| A New Procedure for Orbit Determination Based on Three Lines of Sight (Angles Only) |
APR 93 |
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| Authors:
R. H. Gooding; DEFENCE RESEARCH AGENCY FARNBOROUGH (UNITED KINGDOM)
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 | A new procedure has been developed for the general solution of the minimal angles-only problem in which an orbit is determined from three line-of- sight observations. The basis of the approach is a higher-order Newton correction of the assumed values for two of the unknown ranges, appeal being made to the author's (published) universal solution of Lambert's orbital boundary-value problem. The new procedure is free of the inherent limitations of ... |
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| Orbit Perturbations Due to an Axi-Symmetric Gravitational Field, Analyzed Over Extended Periods of Time |
JAN 92 |
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| Authors:
R. H. Gooding; DEFENCE RESEARCH AGENCY FARNBOROUGH (UNITED KINGDOM) AEROSPACE DIV
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| The author's untruncated orbital theory for perturbations due to the Earth's zonal harmonics, previously developed to cover all terms associated with (j sub 2)sq and J sub l, is being extended to cover the secular and long- periodic effects associated with (J sub 2)cm and (J sub 2)(J sub l). If J sub 2 and J sub l (l > 2) are regarded as first-order and second-order respectively, this means ... |
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| On a Problem Arising in the Computation of Orbit Perturbations |
MAY 91 |
10 pages |
| Authors:
R. H. Gooding; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (UNITED KINGDOM)
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 | In the computation of perturbations for an orbiting satellite, a problem can arise with the integration of a rate-of-change quantity, the prototype expression for which is k cos theta, where theta has a quasi-linear variation with time. The problem can be dealt by the use of definite integrals between epochs rather than indefinite integrals at epochs. |
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| A Procedure for the Solution of Lambert's Orbital Boundary-Value Problem |
MAR 91 |
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| Authors:
R. H. Gooding; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (UNITED KINGDOM)
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| A procedure is described that provides a universal solution for Lambert's problem. Based on the approach of Lancaster and his colleagues, the procedure uses Halley's cubic iteration process to evaluate the unknown parameter, x , at the heart of the approach, initial estimates for x being selected so that three iterations of the process always suffice to yield an accurate value. The overall procedure has been implemented via three Fortran-77 ... |
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| Untruncated Perturbation Analysis for a Satellite Orbiting in a Non- Rotating Gravitational Field |
MAR 91 |
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| Authors:
R. H. Gooding; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (UNITED KINGDOM)
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| In previous work it was assumed that the gravitational field was axisymmetric and due to a mass distribution entirely within the orbital region. By use of a particular system of spherical polar coordinates, an orbital theory was developed that led to compact first-order perturbation formulae associated with the general zonal harmonic, J sub l. No eccentricity truncation was involved in these formulae, though there was an implicit restriction to elliptic ... |
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| On the Universality of Orbital Theory for Satellite Motion Perturbed by Gravitational Harmonics |
MAR 91 |
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| Authors:
R. H. Gooding; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (UNITED KINGDOM)
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| The author's approach to perturbation analysis for a satellite orbiting in a general gravitational field, concisely formulated by the use of a particular system of spherical polar coordinates, was conceived as applying only to elliptic orbits. However,the formulation extends, with surprising ease, to hyperbolic orbits. No change is required in the manner in which some perturbations are applied to the orbital elements and others to the coordinates, though it becomes ... |
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| Perturbations, Untruncated in Eccentricity, for an Orbit in an Axis- Symmetric Gravitational Field |
MAR 91 |
27 pages |
| Authors:
R. H. Gooding; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (UNITED KINGDOM)
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| By recourse to a particular system of spherical polar coordinates based on the mean orbital plane, an orbital theory has been developed that leads to extremely compact first-order perturbation formulae associated with the general zonal harmonic, J sub l. The formulae are complete (untruncated in eccentricity) and generalize, via recurrence relations, the author's earlier results for the effects of J sub 2 (analysed to second order) and J sub 3. ... |
