


Projects: Apophis Mission Design CompetitionThe following project presents four separate scenarios for tracking trajectories of asteroids and comets whose course of movement threatens collision with Earth. We can take the asteroid Apophis as an example of such a smallsized celestial body. When developing the project special attention was paid to the issues of sensitivity and reliability of the tracking systems. Only extremely high sensitivity of the markers and sensors will lead to the highest possible accuracy of trajectory calculations, which will enable us to eliminate the threat to the people of Earth. During the process of development of the tracking systems those items of equipment and machinery were selected that could operate using energy sources which have been applied before to provide energy for spacecrafts. When elaborating the project the decision was made to present the image of an asteroid as a pile of detritus, grit, and dust infirmly bound together by slack gravitation. This notion of an asteroid emphasized potential difficulties connected with landing on the asteroid, fastening the equipment, selecting the site for mounting the equipment, and high risk of machinery failure. The highest possible reliability is a vital requirement to the tracking systems; as a consequence of this, several scenarios make use of excess numbers of markers or sensors. When developing the scenarios I came to the conclusion that every extra sensor can save millions of lives. The demands of high dependability paved the way for using the most primitive sensors or markers designed to pick up and transmit simple primary information. According to the project the data is supposed to be processed on Earth afterwards. Since simplicity is an essential element of reliability the sensors and markers will be placed on the asteroid surface in random order. Out of deference to the undoubted professionalism of the committee members I tried not to make unnecessary demands on their time and avoid cliches and idle speculations. In the following scenarios the text elements which in my opinion are innovative will be highlighted red. The scenario without energy consumption.
In this scenario the movement of the asteroid can be observed from Earth using methods of radiolocation and optical astronomy. The markers, acting as passive transponders, are placed on the surface of the asteroid. Up to ten markers are delivered to the asteroid and scattered on its surface in random order. There are range finders and video cameras on board of the spacecraft, which facilitate measuring of distances and angles between the markers. Direct measurements and calculations attribute the markers to a uniform coordinate system. Unique coordinates are then specified for every marker (a point on the surface of the asteroid). In further calculations the asteroid can be presented as a figure rotating around several axes of an irregular polyhedron. The apices of this polyhedron will be the points of markers placement. The data received in the course of astronomic observations determine the rotation axes of the asteroid, and calculations define the pole coordinates in the uniform coordinate system. The data received in the course of astronomic observations are used to calculate the expected trajectory of the asteroid's movement which is then constantly adjusted as new information is collected. Any extraneous force influencing the trajectory of the asteroid's movement generally affects angular velocities of the markers relative to the rotation axes of the asteroid; the force can be thus calculated taking into account altered parameters of the markers' movement. Observing the markers' movement will enable us to note changes in their angular velocities in relation to certain rotation axes of the asteroid and come to the conclusion about presence, magnitude, and direction of a force influencing the trajectory of the asteroid's movement. The markers themselves are film constructions (possibly inflatable) made of polymeric materials metallized with aluminum or special powder compositions. The marker's minimum dimensions are 10 * 10 meters, which corresponds to the attained surface resolution (as shown by the experience of asteroid radiolocation 1999 JG from Earth). These constructions are capable of dispersing or directional reflecting of the radio wave energy. The technology of using inflatable constructions made of metallized synthetic film as passive transponders was perfected during the field application of American satellites of "Echo" series. The fact that there is no necessity of an energy source is one of the advantages of this scenario. One of the disadvantages though is the longterm observation necessary for determining minor forces influencing the asteroid's trajectory such as solar radiation, gravitational effect of passing asteroids, nonuniform cooling of the asteroid's surface, and others. The high reliability scenario.
