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РАЗДЕЛ 2 МОДЕЛИ, СИСТЕМЫ, МЕХАНИЗМЫ
В ТЕХНИКЕ
УДК 629.786
THE FORECASTING PROJECT OF THE DEEP SPACE SENSING-POSITIONING-COMMUNICATION INFRASTRUCTURE
L. M. Samkov
ПРОГНОЗНЫЙ ПРОЕКТ ИНФРАСТРУКТУРЫ ЗОНДИРОВАНИЯ-ПОЗИЦИОНИРОВАНИЯ-СВЯЗИ ДЛЯ ДАЛЬНЕГО КОСМОСА
Л. М. Самков
Abstract. Background. We present a forecasting project of the system expanding current near-Earth satellite infrastructure of the remote sensing, positioning and global communication. Large-scale development of deep space and celestial bodies will require the creation of such infrastructure, not directed inside but outside relate Earth. The proposed project develops and supplements the forecasting project of the transport infrastructure for development of deep space, published in 2015. Materials and methods. In the formation of the forecasting project used a technique developed and used by the author of a few decades ago, updated in recent years. Results. The proposed project involves the creation of the constellations of the space beacons allocated on the equatorial and ecliptic heliocentric orbits. These beacons should perform sensing functions, positioning, telecommunications. The mentioned functions in the near-earth system is shared between the different satellite groups, but in the means of the deep space development should be combined in a unitary vehicles - beacons. The necessity of such a combination is proved. Reviewed the tasks that the system must solve: the sensing and the monitoring of celestial bodies, timely detection of threat objects, space communications, spacecraft control et al. For the proposed system we define the specific system of units (Julian System of Astronomical Constants) and the coordinate system (ICRS), as well as relevant mathematical models. Conclusions. We consider the next urgent tasks, for which it is advisable to provide for pilot devices -beacons prototypes.
Key words: forecasting project, deep space, navigation, positioning, space beacon, asteroid threat, celestial mechanics, computer network, astronomical constants, ICRS coordinates
Аннотация. Актуальность и цели. Представлен прогнозный проект системы, развивающей существующую околоземную спутниковую инфраструктуру, которая реализует функции дистанционного зондирования Земли, позиционирования и глобальной связи. Широкомасштабное освоение дальнего космоса и небесных тел потребует создания такой же инфраструктуры, но направленной не к Земле, а от Земли. Предложенный проект развивает и дополняет прогнозный проект транспортной инфраструктуры освоения дальнего космоса, опубликованный нами в 2015 г. Материалы и методы. При формировании прогнозных проектов использована методика, раз-
работанная и применявшаяся автором несколько десятилетий назад, усовершенствованная в последние годы. Результаты. Предложенный проект предусматривает создание группировок космических маяков, расположенных вдоль экваториальной и эклиптической гелиоцентрических орбит. Указанные маяки должны выполнять функции зондирования, позиционирования, телекоммуникации. Перечисленные функции в околоземных системах разделены между различными спутниковыми группировками, но в средствах освоения дальнего космоса должны быть совмещены в унитарных средствах - маяках. Обосновывается необходимость такого совмещения. Рассмотрены задачи, которые такая система должна решать: зондирование и мониторинг небесных тел, своевременное выявление опасных объектов, космическая связь, управление космическими аппаратами. Определены специальные системы единиц измерения (Юлианская система астрономических констант) и система координат (ICRS), а также необходимые математические модели. Выводы. В заключении рассмотрены ближайшие актуальные задачи, для решения которых целесообразно предусмотреть пилотные аппараты - прототипы маяков.
Ключевые слова: прогнозное проектирование, дальний космос, навигация, позиционирование, космический маяк, астероидные угрозы, небесная механика, вычислительная сеть, астрономические константы, координаты ICRS.
Introduction
Large-scale exploration of deep space and celestial bodies, the use of mineral resources for the continued existence of humanity is inevitable.
But our planet's resources are being depleted and after a few decades space expansion will be impossible because of the lack of remaining resources. As a result mankind will remain on Earth until realized one of the anticipated global threats which, even after several thousand years, destroy civilization. Launch window for the expansion of humanity into space is different from the Martian launch window so that it does not happen again: now or never.
The large-scale deep space exploration project, however, must be fundamentally different from the current draft episodic expeditions. The purpose of these expeditions is to fly to the moon or to Mars, to stroll there and fly away, producing a pile of rubbles, making a series of reports, spending several billion.
1. Problem definition
Efficient space exploration will require the creation of many automatic and manned stations. Adequate infrastructure is needed for their service.
Creating such an infrastructure - super-long-term project designed for several decades. It can be put on a par with the centenary medieval churches construction projects.
And closer to our topic, consider the space elevator project. Even if the building it with a pace of one kilometre per day (!), require a hundred years to master the altitude of 36,000 km. However, this idea has a lot of admirers. It is surprising that even the employees of respected academic institution not guessed to divide 36,000 kilometres by 365 days [1, 2].
These super-long-term projects are characterized by super long focus on future technological developments. For example, the space elevator will require construction materials, two orders of magnitude stronger than the existing ones.
This admixture fiction, however, inevitable because of the duration of the project. And it must be started immediately, precisely because of it super-long-term.
In the course of its implementation should be guided by foresight scenario architecture and the intended properties of the created system.
It should be ready to reject the already developed technology solutions because of the unexpected innovation appearance. Otherwise, failure of technical solutions can occur due to an incorrect forecast.