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| On Mean Elements for Satellite Orbits Perturbed by the Zonal Harmonics of the Geopotential |
JUL 89 |
9 pages |
| Authors:
R. H. Gooding; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| Users of orbital elements are often puzzled by the different ways in which mean elements are defined. This applies to all the standard elements, but the difficulty is most pronounced in regard to semi-major axis and mean motion. This paper relates mean elements to the perturbations of a satellite caused by the Earth's zonal harmonic J2, and shows how elements can be defined so that perturbations in spherical coordinates take ... |
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| On Universal Elements, and Conversion Procedures to and from Position and Velocity |
JUL 89 |
30 pages |
| Authors:
R. H. Gooding; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| An element set is advocated that is familiar (in traditional terms), and yet applicable to all types of orbit without loss of accuracy. It is not free of singularity, but this is not a serious deficiency. Keywords: Great Britain; Astrodynamics; Celestial mechanics; Orbits; Orbital elements. (JHD) |
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| The Hyperbolic Kepler's Equation, and the Elliptic Equation Revisited |
JUL 89 |
29 pages |
| Authors:
R. H. Gooding; A. W. Odell; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| A procedure is developed that, in two iterations, solves the hyperbolic Kepler's equation in a very efficient manner, and to an accuracy that proves to be always better than 10 to the minus 20th power (relative truncation error). Earlier work on the elliptic equation has been extended by the development of a new procedure that solves to a maximum relative error of 10 to the minus 14th power. Keywords: Great ... |
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| Satellite Motion in an Axi-Symmetric Gravitational Field. Part 2. Perturbations due to an Arbitrary J sub l |
MAY 89 |
104 pages |
| Authors:
R. H. Gooding; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| This Report continues the presentation of the untruncated orbital theory begun in Technical Report 88068. The effects of the general zonal harmonic, J sub l, are now covered, the main results being a trio of formulae are only first-order in J sub l, but, in conjunction with the second-order results for J2 published in Part 1, the complete set of formulae may be regarded as constituting a second-order theory, the ... |
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| Satellite Motion in an Axi-Symmetric Gravitational Field. Part 1. Perturbations Due to J(2) (Second Order) and J(3) |
NOV 88 |
132 pages |
| Authors:
R. H. Gooding; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (UNITED KINGDOM)
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| Full details are given of the untruncated second-order orbital theory. The analysis only takes account of the first two zonal harmonics, J2 and J3 geopotential assumed. The principal merit of the theory derives from the extreme compactness of the results obtained for short-period perturbations in position and velocity, these perturbations being expressed relative to a system of spherical-polar coordinates based on a rotating 'mean orbital plane'. The use of osculating ... |
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| Explicit Forms of Some Functions Arising in the Analysis of Resonant Satellite Orbits |
MAY 88 |
34 pages |
| Authors:
R. H. Gooding; D. G. King-Hele; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The analysis of resonant satellite orbits has been pursued for 18 years, and has led to the most accurate values available for lumped geopotential harmonics of the relevant orders. The basic theory for the resonance effects was developed in the 1960s, but the detailed application of the technique calls for a systematic notation and for the evaluation of two subsidiary functions, namely F, a function of the orbital inclination, and ... |
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| On the Solution of Lambert's Orbital Boundary-Value Problem |
APR 88 |
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| Authors:
R. H. Gooding; ROYAL AEROSPACE ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| During the past 30 years there has been a resurgence of interest in the classical orbital boundary value problem of Lambert, largely because of its relevance to space rendezvous and interception. The present Report is aimed at providing details of a universal solution of Lambert's problem. In particular, the report presents starting formulae for Halley's cubic iteration process, used for evaluation of the unknown parameter, x, at the heart of ... |
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| Analytical Generation of Satellite Orbits at the RAE (Royal Aircraft Establishment) |