This scenario presupposes placement of gyroscopic sensors directly on the asteroid's surface; these sensors measure angular velocities of certain surface points relative to all rotation axes of the asteroid. With the help of a spacecraft from ten to twenty gyroscopic sensors are delivered to the asteroid and scattered on its surface in random order. The range finders and video cameras on board of the spacecraft measure distances and angles between the gyroscopic sensors. Unique coordinates are specified for each gyroscopic sensor (and the corresponding point on the asteroid's surface). It is not essential to use range finders to affix the gyroscopic sensors to the uniform coordinate system (and to specify unique coordinates). The following conditions must be met:
Making use of the fact that the axes of all gyroscopes are unidirectional and parallel to each other and the data transfer begins for all sensors at one reference point in time we can reproduce movement trajectories of all sensors in the uniform coordinate system from the certain reference point in time using threedimensional modeling space. The threedimensional modeling space will show that all sensors move in spiral paths in relation to the origin of coordinates. These spiral paths of all sensors will outline a multitude of points in our threedimensional modeling space which can belong to only one rotating polyhedron. The specific program will provide solution for the resulting polyhedron (determine distances and angles between its vertices) and consequently enable us to specify unique coordinates in the uniform coordinate system for each sensor (and the corresponding point on the asteroid's surface). The range finding equipment on board of the spacecraft is not absolutely necessary. However, to increase accuracy when determining the coordinates it is advisable to use combined data received by calculations and range finders' measurements. Information from the gyroscopic sensors accumulated during a specific time interval will enable us to determine the quantity of the asteroid's rotation axes and pole coordinates of these axes in the uniform coordinate system. Later we will be able to trace the parameters of each sensor's rotational motion in the uniform coordinate system and alteration of each sensor's angular velocities in relation to any of the asteroid's rotation axes. The data received in this way will serve as the basis for outlining expected trajectory of the asteroid's movement in the threedimensional modeling space; this trajectory will be constantly adjusted as the new data are collected. Any forces influencing the trajectory of the asteroid's movement will be immediately detected when changes occur in the angular velocities of the sensors in relation to certain rotation axe of the asteroid. Currently ring laser gyroscopes and fiberoptic gyroscopes can offer the sensitivity of 108 rad/sec (0,001°/h) for gyroscopic sensors noting angular velocities. The system making use of a great number of gyroscopic sensors will offer much higher sensitivity. When working on calculations we can use the data received from different quantity and placement combinations of sensors. This will enable us to reduce the number of errors, detect forces of minor influence and screen faulty sensors. Each sensor for picking up, processing and transferring information needs an electrical energy source of 1015 watt. Electrochemical sources, solar batteries, radioisotope energy sources or hybrid systems can be used as these energy sources. The choice of the electrical energy source depends on the term of the sensors' operation. For instance, if the mission lasts 6 months we can use electrical storage cells designed to be recharged from solar batteries. If the mission is projected to take years we will have to use radioisotope sources. High reliability of the system's performance, high sensitivity and rapid force detection are the advantages of this scenario. The proposed system can easily detect slight and minor forces affecting the asteroid's trajectory, such as solar radiation, gravitational effect of passing asteroids, nonuniform cooling of the asteroid's surface, and others. The requirement of a significant quantity of energy sources is the disadvantage of this scenario. The scenario with one energy source.
This scenario presupposes monitoring trajectory of two points on the asteroid's surface in the uniform coordinate system specified by a precision gyroscope. One of these points is the spacecraft's attachment point to the surface of the asteroid; the other point is the asteroid's center of gravity. The precision gyroscope and the data pickup system are based on the spacecraft. The data pickup system traces the trajectories of the two points in the basic coordinate system of the precision gyroscope in relation to the origin of coordinates. After landing and attaching the spacecraft to the surface of the asteroid the system begins recording data about the spacecraft's movement relative to the origin of coordinates of the basic coordinate system. In the basic coordinate system the spacecraft will rotate around the gyroscope rotor. The spacecraft's rotational motion will have a complicated though repetitive pattern. The trajectory of this motion may be reproduced in the threedimensional modeling space and described by mathematic equations. Changing parameters of this trajectory in time will allow us to detect appearance of forces affecting the asteroid in the spacecraft's attachment point. To determine the magnitude and direction of these forces we will have to solve a standard task of evaluating parameters realizing maximum or minimum of a certain related quantity. The next stage will demand defining the coordinates of the asteroid's center of gravity in the basic coordinate system. To do this it will be necessary to determine the direction from the origin of coordinates to the asteroid's center of gravity and the distance to the asteroid's center of gravity. To define the direction to the center of gravity we can use gravitation sensors or the already available precision gyroscope. Using the Newtonian law of universal gravitation we can calculate the distance to the asteroid's center of gravity. It is sufficient to measure the weight twice (spring compression under weight) at different distances from the asteroid's surface. It is also possible to use gravity meters of different model. After we have defined the distance to the asteroid's center of gravity, we can describe the trajectory of its movement by mathematic equations and outline it in the threedimensional modeling space. In time coordinates we will receive a complex helical path in which instantaneous axes of the spacecraft's rotation intersect and produce a great number of cross points. These many points belong to a curve with a big radius of curvature. Adjusting the curve in accordance with valid data available from other sources we will be able to draw the expected trajectory for movement of the asteroid's center of gravity. To facilitate calculations we can transfer the origin of coordinates to the asteroid's center of gravity. In this case the trajectory of movement will approximate a straight line (allowing for the orbit's curvature). Any deviations from the expected trajectory will result from certain forces affecting the asteroid. We will be able to use mathematical methods for defining the magnitude and direction of these forces. Thus, we can use two variants of parameters calculation for forces affecting the asteroid. The results of the calculations will slightly differ because of varying distances between the point of force application and the spacecraft's attachment point and correspondingly the asteroid's center of gravity. Eventually the accuracy of the calculations will be increased. The sensitivity of precision gyroscopes when determining angular velocity can reach 109 rad/sec. Research and investigation of NASA satellite Gravity ProbeB (GPB) perfected usage of precision gyroscopes in space conditions and increased the speed and quality of information processing. Among the advantages of the proposed scenario one might note simplified requirements to the spacecraft  which now has to be able only to land on the asteroid, demand of only one source of energy, and use of approved equipment units. The disadvantage of this scenario is low reliability of precision gyroscopic sensors with electrostatic suspension of rotors; these mechanisms are complicated and rather capricious. The innovative scenario.
