae and the solar oblateness' by R. H. Dicke.

Dicke has recently contested our statement in an earlier paper that faculae could account for a large part, if not all, of the solar oblateness signal measured by Dicke and Goldenberg in 1966. Using the facular oblateness signal published in our earlier paper and some hitherto unpublished data from his 1966 observations, he concludes that faculae account for only a small part (11%) of the observed excess oblateness. His analysis considers data only from a restricted 48-day sample and is based on the assumption that only the observed oblateness signal is subject to error. Our analysis considers data from all 64 days on which observations were made, and is based on the assumption that both the observed oblateness signal and the facular signal are subject to error. We find that faculae account for at least one-third to one-half of the observed excess oblateness, depending on whether 48 days or 64 days are used in the analysis.

Chapman, G. 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 NTRS1975

Effect of the Jovian oblateness on Pioneer 10/11 radio occultations

The oblateness of Jupiter, which was neglected in the standard inversion technique for radio occultation data, has a substantial effect on the refractivity profiles of the neutral Jovian atmosphere derived from the Pioneer 10/11 occultations. The geometry of the Pioneer 10 entry and exit occultations has the effect that oblateness should account for much of the discrepancy of the results with plausible atmospheric models. The effect of the oblateness on Pioneer 11 entry is smaller, where much of the discrepancy could be due to other effects, such as cycle-slip in the spacecraft transponder. Theory indicates that the Pioneer 11 exit occultation should be affected by the oblateness in the opposite sense from the first three occultations; and, indeed, the data which had not been invertible under the spherical assumption produced reasonable results when an oblateness correction was applied.

Hubbard, W. B.↗
NASA NTRS1984

Oblatenesses of Uranus and Neptune

The oblateness of a planet is closely related to its rotation rate and internal mass distribution, and is therefore an important indicator of gross planetary structure. Analysis of Stratoscope II images of Uranus yields epsilon = 0.022 + or - 0.001, and stellar occultation observations yield epsilon = 0.024 + or - 0.003. Because of the current pole on aspect of Uranus, it is unlikely that a significantly more accurate value can be determined by stellar occultations before Voyager 2 encounters Uranus in January, 1986. Neptune's oblateness has been determined from stellar occultation observations made in 1968 and 1983. The 1968 observations yield an oblateness of 0.021 + or - 0.004. A recent determination of Neptune's oblateness using both the 1968 and 1983 observations is consistent with this value. Space Telescope observations of several stellar occultations by Neptune could provide a significantly more accurate determination of the oblateness before the Voyager 2 encounter in 1990.

French, R. G.↗
NASA NTRS1972

Photospheric faculae and the solar oblateness.

Dicke and Goldenberg (1967) on the basis of the value of the solar oblateness obtained had concluded that the excess perihelion motion of mercury is not in accord with Einstein's prediction according to general relativity. However, the observations from which the oblateness value was derived might be simply the result of an excess brightness at the equatorial solar limb. Such brightness might be due to the presence of faculae. Dicke (1970) had concluded that the effect of faculae on the oblateness determination is insignificant. In a reexamination of Dicke's argument it was found that his reasons for rejecting faculae as a source of oblateness are unjustified.

Chapman, G. A.↗
NASA NTRS1995

The effect of oblateness and gravity darkening on the radiation driving in winds from rapidly rotating B stars

We calculate the radiative driving force for winds around rapidly rotating oblate B stars, and we estimate the impact these forces should have on the production of a wind compressed disk. The effects of limb darkening, gravity darkening, oblateness, and an arbitrary wind velocity field are included in the computation of vector 'oblate finite disk' (OFD) factors, which depend on both radius and colatitude in the wind. The impact of limb darkening alone, with or without rotation, can increase the mass loss by as much as 10% over values computed using the standard uniformly bright spherical finite disk factor. For rapidly rotating stars, limb darkening makes 'sub-stellar' gravity darkening the dominant effect in the radial and latitudinal OFD factors, and lessens the impact of gravity darkening at other visible latitudes (nearer to the oblate limb). Thus, the radial radiative driving is generally stronger over the poles and weaker over the equator, following the gravity darkening at these latitudes. The nonradial radiative driving is considerably smaller in magnitude than the radial component, but is directed both away from the equatorial plane and in a retrograde azimuthal direction, acting to decrease the effective stellar rotation velocity. These forces thus weaken the equatorward wind compression compared to wind models computed with nonrotating finite disk factors.

