Using Mars to inspect the asteroid belt

The main asteroid belt encircles the inner solar system. Roughly 3.2 AU from the sun, it is thought that the asteroid belt was not formed from by a planetary collision because the total combined mass of all asteroids is far too small (not even as much as Earth’s moon).

At Redmoon Systems, our intent is to detect, track and characterize the objects in the belt using infrared sensing technologies. One of these technologies is known as Firecat Observatory, Mars Mission.

Firecat is a passive sensor system located on the surface of Mars. Miniaturized and remotely deployed, the sensor consists of a single aperture through which an infrared multi-spectral detector array can detect light reflected from the asteroids nearest to Mars.

Inspired by a NASA review panel led by Jessy Cowan Sharp of NASA Ames, our team is running simulations to determine the best configuration for Firecat Observatory Mars Mission. Factors to be considered are the number of pixels, the pointing system, the power source, and transmitter configuration.

 

According to our initial design study, we have determined that the signal levels from three different rings or locations with the asteroid belt will be approximately:

The low signal levels require a more sensitive detector than expected, as compared to our moon-based debris observation mission.

 

The following figure shows the location and field depth of the main asteroid belt.

Manned Missions such as the Mars One mission plan to place humans on Mars by 2033. The presence of humans will only further the prospects of the Firecat Mars Observatory.

How to use both mars and the moon for space debris operations

A new technology currently named Firecat is being developed at Redmoon. We are exploring the use of natural resources in space to further our own exploration (of space). One example coming to us by NASA during a conference at NASA Ames a few years ago was the use of asteroids orbiting the sun, just beyond the reach of Mars as a naturally occurring resource. We don’t currently know what exists in the asteroid belt, but we know that it would be helpful to learn more about the belt itself. The combination of solar and interplanetary gravitational forces (i.e. gravitational tides) generate resonances and other beautiful dynamics.

A Cosmic Fireball, for which Firecat is named

One approach to learning more about these resonances would be to observe the motions of the asteroids. Currently we have several missions undertaking this scientific objective. However NASA and the other spacefaring countries could potentially be open to new opportunities for studying the asteroids.

Two relatively new ideas are the placement of a robotic lander with infrared observing capabilities on the far side of the moon, and the same undertaking but located on the martian surface.

Our goal at Redmoon Systems is to study both of these missions and to better understand the science that could be possible.

NASA (origin)

How spectrometry can help space debris operations

For the Firecat proposal/mission, we have shifted our focus from LIDAR to passive infrared sensing. An active sensor generates its own light, and a passive sensor just receives light. A quick calculation indicates that there is a large amount of light due to solar glinting available to the lunar sensor and module. Here is some background info on infrared light 

Infrared light is radiated by a candle which we can “feel” with our hands as heat. Here is an image of a candle flame in the infrared:


Candles, Infrared and Heat

Space debris around the Earth is exposed to direct sunlight, which contains infrared radiation. Some of this radiation is absorbed by dust and debris, and some of it is reflected. Our team has experience in design and implementation of infrared telescopes and sensors from our work in the aerospace industry.

 

From the infrared standpoint, it is very helpful to characterize the parts of the fire which are radiating differently. This way we know how to interpret the image generated by our detector. The picture above shows that the outer flame is much hotter than the inner flame, and the melted wax also generates a heat signature. Likewise, we would like to understand and model how different parts of space debris radiate in the infrared part of the spectrum. This is called “phenomenology”, and involves physics and electromagnetic.

How to apply quantum principles to infrared tech

[latexpage]

When we learn physics in school, it is difficult to understand how to represent a falling ball as a math problem whose solution describes the real world. The first method we learned was Newtonian mechanics which is where everyone draws a force diagram, little arrows representing how a flower wants to evolve.

In college, we may learn something called Lagrangian mechanics which is a little different. For instance, instead of modeling forces, we talk about energy. Energy is often easier to find because it is always mass times velocity squared.