This scenario suggests Earthbased observation of the markers placed on the asteroid using radiolocation methods. Simultaneously the parameters of movement of a certain section in relation to the inertial coordinate system are to be measured directly on the asteroid's surface. This double system of monitoring changes in the asteroid's trajectory simultaneously from inside and outside has huge information capacity. I can go as far as to say that it has maximum information capacity. With the help of this combined system we can receive information immediately after an extraneous force starts acting and adjust our data as we monitor the markers' rotation parameters from Earth. The spacecraft goes around the asteroid at the minimum permissible level and wraps the asteroid with the measuring tape (the marker) in random direction. After landing the spacecraft serves on the following stages as an energy source and a transmitter. We can also use the available radioisotope energy plants as an energy source. Alternatively we can use radioisotope energy plants which are under development now, for example the MMRTG project (MultiMission Radioisotope Thermoelectric Generator). The RSG project (Radioisotope Stirling Generator) currently being developed by the company Lockheed Martin Astronautics is also suitable for our purposes. The measuring tape is metallized polymeric film with maximum width of 10 meters interlaced with radio wave reflecting sections. This kind of measuring tape will always remain visible from Earth. Together with the measuring tape the asteroid is wrapped with one loop of the optic gyroscope whose functions are determined by the Sagnac effect. To prevent mechanical damage to the loop it is advisable to wrap the asteroid with several optical fibers protected with a membrane. Here we can encounter a technical problem the solution of which has not yet been practiced in space conditions. The problem concerns attachment of the second end of the optical fiber to the light source. The problem of fiber fusion is currently solved on Earth with the help of many different methods. Some of these methods can be used in space. The ray of light is cast in two opposite directions in the circular optical path. While the optical system is idle in relation to the inertial coordinate system both light rays propagate along optical paths of identical length and there is no phase shift in ray composition. We can take an arbitrary instant of time as our reference point; for our further calculations this will denote the instant of time in which the optical system is idle. Phase difference ΔΨ between the optical waves occurs when the optical system rotates in relation to the inertial coordinate system with a certain angular velocity. The formula for calculating the phase difference ΔΨ introduces the S variable  which stands for the area framed by the optical path. ΔΨ=kS/c*Ω In our situation with the diameter of the asteroid exceeding 300 meters, the area framed by the optical path approximates 100.000 square meters, which will mean high sensitivity when determining the phase difference of the optical rays. During the asteroid's orbital motion the section of the asteroid framed by the optical path will perform a complicated rotational motion. Consequently the phase difference ΔΨ will change in accordance with a complex periodic law. Linking the change patterns of the phase difference with the movement patterns of the measuring tape (the marker)  which is the perimeter of the allocated section  we will receive a sensitive system for tracking the asteroid's deviations from the calculated expected trajectory. Any extraneous force affecting the trajectory of the asteroid's movement will change angular velocities in certain points of the loop of the optical gyroscope. This, in turn, will alter the regular change pattern of phase difference ΔΨ in time and prompt us to use radio astronomy methods of observation. As the data of measurements and observations are adjusted, we can update our model of the asteroid's trajectory. The advantages of this scenario are high sensitivity, ability to detect minor extraneous forces affecting the asteroid's trajectory, requirement of one energy source, and the simplicity of the gyroscope in use. The disadvantages of this scenario are complicated technology of unwrapping the measuring tape and the minimum permissible orbit from which the tape should be wrapped around the asteroid.  