Cranmer, Steven R.↗
NASA NTRS1973

Faculae and the solar oblateness - A summary

Dicke and Goldenberg (1967) inferred a value of the solar oblateness by projecting an image of the sun on a circular occulting disk and measuring the light flux from the portion of the sun exposed beyond the disk. These measurements have the implication that if the optical oblateness measured is mirrored in a true gravitational oblateness, then the non-Newtonian part of Mercury's perihelion advance cannot agree with Einstein's prediction based on general relativity. The present analysis shows that faculae may have contributed all of Dicke and Goldenberg's excess signal. There is overwhelming evidence that this signal is contaminated by faculae at some level, and very little evidence to exclude faculae as a cause of the signal.

Chapman, G. A.↗
NASA NTRS1976

Ray propagation in oblate atmospheres

Phinney and Anderson's (1968) exact theory for the inversion of radio-occultation data for planetary atmospheres breaks down seriously when applied to occultations by oblate atmospheres because of departures from Bouguer's law. It has been proposed that this breakdown can be overcome by transforming the theory to a local spherical symmetry which osculates a ray's point of closest approach. The accuracy of this transformation procedure is assessed by evaluating the size of terms which are intrinsic to an oblate atmosphere and which are not eliminated by a local spherical approximation. The departures from Bouguer's law are analyzed, and it is shown that in the lowest-order deviation from that law, the plane of refraction is defined by the normal to the atmosphere at closest approach. In the next order, it is found that the oblateness of the atmosphere 'warps' the ray path out of a single plane, but the effect appears to be negligible for most purposes. It is concluded that there seems to be no source of serious error in making an approximation of local spherical symmetry with the refraction plane defined by the normal at closest approach.

Hubbard, W. B.↗
NASA NTRS1977

Optimal low-thrust takeoff from an orbit about an oblate planet

Future space missions to the outer planets may depend upon the use of low-thrust propulsion systems. As these planets are decidedly oblate, the question of the effect of that oblateness on a low-thrust trajectory is of some interest. In this paper the problem of optimal energy increase is attacked under the assumption that the coefficients for the second zonal harmonic, and the nondimensional thrust acceleration are the same order of magnitude. By means of a two-variable asymptotic expansion technique, a near optimal control program is generated and the first-order uniformly valid approximation for the corresponding trajectory is obtained. Tangential thrust is shown to be a good near-optimal thrust program even in the presence of oblateness effects. The optimal control program is found to be oscillatory and quite similar to the optimal control for energy increase in an inverse square gravitational field.

Jacobson, R. A.↗
NASA NTRS1986

On the oblateness and rotation rate of Neptune's atmosphere

Recent observations of a stellar occultation by Neptune give an oblateness of 0.022 + or - 0.004 for Neptune's atmosphere at the 1-microbar pressure level. This results is consistent with hydrostatic equilibrium at a uniform atmospheric rotation period of 15 hours, although the error bars on quantities used in the calculation are such that an 18-hour period is not excluded. The oblateness of a planetary atmosphere is determined from stellar occultations by measuring the times at which a specified point on immersion or emersion occultation profiles is reached. Whether this standard procedure for deriving the shape of the atmosphere is consistent with what is known about vertical and horizontal temperature gradients in Neptune's atmosphere is evaluated. The nature of the constraint placed on the interior mass distribution by an oblateness determined in this manner is consided, as is the effects of possible differential rotation. A 15-hour Neptune internal mass distribution is approximately homologous to Uranus', but an 18-hour period is not. The implications for Neptune's interior structure if its body rotation period is actually 18 hours are discussed.

Hubbard, W. B.↗
NASA NTRS1987

Oblateness, radius, and mean stratospheric temperature of Neptune from the 1985 August 20 occultation

The oblateness and equatorial radius of Neptune at the 1-microbar pressure level, together with the position angle of the projected spin axis, are the goals of a general oblate atmosphere model for Neptune employing a data ensemble obtained from the occultation of a bright IR star that provided accurate measurements of the limb position at these and several other stations. The observed reduction in central flash intensity is explained by a 150-135 K temperature decrease as pressure rises from 1 to 400 microbar. Attention is given to the implications of these oblateness results for models of the Neptune interior.

Hubbard, W. B.↗
NASA NTRS1993

Aerodynamics of a sphere and an oblate spheroid for Mach numbers from 0.6 to 10.5 including some effects of test conditions

Wind-tunnel tests were made for spheres of various sizes over a range of Mach numbers and Reynolds numbers. The results indicated some conditions where the drag was affected by changes in the afterbody pressure due to a shock reflection from the tunnel wall. This effect disappeared when the Mach number was increased for a given sphere size or when the sphere size was decreased for a given Mach number. Drag measurements and Schlieren photographs are presented that show the possibility of obtaining inaccurate data when tests are made with a sphere too large for the test section size and Mach number. Tests were also made of an oblate spheroid. The results indicated a region at high Mach numbers where inherent positive static stability might occur with the oblate-face forward. The drag results are compared with those for a sphere as well as those for various other shapes. The drag results for the oblate spheroid and the sphere are also compared with some calculated results.

