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Code Organization | ||
================= | ||
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Goals of NEOSpy | ||
--------------- | ||
NEOSpy is a collection of tools for calculating the orbits and expected fluxes for minor | ||
planets specifically for the purpose of estimating which objects are visible in current, | ||
past, or future sky surveys. Specifically the goal is that these calculations may be | ||
performed on the full set of all known asteroids in a reasonable amount of time on a | ||
laptop. | ||
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Propagation | ||
~~~~~~~~~~~ | ||
There are a number of existing tools which enable the propagation of orbits for | ||
many millions or billions of years, but these typically are designed for a comparatively | ||
small number of objects (perhaps 10-100 thousand), whereas NEOSpy's design intent is | ||
10-100 million objects over the course of decades. The total compute approximately | ||
scales like:: | ||
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computation time ~ (number of objects) x (length of time being simulated) | ||
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However solving the large number of objects for a relatively short length of time can be | ||
optimized differently than a small number of objects for Giga-years. | ||
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Flux Estimation | ||
~~~~~~~~~~~~~~~ | ||
After propagation has been performed, it is important to estimate the total expected | ||
flux of the objects from the point of view of an observer. There are a number of models | ||
for this available, including the Near Earth Asteroid Thermal Model (NEATM), the Fast | ||
Rotator Model (FRM), and the HG-Magnitude system which is common for asteroids in the | ||
visible band. | ||
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SPICE Kernel Interoperability | ||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | ||
SPICE is a commonly used software package which has been in development for several | ||
decades at this point, and is often used to keep track of the ephemeris of planets, | ||
satellites (both natural and artificial), asteroids, and comets. Essentially the motion | ||
of anything in the Solar System can be encoded in some flavor of SPICE kernel. The | ||
primary downside of using cSPICE is that there is no native support for multi-core cpu | ||
queries (an artifact of the age of the code). NEOSpy has native multi-core support for | ||
the majority of all commonly used SPICE kernels. | ||
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High level Structure | ||
-------------------- | ||
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Why Rust? | ||
~~~~~~~~~ | ||
Given the goals listed above, it is clear that performance plays a key roll in design | ||
considerations of the tool. As a result of this, the Rust language was chosen as the | ||
primary language for a majority of the business logic. A Python "wrapper" was written on | ||
top of the Rust core, allowing users to call the compiled Rust code from Python. This | ||
wrapper lowers the barrier to entry for users doing data-analysis or simulations without | ||
having to learn the underlying Rust. | ||
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Rust has a number of advantages over existing languages, it's performance is typically | ||
comparable to C++/C, however due to the structure of the language it is less prone to | ||
the most common type of errors to do with memory allocation and management. In addition | ||
to this, Rust has excellent native multi-core support, especially for embarrassingly | ||
parallel problems such as the orbit propagation required for NEOSpy. | ||
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NEOSpy Core | ||
~~~~~~~~~~~ | ||
The Rust core of the library, which does the underlying orbit and flux calculations is | ||
written entirely without any reference to Python. This core part is available as | ||
`neospy_core`, and programming can be done entirely within Rust for tools which do not | ||
require the Python wrapper. This design was chosen so that systems tools which would | ||
benefit from orbit computation can be written without having to have Python installed. | ||
It is important to note that if performance is a concern, then removing the Python is an | ||
important step to get the maximum possible performance. | ||
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Core Python Wrapper | ||
~~~~~~~~~~~~~~~~~~~ | ||
The Rust library described above then has Python wrappers written over it, allowing | ||
users to call these compiled tools inside of Python. In order to do this, some | ||
boiler-plate code is required to glue these independent parts together. This is where | ||
the `rust` folder inside of NEOSpy comes from. Inside of this folder there are rust | ||
files which are mostly a one-to-one mapping to their respective counterparts inside of | ||
the `neospy_core`. Ideally there should be no 'business' logic contained within these | ||
wrappers, and they should largely exist to provide convenient mappings from the Python | ||
concepts to the Rust internal organization. | ||
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NEOSpy Python | ||
~~~~~~~~~~~~~ | ||
The remaining part of the code which is strictly Python is mostly quality of life | ||
functions, plotting, and web query code. There is little to no mathematics or physics | ||
contained within the Python. The exception being the population related code, which | ||
manages the fair sampling of the known asteroids to generation synthetic populations. |
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:maxdepth: 2 | ||
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background | ||
code_structure | ||
propagation | ||
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.. toctree:: | ||
:maxdepth: 1 | ||
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Orbit Propagation | ||
================= | ||
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Orbit propagation can be an immensely complicated topic, spanning from two-body | ||
Keplerian motion, to models of gravitational fields including thousands of terms. Being | ||
able to pick the correct amount of precision required is difficult, and NEOSpy makes a | ||
number of judicious choices which are reasonable for the vast majority of cases. | ||
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What follows is a discussion of the pros-cons of various models of gravitational forces, | ||
and when the model is "good enough" for the problem at hand. | ||
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If we wish to predict the on-sky position or motion of an object, the level of precision | ||
