Publication: Analysis and implementation of gravity field models for planets and asteroids
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2014-06-21
Defense date
2014-07-09
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Abstract
Gravitational models are an essential tool to develop, simulate and predict
the behaviour of satellites, asteroids and other bodies of celestial nature.
The accuracy of these models is of critical importance in surveillance, orbit
determination and propagation.
In the following pages, it will be presented two different models to study the
effect of gravity fields produced by both Planets and Asteroids.
The reader must always note the importance of improving the results obtained by means of classical gravitational theories as modern society dependence in man-made space satellites is constantly growing, implying a direct
application in the industrial and academic fields. For example, Rummel
expects that the data retrieved by GRACE and GOCE missions will help to
model with even higher precision the gravity levels as well as time variations
due to tidal effects (both fl
uid and solid tides). The models here presented
try to average this effects and to predict accurately the gravity vector field
near Earth but always neglecting time variations of the gravitational field.
These models have been prototyped in MatLab and implemented in C programming languages. MatLab may be used for preliminary results as well as
for data analysis and interpretation. Mathematically speaking, these models
cover wide numerical ranges of magnitude that can lead to over
ow or underflow. Not in vane, big effort has been devoted to normalize the magnitude of
the data used in calculations as well as special care in function evaluations.
Also, MatLab parallel toolbox allows to perform easily parallel calculation
without extra-effort.
The implementation of such algorithms has already been a matter of concern
as the algorithms have to be evaluated as fast as possible. The polyhedron
algorithm that will be presented later can be highly parallelized and hardware
may make the difference rather than software. For example in [2] it can
be found a performance analysis comparing single-threaded implementation
with massively parallelized algorithm in CUDA GPU.
The theories presented are based on classical Newton's laws but are intended
to improve the predictions of Newton's law of universal gravitation. However it is not the scope of this report to introduce relativistic effects as the
variations in the results as it will be shown are below the uncertainty level of the predictions done with the available data. Neither atmospheric drag nor
solar radiation pressure have been modelled as they depend on the shape of
the body. Only gravitational forces are studied.
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Keywords
Planetas, Asteroides, Gravitación, Satélites, Astrodinámica