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  • 1
    Electronic Resource
    Electronic Resource
    The use of angles and angular rates (1977)
    Springer
    Celestial mechanics and dynamical astronomy 16 (1977), S. 481-488 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract MIT's Lincoln Laboratory has developed a computer driven, rapidly slewing (≃4° s−1), electro-optical (≃3″ resolution) telescope. This enables the rapid measurement of angles and instantaneous angular rates for artificial satellites. The simultaneous acquisition of angles and angular rates constitutes a new initial orbit problem which has been solved. Three different methods of solution are presented including an exact, analytical one. Numerical tests on six widely different satellite orbits indicate that the topocentric distance can be determined to better than 1% (and usually as well as 0.1%) for most satellites after a 5–10 min observation interval.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229289
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  • 2
    Electronic Resource
    Electronic Resource
    The use of angles and angular rates (1980)
    Springer
    Celestial mechanics and dynamical astronomy 21 (1980), S. 281-290 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Earlier work on the angles and angular rate initial orbit determination problem has been extended to allow the incorporation of arbitrary amounts and mixtures of angles and angular rate data. The statistical estimation technique used is that of Maximum Likelihood. Numerical tests on six widely different satellite orbits indicate that the orbital elements can generally be computed to 1% from data acquired during a single apparition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230226
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  • 3
    Electronic Resource
    Electronic Resource
    Differential correction for near-stationary satellites (1982)
    Springer
    Celestial mechanics and dynamical astronomy 26 (1982), S. 423-431 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper presents a new concept for the differential correction of orbits. It is developed in detail for the case of near-stationary artificial satellites. For these satellites a few (〈10) observations over a short (5–15m,≲1% period) time interval allows the reacquisition of the satellite an hour later. Moreover, the addition of only a few more observations spanning a slightly longer time interval allows the production of an excellent set of orbital elements. The technique is self-starting and does not use any of the classical initial orbit determination procedures. It can be used for radar observations or extended to include angular velocity data. Its success appears to be based on the ability to find a coordinate system in which the object's motion is nearly stationary and the extensive use of analytical (instead of numerical) procedures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230422
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  • 4
    Electronic Resource
    Electronic Resource
    Two locations, two times, and the element set (1985)
    Springer
    Celestial mechanics and dynamical astronomy 37 (1985), S. 149-159 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We have delved into that aspect of classical initial orbit determination wherein one transforms two locations at two times into an orbital element set. The particular realm of application we have in mind is artificial satellites whose locations are uncertain to ≃1 km3, the two locations being separated in time by no more than 30 min. Not only have we investigated Gauss's method, iteration on the semi-latus rectum, iteration on the true anomaly, and the Lambert-Euler technique, we have made substantial practical progress with the latter two algorithms. Specifically, we have performed an essential analytical simplification that reduces all these methods to the solution of a single equation in one unknown, instead of the usual coupled triplet of three equations in three unknows. An extensive series of numerical trials shows the robustness of the new formulation and the unsatisfactory nature of the traditional schemes in our application. Because the essence of our advance is analytical in nature, we expect this new approach to be superior in all realms of initial orbit determination.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230924
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  • 5
    Electronic Resource
    Electronic Resource
    Unsolved problems of celestial mechanics (1987)
    Springer
    Celestial mechanics and dynamical astronomy 41 (1987), S. 411-412 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01238775
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  • 6
    Electronic Resource
    Electronic Resource
    On solving Kepler's equation (1989)
    Springer
    Celestial mechanics and dynamical astronomy 46 (1989), S. 163-176 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Intrigued by the recent advances in research on solving Kepler's equation, we have attacked the problem too. Our contributions emphasize the unified derivation of all known bounds and several starting values, a proof of the optimality of these bounds, a very thorough numerical exploration of a large variety of starting values and solution techniques in both mean anomaly/eccentricity space and eccentric anomaly/eccentricity space, and finally the best and simplest starting value/solution algorithm: M + e and Wegstein's secant modification of the method of successive substitutions. The very close second is Broucke's bounds coupled with Newton's second-order scheme.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00053046
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  • 7
    Electronic Resource
    Electronic Resource
    A new method of initial orbit determination (1986)
    Springer
    Celestial mechanics and dynamical astronomy 39 (1986), S. 181-190 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a new method of initial orbit determination for angles-only data. The technique is applicable with only three data sets but the formalism can incorporate arbitrarily large amounts of data. The algorithm rests on the fact that the orbital plane is usually very well determined, as a consequence of the central nature of the gravitational force, and a theorem of W. R. Hamilton's from 1846. His result states that the velocity vector describes a circle in the orbital plane in a particular manner. Tests on a variety of deep-space artificial satellites show that the method has promise. Unfortunately it does not work very well on the stressing cases of current practical application-high eccentricity orbits. As no other method does either, the opportunities still exist for a significant advance in this area of celestial mechanics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230850
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  • 8
    Electronic Resource
    Electronic Resource
    An analysis of the Hubble Space Telescope Fine Guidance Sensor Coarse Track mode (1990)
    Springer
    Experimental astronomy 1 (1990), S. 237-266 
    Details
    ISSN: 1572-9508
    Keywords: Hubble Space Telescope ; Fine Guidance Sensor ; Coarse Track ; pointing stability ; guidance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract There are two guiding modes of the Hubble Space Telescope used for the acquisition of astronomical data by one of its six scientific instruments. The nominally more precise one is called Fine Lock and the other is known as Coarse Track. Two of the three Fine Guidance Sensors are locked onto Guide Stars, in one of these two modes, thus maintaining the spacecraft's line of sight to a few milli-arc seconds (nominally 7 milli-arc seconds for Fine Lock and 17 milli-arc seconds for Coarse Track). In this paper I report on the most realistic and extensive simulations to date of the Coarse Track guidance mode. These simulations clearly show that the precision of Coarse Track is influenced by one adjustable parameter and that for default operating conditions its precision is 12 milli-arc seconds. A factor of two improvement should be possible by modifying the key parameter which governs the precision of Coarse Track. The importance of this for the scientific mission on the Hubble Space Telescope is that the use of Coarse Track in place of Fine Lock will result in a ∼1/3 reduction of engineering overhead per scientific target acquisition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00428518
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  • 9
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    The use of angles and angular rates (1977)
    Springer
    Details
    Publication Date: 1977-12-01
    Print ISSN: 0923-2958
    Electronic ISSN: 1572-9478
    Topics: Physics
    Published by Springer
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  • 10
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    On solving Kepler's equation (1989)
    Springer
    Details
    Publication Date: 1989-01-01
    Print ISSN: 0923-2958
    Electronic ISSN: 1572-9478
    Topics: Physics
    Published by Springer
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