OCT 84 |
18 pages |
| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| This Paper traces the development, at the Royal Aircraft Establishment, of computer programs for orbit determination and orbit evolution. The principal program, PROP, is still in regular use, having an accuracy of 50 to 100 m for the orbits of close satellites determined over a period of a few days even when the drag is severe. The chief limitation of PROP is the absence of lunisolar perturbations, but these are ... |
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| An Introduction to Satellite Orbits |
SEP 84 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| An elementary introduction to artificial satellite orbits is presented, with a convenient classification in terms of the height of perigee and apogee, orbital inclination being another parameter of importance. The main sources of orbital perturbation are described, and special attention is paid to orbits with repeating ground-track. Additional keywords: Mathematical curves. (Author). |
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| Second-Order Perturbations Due to J2, for a Low-Eccentricity Earth-Satellite Orbit. |
AUG 1979 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The second order perturbations of J sub 2 in the orbital elements of an earth satellite are analysed by an elementary treatment that neglects terms of second order J sub 2. The resulting expressions are combined into a triad of cylindrical polar coordinates, defined by a plane of fixed inclination and uniform rotation rate, since this leads to very simple formulae for perturbations in coordinates. |
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| Evaluation of 14th-Order Harmonics in the Geopotential. |
01 FEB 1978 |
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| Authors:
D. G. King-Hele; Doreen M. C. Walker; R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The Earth's gravitational potential is now usually expressed in terms of a double series of tesseral harmonics with several hundred terms, up to order and degree at least 20. The harmonics of order 14 can be evaluated by analysing changes in satellite orbits which experience 14th-order resonance, when the track over the Earth repeats after 14 revolutions. This report describes the first evaluation of individual 14th-order coefficients in the geopotential ... |
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| The Orbit of Ariel 4 (1971 - 109A). |
JUL 1975 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The definitive orbit of Ariel 4 has been computed, from Minitrack observations, for the two periods during which orbital parameters were required for use in telemetry analysis - from December 1971 (launch) to May 1973, and from October 1973 to December 1973. The orbit was represented by a model with eight independent orbital parameters, and the values of these parameters were determined, and are listed in this Report, at three-day ... |
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| Geopotential Harmonics of Order 15 and Odd Degree from Analysis of Resonant Orbits. |
MAR 1975 |
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| Authors:
D. G. King-Hele; Doreen M. C. Walker; R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The authors have analyzed the variations of inclination in 13 satellite orbits as they pass slowly, under the action of air drag, through 15th-order resonance with the geopotential, when successive equatorial crossings are 24 degrees apart and the ground track repeats after 15 revolutions. The size and form of the change in inclination are determined mainly by the values of the geopotential harmonics of 15th order and odd degree, C ... |
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| The Evolution of the PROP6 Orbit Determination Program, and Related Topics. |
DEC 1974 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| Numerous changes have been made to the orbit determination program PROP, since the PROP3 Users' Manual was published in 1968. A recent change has been made to the orbit generator, which, though its effect is numerically slight in most applications, needed to be documented. This Report gives such a documentation, and compares the PROP orbit generator, before and after the change, with the generators of other programs in use at ... |
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| Geopotential Harmonics of Order 15 and Even Degree, from Changes in Orbital Eccentricity at Resonance. |
SEP 1974 |
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| Authors:
D. G. King-Hele; Doreen M. C. Walker; R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| When a satellite orbit decaying slowly under the action of air drag experiences 15th-order resonance with the Earth's gravitational field, so that the ground track repeats after 15 revolutions, the orbital eccentricity may suffer appreciable changes due to perturbations from the gravitational harmonics of order 15 and even degree (16,18,20 ...). In this paper the changes in eccentricity at resonance for six satellites in near-circular orbits at inclinations between 56 ... |