Lagrangian mechanics allows you to solve complex problems easily because you never need to know the forces at work.

But there is a trick to it. It requires identifying something called generalized coordinates, which can sometimes be challenging.

Actually, the invisible science behind Lagrangian mechanics revolves around a method or process known as the Calculus of Variations.

 

This involves two ideas: 1: that the differential equations of motion governing the dynamics of a classical or mechanical system can be deduced from a cost function and the fact that nature seeks to minimize the integral of this cost function. 2: that the way to identify the equations of motion require that we make small, even infinitesimal, changes in our path through the solution space.

In classical mechanics, the cost function has to do with energy minimization along a solution curve. Specifically, the cost function (Lagrangian) is defined on the tangent bundle (i.e. set of all tangent spaces to the solution curve, which contains velocity vectors). In Euclidean geometry, the “cost” function is actually the Euclidean distance, and is a metric defined on the solution curve or manifold itself (not the tangent bundle). The solution to problem in classical mechanics is a geodesic curve, i.e. one which minimizes the Lagrangian cost function.

In other domains, such as the infrared, it may be possible to construct a cost function based on the least action principle. However we must expand our notion of cost function.

 

       Greybody Curves

In the example below, the epsilon parameter is a constant between 0 and 1 for each colored curve. Epsilon determines the scale of the effective blackbody curve, which is represented by the value epsilon = 1.

In the absence of any experimental data on the thermal radiator, all values of epsilon are equally likely. One may think of the radiator in as existing (from our perspective) in an undetermined state. By analogy to the Everett interpretation of coherent quantum states, unique versions of the radiator can be said to exist in separated realities. When an experimental observation of the radiator is made, a specific radiation curve is identified. The precise nature of the radiator is then known in “our” reality. In quantum mechanics, this process is called decoherence. A macroscopic object is unlikely to be in a true quantum state as such states require very low temperatures, however the uncertainty in radiant flux can be interpreted using the Everett representation.

The modeling task therefore is to perform a controlled decoherence of a large number of possible co-existant states into a single macroscopic state.

This can be performed using linear algebra, and the idea of a quadratic form as the cost function defined on a solution manifold. The matrix representing the form controls the mixing of individual time streams (realities). [per the Everett interpretation]

Note that the gray body curve is smooth, in contrast to the curve of the selective radiator. An example of a selective radiator would be a metal such as copper which when reduced to powder and burned in an open flame produces a specific set of peaks corresponding to its valence energy levels.

 

The following Juypiter Notebooks file and latex writeup show a graphical implementation of these ideas in python 🙂

And the possible conclusions are startling!

 

How to optimize in image exploitation

The following image shows a frequency fingerprint of a radiating object, as seen by an infrared camera or sensor.

The dashed red line is the theoretical fingerprint based on a smooth blackbody radiation curve or model. This assumes that the object has certain properties which may or may not be actually present. These assumptions are the main reason why the actual observed fingerprint (the sold red line) does not match the theoretical model.

When data is taken of an object in space for example, all that we know is the frequency spectrum or fingerprint of the object. We usually do not know what the object is actually made of, it’s shape, etc. We have to make predictions or really educated guesses for that based on the observations.

Our goal at Pinkmoon is to develop a computer algorithm or model which can rapidly identify possible sources of discrepancies between the theory and observations, such as noise in the detector or camera, dynamics such as rotation, or background illumination.

 

One way to approach this problem is to do a kind of decomposition of the original curve into a set of known components (i.e. transformations or convolutions of the theoretical model). This is similar to a Fourier transform. Because multiple solutions might be possible, a cost function is desired which identifies which level sets or solutions might be more likely than others.

We are using open source tools such as Anaconda, Pyradi, and other technologies including AI to arrive at an algorithm for this problem set.

Using Modeling and Simulation to solve Lambert’s problem to enable space travel

Spaceflight involves finding a path between an origin and a destination. In spaceflight mechanics, position and velocity are important because mathematically they determine the coordinates for both the origin and destination. The path between is called the orbit.