Spearman, M. Leroy↗
NASA NTRS1994

Obliquity-oblateness feedback: Are climatically sensitive values of obliquity dynamically unstable?

A new model is presented for feedback between rotational and climatic variations, operative on time scales of 10(exp 4) - 10(exp 7) years. Due to the combined effect of planetary perturbations to the Earth's orbit plane and luni-solar torques on the oblate figure of the Earth, the obliquity varies by approximately 1 deg on a 4 x 10(exp 4) year time scale. Associated changes in the seasonal and latitudinal pattern of incident solar radiation cause major glaciations. Mass transport from the oceans to the polar ice sheets during these glaciations can change the gravitational oblateness of the Earth by amounts approaching 1%. As the rate of spin axis precession is directly proportional to the oblateness, the climatically forced mass transport can by dynamically significant. A simple parameterization of this coupled orbital-rotational-climatic system suggests that there is a strong tendency for the system to evolve away from climatically sensitive values of the obliquity. This may explain the mid-Pleistocene transition from an obliquity dominated regime to the present regime in which most climatic variability is concentrated at longer (10(exp 5) year) periods.

Bills, Bruce G.↗
NASA NTRS1961

An Investigation of the Natural Frequencies and Mode Shapes of Liquids in Oblate Spheroidal Tanks

An experimental investigation was conducted to gain some understanding of the character of the free vibration modes of liquids In oblate spheroidal tanks applicable in missile and space vehicle systems, Measured natural frequencies were obtained for the lowest three or four, antisymmetric modes of oscillation as a function of the liquid depth for three orientations of each of several such tanks of different size and oblateness. The orientations considered were such that: (a) the equator of the spheroid was horizontal and oscillations were along a diameter of the circular liquid surface; (b) the equator of the spheroid was vertical and the oscillations were along the minor axis of the elliptical liquid surface; and (c) the equator of the spheroid was vertical and the oscillations were along the major axis of the elliptical liquid surface; The frequency data are presented as dimensionless parameters developed for each orientation to permit the application of the experimental results to the prediction of the natural frequencies of tanks of different size and oblateness. Photographs we re made of representative surface wave or mode, shapes for each orientation.

Leonard, H. Wayne↗
NASA NTRS2011

Taylor Series Trajectory Calculations Including Oblateness Effects and Variable Atmospheric Density

Taylor series integration is implemented in NASA Glenn's Spacecraft N-body Analysis Program, and compared head-to-head with the code's existing 8th- order Runge-Kutta Fehlberg time integration scheme. This paper focuses on trajectory problems that include oblateness and/or variable atmospheric density. Taylor series is shown to be significantly faster and more accurate for oblateness problems up through a 4x4 field, with speedups ranging from a factor of 2 to 13. For problems with variable atmospheric density, speedups average 24 for atmospheric density alone, and average 1.6 to 8.2 when density and oblateness are combined.

Scott, James R.↗
NASA NTRS1977

Transformations from an oblate spheroid to a plane and vice versa: The equations used in the cartographic projection program MAP2

The relationships between the coordinates of a point on the surface on an oblate spheroid and the coordinates of the projection of that point in several common map projections are discussed. Because several of the projections are conformal, the theory of conformally mapping an oblate spheroid to the plane is summarized. For each projection considered, the equations which map the spheroid to the plane and their inverses are given.

Elliott, D. A.↗
NASA NTRS1978

Measurement of solar gravitational oblateness with gravity gradiometers

A very high sensitivity rotating gravity gradiometer onboard the spacecraft is described for measuring the gravitational oblateness of the Sun during a solar probe mission. The proposed instrument would be a self-contained structure in a thermal-vacuum-magnetic shield in the shape of a cross, with a mass of 20 kg and arm length of 1.0 m and thickness of 0.1 m. The sensor inside would have a resonant frequency of 1/30 Hz, a mechanical Q of one million and would use gravitational radiation antenna technology to achieve a sensitivity of 6 x 10 to the minus 8th power Eotvos, which would provide a measurement of the solar oblateness to an accuracy of 1.5 to 6 x 10 to the minus 8th power. The gravity gradiometer will require a spinning spacecraft, so that it will not sense the spacecraft gravity fields, but the gradiometer does not need to be at the spacecraft center of mass, or even on the spacecraft spin axis. Major problem areas to be addressed are demonstration of the instrument sensitivity prior to flight and the measurement and compensation for any residual spacecraft angular rates.

Forward, R. L.↗