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| Digestive Processes of Haematophagous Insects. VII. Comparison of Animal-Fed and Membrane-Fed Adults of 'Glossina morsitans morsitans' Westw. (Diptera, Glossinidae), |
02 NOV 1973 |
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| Authors:
R. H. Gooding; ALBERTA UNIV EDMONTON DEPT OF ENTOMOLOGY
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| The Look-Angle Prediction Programs PLAP, ESPLAP and 6130PLAP. |
AUG 1973 |
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| Authors:
R. H. Gooding; A. W. Odell; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| Descriptions are given of three Fortran programs for the predictions of satellite look angles: PLAP, a member of the PROP family of programs, is limited to prediction for a single station; ESPLAP, based on three ESRO programs, will provide a 'world map' of predictions for up to 16 stations; 6130PLAP, a new program capable of predictions for up to seven stations, has been written for efficient operational use on the ... |
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| The Digestive Processes of Haematophagous Insects. IV. Secretion of Trypsin by 'Aedes aegypti' (Diptera: Culicidae), |
23 OCT 1972 |
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| Authors:
R. H. Gooding; ALBERTA UNIV EDMONTON DEPT OF ENTOMOLOGY
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| There is a correlation between the amount of blood ingested by Aedes aegypti (L.) and the trypsin activity in the midgut 16 and 24 hr after feeding. Puromycin and dactinomycin ingested with a blood meal depress the level of midgut trypsin. Trypsin purified from the midguts of A. aegypti fed upon defibrinated blood containing (14)C-amino acids contains radioactivity. Midguts from blood-fed mosquitoes did not produce significant amounts of trypsin when ... |
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| The Digestive Processes of Haematogphagous Insects. III. Inhibition of Trypsin by Honey and the Possible Functions of the Oesophageal Diverticula of Mosquitoes (Diptera), |
17 AUG 1972 |
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| Authors:
R. H. Gooding; A. C. Cheung; B. M. Rolseth; ALBERTA UNIV EDMONTON DEPT OF ENTOMOLOGY
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| Honey inhibits esterolytic and proteolytic activity of trypsin from Aedes aegypti, Culex pipiens quinquefasciatus, and cattle. The inhibitor is heat stable and only a portion of the inhibition capacity is lost from the honey by dialysis. Glucose, fructose, and sucrose have no effect upon trypsin but ascorbic acid and riboflavin are inhibitory while gluconic acid is an activator. Nectar from lilies but not from honeysuckles inhibits C. pipiens quinquefasciatus trypsin. ... |
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| Digestive Processes of Haematophagous Insects. I. A Literature Review, |
1972 |
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| Authors:
R. H. Gooding; ALBERTA UNIV EDMONTON DEPT OF ENTOMOLOGY
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| About 240 papers published between 1903 and early 1971, providing information on more than 150 species of haematophagous insects, are reviewed. Aspects of digestive physiology covered are size of the blood meals and their distribution within the alimentary canal, properties of the salivary glands, gross and histological changes in the gut and its contents, the enzyme content of the gut and the properties of the digestive enzymes. The relationship of ... |
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| Lumped Geopotential Coefficients (C Bar Sub 15,15) and (S Bar Sub 15,15) Obtained from Resonant Variation in the Orbit of Ariel 3. |
APR 1971 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The orbital inclination of the satellite Ariel 3 unexpectedly decreased early in 1968. This decrease may now be explained as the consequence of a 15th-order resonance with the earth's gravitational field. Analysis of the resonance leads to a derivation of 'lumped' values of the harmonic coefficients C bar sub(15,15) and S bar sub(15,15) appropriate to the inclination (80 degrees) and height (500 km) of Ariel 3, viz. (-19.9 plus or ... |
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| Orbit Determination at the Royal Aircraft Establishment. |
NOV 1970 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The paper describes the development of a series of computer programs for the orbit determination of earth satellites. The paper is based on the first of two lectures given at the ESRO summer school on Spacecraft Operations held at Gravenbruch, near Frankfurt, West Germany, in August 1970. (Author) |
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| Applications and Results of Orbit Determination, |
NOV 1970 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The paper summarizes the reasons for determining the orbits of earth satellites, and describes how knowledge of the earth's gravitational potential and its atmosphere has improved as a result of orbit determination. The paper is based on the second of two lectures given at the ESRO summer school on Spacecraft Operations, held at Gravenbruch, near Frankfurt, West Germany, in August 1970. (Author) |