required depends greatly upon the distance which the object is from the observer. | ||
Being accurate to 100nm when we are looking 5 au away is not necessary, alternatively, | ||
when we are considering an NEO such as Apophis (which will come very close to hitting | ||
the Earth), meters matter. | ||
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.. figure:: images/orbit_models.png | ||
:width: 600 | ||
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This is a plot of an arbitrary, rather large Main Belt Asteroid, and its orbital | ||
propagation error going back 100 years. Specifically error in orbit propagation | ||
comparing internal propagation against JPL Horizons SPICE kernels. This compares the | ||
difference in position for the two-body approximation, orbit propagation assuming | ||
there are no massive asteroids in the main belt, and finally including the 5 most | ||
massive main belt asteroids. Note that JPL Horizons includes at least 16 of the | ||
largest asteroids, so there is still residual error over the course of 100 years. | ||
This error however is only on the order of 100km. | ||
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Forces | ||
------ | ||
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First it is useful to list out forces which objects in space may experience, to get an | ||
understanding of what is required in order to accurately model their motion. These are | ||
listed in approximately the order of their effects on objects (though order may change | ||
due to varying circumstances). | ||
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- *Newtonian Gravity* - Typically what is imagined when people say the force of gravity. | ||
- *Corrections for Relativity (GR)* - The orbit of Mercury precesses due to effects from | ||
relativity, and in fact many NEOs, or even objects which get close enough to planets | ||
will experience effects from relativity. | ||
- *Gravity from Minor Planets* - Main belt asteroids are often non-negligible. | ||
The motion of objects through the main belt often needs to include the mass of | ||
asteroids such as Ceres, which makes up an appreciable fraction of the total mass of | ||
the belt. | ||
- *Oblateness of the Sun/Planets* - The Sun and Planets are not ideal spheres, and as a | ||
result, cannot be exactly modeled as a point source. This non-sphericity can be | ||
written as an expansion of spherical harmonic-like terms, commonly written as `J` | ||
terms. The first non-trivial term of this expansion is the oblateness, referred to | ||
as `J2`. This term by itself will cause objects in orbit of the central mass to | ||
have their longitude of ascending node precess as a function of how inclined they | ||
are with respect to the equator of the central mass. | ||
- *Non-gravitational Forces* - The forces above are a result of gravity, however there | ||
are many potential forces which an object may experience, these include things such | ||
as outgassing, radiation pressure, the Yarkovsky effect, and the Poynting-Robertson | ||
effect. These effects typically have some relation to the total solar radiation that | ||
the object is receiving, and can frequently be written as a polynomial with respect | ||
to the distance that the object is from the Sun. | ||
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Accuracy | ||
-------- | ||
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Accuracy of the orbit propagation depends on how precisely the forces above are | ||
computed, and the precision of the numerical integrator used. Forces such as the | ||
Yarkovsky effect cause relatively small forces on asteroids, but will add up to be | ||
non-negligible over the course of kilo-year or mega-years. A common issue however is | ||
that we often don't have accurate enough measurements of the objects to be able to | ||
accurately measure the contribution of these forces. | ||
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Close encounters with other objects also cause significant accuracy issues as well. The | ||
force between objects follows a `1/r^2` relationship, meaning as the distance goes to | ||
zero, small changes in the distance cause large changes in the force. We do not have | ||
infinitely precise measurements of the objects orbits, meaning there is some positional | ||
error in our knowledge of every object. This error "blows up" during close encounters | ||
because of the small `r` effect. Many objects which cross the path of planets frequently | ||
will have relatively close encounters with planets with some regularity, making long | ||
term predictions of their orbits difficult. Typically it only takes a few close | ||
encounters to completely ruin any hope of predicting the position of an object in the | ||
future or past. This makes the inner solar system a chaotic system in the mathematical | ||
sense, small deviations of input parameters have large implications for future behavior | ||
(despite the fact that everything should in theory be precisely computable). | ||
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The result of the problems above, objects in the inner solar system of often very | ||
difficult to model more than a few hundred/thousand years into the future with any | ||
accuracy. | ||
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Performance | ||
----------- | ||
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To achieve the highest accuracy, all forces listed above must be included. The downside | ||
for this is that it can be computationally expensive. If we wish to predict the position | ||
of minor planets for NEOWISE frames as an example, which are captured every 10-15 | ||
seconds, it would be wildly inefficient. Over the course of a few minutes objects motion | ||
can be modeled as linear, over hours (even days) the two-body approximation is often | ||
good enough. As a result of this, NEOSpy has tools for adaptively changing the | ||
approximation used in order to get good computational performance. The typical method is | ||
to use a full N-Body simulation to get the highest precision, then use that solution for | ||
the next day or so (adjustable) with two-body mechanics to query hundreds of times. | ||
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.. figure:: images/orbit_models_short.png | ||
:width: 600 | ||
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Demonstration of how quickly linear motion, two-body motion, and N-Body deviate from | ||
the true position over the course of a few weeks. Linear motion is invalid within a | ||
few minutes, but two-body takes several days for this object to become significantly | ||
inaccurate. The dotted black line is how far an object must move tangentially to | ||
have an error of 0.1 arcseconds when it is 1 au from the observer (about 74km). |
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