117,330 research outputs found
Orbit determination with the two-body integrals
No full textWe investigate a method to compute a finite set of preliminary orbits
for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern
sets of astrometric observations, where often the information
contained in the observations allows only to compute, by interpolation,
two angular positions of the observed body and their time derivatives
at a given epoch; we call this set of data attributable.
Given two attributables of the same body at two different epochs we
can use the energy and angular momentum integrals of the two-body
problem to write a system of polynomial equations for the topocentric
distance and the radial velocity at the two epochs. We define two
different algorithms for the computation of the solutions, based on
different ways to perform elimination of variables and obtain a
univariate polynomial.
Moreover we use the redundancy of the data to test the hypothesis
that two attributables belong to the same body (linkage problem).
It is also possible to compute a covariance matrix, describing the
uncertainty of the preliminary orbits which results from the
observation error statistics.
The performance of this method has been investigated by using a large
set of simulated observations of the Pan-STARRS project.
We expect that this method can be used when the two epochs are well
separated, even if the time span is such that the algorithms based
upon propagation of a swarm of virtual objects become inadequate
Orbit determination for the radio science experiment of the NASA mission Juno
No full textJuno is a NASA New Frontiers mission to the planet Jupiter, launched from Cape Canaveral on August 5,
2011. The spacecraft will arrive to Jupiter in 2016 and will be placed for one year in a polar high-eccentric
orbit to study the composition of the planet, the gravity and the magnetic field, and the magnetosphere. The
Italian Space Agency (ASI) contributed to the mission providing the radio science instrument KaT (Ka-Band
Translator, developed by the University of Rome “La Sapienza” and Thales Alenia Space) used for the gravity
experiment, which has the goal of studying the Jupiter’s deep structure by mapping the planet’s gravity. Such
instrument takes advantage of synergies with a similar tool in development for BepiColombo, the ESA cornerstone
mission to Mercury. The Celestial Mechanics Group of the University of Pisa and SpaceDyS s.r.l. are responsible,
under an ASI contract, for the development of an orbit determination and parameters estimation software for
processing the real data independently from NASA software ODP. We shall present the state of the art of such
software highlighting the theoretical models used, the problems addressed and first results about the scientific
goals obtained with simulated data
On the computation of preliminary orbits for Earth satellites with radar observations
No full textWe introduce a new method to perform preliminary orbit determination
for satellites on low Earth orbits (LEO). This method works with
tracks of radar observations: each track is composed by
topocentric position vectors per pass of the satellite, taken at
very short time intervals. We assume very accurate values for the
range , while the angular positions (i.e. the line of sight,
given by the pointing of the antenna) are less accurate. We wish to
correct the errors in the angular positions already in the
computation of a preliminary orbit. With the information contained
in a pair of radar tracks, using the laws of the two-body dynamics,
we can write 8 equations in 8 unknowns. The unknowns are the
components of the topocentric velocity orthogonal to the line of
sight at the two mean epochs of the tracks, and the corrections
to be applied to the angular positions. We take advantage
of the fact that the components of are typically small.
We show the results of some tests, performed with simulated
observations, and compare this method with Gibbs'
and the Keplerian integral
Orbit determination with the two-body integrals. II
No full textInternational audienceThe first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or by radar observations. We write polynomial equations for this problem, which can be solved using the powerful tools of computational Algebra. An algorithm to decide if the of two short arcs is successful, i.e. if they belong to the same observed body, is proposed and tested numerically. This paper continues the research started in Gronchi et al. (Celest. Mech. Dyn. Astron. 107(3):299-318, 2010), where the angular momentum and the energy integrals were used. The use of a suitable component of the Laplace-Lenz vector in place of the energy turns out to be convenient, in fact the degree of the resulting system is reduced to less than half
Gravimetry, rotation and angular momentum of Jupiter from the Juno Radio Science experiment
No full textJuno is a NASA space mission to Jupiter, arriving at the planet in July 2016. Through accurate Doppler tracking in X and Ka-band, the Radio Science experiment will allow to map Jupiter's gravity field, crucial for the study of the interior structure of the planet. In this paper we describe the results of numerical simulations of this experiment, performed with the ORBIT14 orbit determination software, developed by the Department of Mathematics of the University of Pisa and by the spin-off Space Dynamics Services srl. Our analysis included the determination of Jupiter's gravity field, the Love numbers, the direction of the rotation axis and the angular momentum magnitude, the latter by measuring the Lense-Thirring effect on the spacecraft. As far as the gravity field is concerned, the spherical harmonics coefficients of Jupiter's gravitational potential are highly correlated and the accuracy in the determination of the zonal coefficients of degree l is degraded for l>15l>15. We explore the possibility of using a local model, introducing ring-shaped mascons, so as to determine the gravity field of the portion of the spherical surface bounded by latitudes 6°N and 35°N, the latitude belt observed during Juno's pericenter passes. Finally, the determination of Jupiter's angular momentum magnitude turned out to be compromised by the impossibility of separating the effects of the Lense-Thirring acceleration and of a change in Jupiter's rotation axis direction
Innovative observing strategy and orbit determination for Low Earth Orbit Space Debris
No full textWe present the results of a large scale simulation, reproducing the
behavior of a data center for the build-up and maintenance of a
complete catalog of space debris in the upper part of the low Earth
orbits region (LEO). The purpose is to determine the performances of
a network of advanced optical sensors, through the use of the newest
correlation and orbit determination algorithms. This network is
foreseen for implementation in a Space Situational Awareness system,
such as the future European one. The conclusion is that it is
possible to use a network of optical sensors to build up a catalog
containing more than 98\% of the objects with perigee height between
1100 and 2000 km, which would be observable by a reference radar
system selected as comparison. It is also possible to maintain such
a catalog within the accuracy requirements motivated by collision
avoidance, and to detect catastrophic fragmentation events. The
obtained results depend upon specific assumptions on the sensor and
on the software technologie
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Optimization of Space Surveillance Resources by Innovative Preliminary Orbit Methods
No full textThe number and performance of the sensors to be used
for a survey is a function of the minimum number of observations
required to determine an orbit. This is critical
for the definition of the sensor network and the observation
planning.
Our goal is to obtain an orbit with a smaller number of
observations with respect to the classical methods, such
as Gauss/Laplace. In the context of space debris surveys,
the goal is a full 6-elements orbit from just 2 tracklets,
which could be obtained with only 2 exposures. The information
contained in a tracklet can be summarized in a
4-dimensional vector called attributable, thus two tracklets
are enough for the orbit determination problem to be
over-determined.
We have proposed an algorithm based upon the integrals
of the 2-body problem. We outline the equations and
the solution methods which are used in our implementation.
We report on the results of a validation test, based
upon the processing of one year of data from ESA Optical
Ground Station. We conclude that the method is
very effective and can be used to find correlations between
tracklets, to be confirmed with additional correlations,
thus providing a catalog of full 6-elements orbits
Square Dancing with the Stars to Enhance Dynamic Hirschman Linkages?
No full textIn this Presidential Address, the author takes the reader on a reconnaissance of his life and time as a regional scientist. He points out scenery he found scintillating along the way, hoping that some may pick up the banner and chew on a few of the ideas for a while. He suggests a revisit to Albert O. Hirschman’s notion of key sectors and more empirical analysis related to Marcus Berliant’s and Masahisa Fujita’s notion of knowledge creation and transfer.Presidential Address, San Antonio, Texas, March 29, 2014 (53rd Meetings of the Southern Regional Science Association
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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