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| A RECURRENCE RELATION FOR INCLINATION FUNCTIONS. |
APR 1970 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| When the terms of the series expansion for the gravitational potential of the earth are expressed in terms of the orbital elements of an arbitrary earth satellite, the orbital inclination, i, appears in each term as the argument of a function of inclination only. For the special case when the field is axi-symmetric, studied in an earlier paper, a recurrence relation was given for a normalized inclination function, A(sup K ... |
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| THE ORBIT OF ARIEL 3 (1967-42A). |
DEC 1969 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The definitive orbit for Ariel 3 has been computed, from Minitrack observations, for a period of 27 1/2 months from the launch of the satellite. The orbit was represented by a model with seven independent orbital parameters and the values of these parameters were determined, and are listed, at three-day intervals. Typical accuracies are 0.00001 in eccentricity and 4 seconds in angular parameters, that is, about 1/2 km in position. ... |
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| A PREP USERS' MANUAL, |
MAY 1969 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| PREP is a computer program for printing ephemerides of earth satellites, using the PROP analytical model which is based on Merson's mean orbital elements. A description of the program is given, with instructions on how to use it. (Author) |
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| Studies on Proteinases from Some Blood-Sucking Insects, |
1969 |
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| Authors:
R. H. Gooding; ALBERTA UNIV EDMONTON DEPT OF ENTOMOLOGY
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| By use of synthetic substrates, trypsin and chymotrypsin have been demonstrated in the midguts of blood-fed Aedes aegypti, Culex fatigans, Melophagus ovinus, and Pediculus humanus, but not in those of Cimex lectularius or Rhodnius prolixus. The trypsin and chymotrypsin have been partially separated by Sephadex Gel filtration. Both enzymes are inhibited by phenylmethyl sulfonyl-fluoride and soybean trypsin inhibitor. The trypsins are inhibited by N-a-p-tosyl-lysine chloromethyl ketone but not by L-1-tosylamide-2-phenyl-ethylchloromethyl ... |
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| A PROP3 USERS' MANUAL. |
DEC 1968 |
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| Authors:
R. H. Gooding; R. J. Tayler; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| PROP3 is the third version of a computer program for refining the orbital parameters of an earth satellite. A description of the program is given, together with full instructions on how to use it. (Author) |
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| ON THE USE OF RANGE AND RANGE RATE MEASUREMENTS IN THE NEW R.A.E. ORBIT DETERMINATION PROGRAM. |
JUL 1967 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The new orbit determination program PROP can use range and range rate observations as well as observations of direction. The orbit of Ogo 2 (1965-81A) has been determined at epoch 1965 November 10.0, using Minitrack observations and Goddard Range and Range Rate observations. The results show reasonable agreement between observations from the two systems and suggest that random errors in the range and range rate observations are of the order ... |
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| ORBIT DETERMINATION FROM MINITRACK OBSERVATIONS. |
NOV 1966 |
20 pages |
| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
|
| Although Minitrack observations are only accurate to about 1 minute of arc, accurate orbits have been obtained for a number of satellites. This is due to the excellent global coverage of the NASA Minitrack network. The accuracy obtained for eccentricity is typically about 0.00001, and comparable values are obtained for the other orbital elements. The main source of observational error is thought to be inadequate correction for ionospheric refraction. Apparent ... |
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| THE ORBIT OF ARIEL 2 (1964-15A) - THE FIRST TWELVE MONTHS. |
DEC 1965 |
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| Authors:
R. H. Gooding; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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| The definitive orbit for Ariel 2 (1964-15A) is computed, from Minitrack observations, for a period of twelve months from the launch of the satellite. The orbit is described by a model with eight orbital parameters and these parameters are listed at every twenty-fifth nodal passage. The angular observations are accurate to about 1 minute and, as a result, the average computed standard deviations of the eight fitted orbital parameters are ... |
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