The determination of an orbit given two position vectors and the time of flight is known in celestial mechanics as Lambert’s problem, also known as two point boundary value problem. This contrasts with Kepler’s problem or propagation, which is rather an initial value problem.

The package poliastro.iod allows as to solve Lambert’s problem, provided the main attractor’s gravitational constant, the two position vectors and the time of flight. As you can imagine, being able to compute the positions of the planets as we saw in the previous section is the perfect complement to this feature!

For instance, this is a simplified version of the example Going to Mars with Python using poliastro, where the orbit of the Mars Science Laboratory mission (rover Curiosity) is determined:

ate_launch = time.Time(‘2011-11-26 15:02′, scale=’utc’)
date_arrival = time.Time(‘2012-08-06 05:17′, scale=’utc’)
tof = date_arrival – date_launch

ss0 = Orbit.from_body_ephem(Earth, date_launch)
ssf = Orbit.from_body_ephem(Mars, date_arrival)

from poliastro import iod
(v0, v), = iod.lambert(Sun.k, ss0.r, ssf.r, tof)

And these are the results:

>> v0
<Quantity [-29.29150998, 14.53326521, 5.41691336] km / s>
>>> v
<Quantity [ 17.6154992 ,-10.99830723, -4.20796062] km / s>

A Sensitivity Analysis Using Pyradi, for Ophelia and Skyla

This article is devoted to PyRadi, which is an infrared modeling toolkit written for Python. Python is a computer language similar to MATLAB which runs on most computer systems and is completely free.

PyRadi is useful because it simplifies the process of designing and evaulating infrared vision systems. Infrared vision systems are able to detect heat signatures of life on Earth, and in other places. Additionally they can also detect many naturally occuring phenomena such as bacteria in the ocean which help our planet support life.

In my experience, infrared systems can be used for remote sensing, which means that they are deployed in space and used to observe the Earth. NASA has a mission similar to this called VIIRS which monitors ocean algae populations and tracks the rate at which they bloom.

PyRadi is completely open ended and can be played with and modified by anyone with internet access. I have been doing this for years.

Here is a summary some of the things you can do with Pyradi.

WHen you want to design a system for seeing infrared radiation, whether on the Earth or moon or both, you need to determine the performance as you generate your design. This is because the performance helps you understand how well your design will work, efficiently.

PyRadi helps with this. If you give it some information about the source of infrared light (just a rough light curve, not too hard to find for most objects), and some other basic information about your system (i.e. telescope, etc) then PyRadi will show you its guess at the performance. This is measured by the amount of signal that your system will be able to receive from it’s target or source.

Here is some output from PyRadi.

Two graphs showing output from PyRadi!

The first graph shows several curves which can be thought of as components of a transfer function, as commonly used in control theory. For anyone who doesn’t know this already, a transfer function is represented as a product of several smaller functions. It is part of the solution to a differential equation, which is the basic mathematical model of a system that evolves with respect to time (i.e. dynamical system).

Here is an example:

In this figure, the box labeled Plant is the portion of the system which we are interested in studying or modeling. The “transfer function” is basically all of the interesting aspects of the physical system which we care about. In the case of Pyradi, it includes the following:

  • Source basic radiant properties
  • Source emisivity or tendancy to illuminate debris
  • Intervening atmosphere
  • Optics passivity
  • Camera sensitivity
  • etc.

In summary, the PyRadi enables you to do what is called a Sensitivity Analysis of your experiment.

A Test of Einstein’s Theory

A recent study explored the understanding of relativity at an extra-galactic scale, which basically determines how gravity will behave over very large distances. To date, relativity remains the best description of gravitational attraction over long distances. To some, it was hoped that one day perhaps a shortcoming in the theory of relativity might point the way to a better understanding of the nature of the universe. As of yet, relativity has proved to be highly accurate. Now, a new study has opened up a new area of research.

The Hertsprung-Russel diagram showing