This method of building a forecasting project, we used half a century ago in the planning of R&D of the special technical facilities. The updated version of the methodology outlined in the [3].
It comprises a combination of three elements - the traditional prediction (forecast), the construction of scenarios for the future state of the Universe and the road map traffic to it (foresight [4]), and the construction of the problem tree and inverting roadmap to address these problems (forethought).
The forecasting project of the deep space transportation infrastructure has been proposed in our recent publication [5].
It was designed to use only the modern technological means, but possible future achievements are not taken into account. We now offer an important forecasting subproject to complement the said project.
A nuclear electric rockets rockets [6] allow the use of not only the passive motion of the spacecraft in orbit, but also an active flight on the route with the ability to maneuver. The possibility of implementing this innovation will take into account in our project.
2. Infrastructure functions
Henceforth, in addition to the routine overflights between celestial bodies and/or space stations it will be the pursuit of artificial or natural objects ending with the docking or the landing.
When the spacecraft crosses the border between planetocentric and heliocentric areas should be carried out continuous control of its propulsion device for high efficiency.
Such a navigation task is the development of terrestrial navigation tasks, supported by the GPS/GLONASS infrastructure. However, it focuses on the Earth and will need to create a similar infrastructure, which would be aimed at deep space.
Consequently, the deep-space navigation tasks have a high computational complexity and require high accuracy and immediacy of spacecraft positioning.
This requires deep-space positioning infrastructure objects, the prototype of which is the GPS-guided ballistic missile system [7].
The fundamental difference between terrestrial and deep-space infrastructures lies in the fact that the pseudorange will not milliseconds, like on Earth, but minutes.
Also it would require a more precise measurement of the speed at each point of the spacecraft trajectory using the Doppler effect.
Near-Earth satellite infrastructure in addition to the global positioning system also includes satellite constellations, performing remote sensing of the earth and global telecommunications. In deep space, these three tasks must be carried out not independently, but together.
Orbital calculations in real time would require creating a peer computer network, wherein the exchange of the positioning signals, the control and data exchange are combined.
Unlike systems for remote sensing, space objects are mobile and therefore their sensing closely related to positioning.
The same can be said with regard to the monitoring function of coordinates and velocities of asteroids and meteoroids, calculating their orbits to detect dangerous for vehicles and the Earth itself.
Positioning of the celestial bodies is combined with the sensing of the surface to search for mineral resources.
The problem of early detection of dangerous bodies combine:
- the positioning functions,
- the calculation of the orbit,
- the operational warnings about the dangers
- the complement dangerous objects database.
In addition to the exchange of technical signals, the system must support the reception of data from automated stations and traffic communication with the crews of manned spacecrafts.
Thus, deep-space infrastructure should integrate sensing functions, positioning and communication, using a combined devices - beacons.
To ensure the navigation spacecraft need to solve a number of variational problems, for example:
- the minimization of fuel consumption,
- the minimizing of flight time,
- the maximization of the difference of the spatial coordinates of two bodies, to prevent the collision,
- the minimization of the relative velocity of the two bodies, for their docking or landing on a celestial body.
- the minimizing the distance between the devices and the relative speed at the joint flight.
Consider the process of crossing the border between planetocentric and heliocentric areas. In such cases it is necessary to solve the gravitational three-body problem. In general, it is analytically unsolvable.
Consider the methods of its numerical solution under the conditions of the proposed infrastructure.
3. Mathematical model
Model dynamics of the i-th Solar System body having ecliptic coordinates (Ri, Pi, X) is as follows:
0(R1:R2, ...,RNt) ^ minimum, or ■■■,-^N,0 < A>
(1)
^(0) = Vi0, Rt(0) = Ri0,
where O - functional on the set of orbits R(t), W - non-gravitational acceleration of the i-th body. For jet propulsion it is determined by the law of momentum conservation in the rest frame of the i-th body
dvu> = u^dm ^ w ^y^dMrnj ' dt dt ' dt
where U - the specific impulse of the jet engine. For light sail [8, 9]:
Wi = Wi0- f^cos2e,
where W0 - acceleration of the spacecraft at a distance Ri0 from the radiator (Sun or laser source), if the sail is perpendicular to the direction of the light source; 9 -the angle between the normal vector to the sail and the direction of the light source.
Consider the problem of approaching of the two devices for subsequent docking or joint flight.
Assuming that the devices do not interact gravitationally with each other, and not taking into account the gravity of the planets, we obtain the following vari-ational problem
t
- I WRv-RA2 • dt<A
t-t0J 2 111
to
dVj = v dln(mj) mQ • Rj dt ~ ' dt |ffj|3
^(0)=^, *i(0)=*io, ¿ = 1,2
for small values of ||R2 - Ri|| squaring the expression for the Radius differential in Spherical coordinates we can put
||tf2 - «J2 •* (R2 - R1)2 + R2 • (fi2 - ft)2 + R2 • sin2p • (A2 - A,)2
, n R1+R2 n P1+P2
where R = ——B = .
2 K 2
The variation is carried out on the set of osculating Keplerian orbits of spacecraft since the last control action at time t0
4. Units of measurement and positioning accuracy
In these equations, we use a system of units, which do not need the gravitational constant.
It should be noted that Newton himself did not define the gravitational constant, and only used the ratio of the masses of the celestial bodies. Masses of celestial bodies had actually been their gravitational parameters [10, 11].
Following this approach, we previously offered Julian System of Astronomical Constants (JSAC) [5], which is a modification of the standard System of Astronomical Constants (SAC) [12, 13].
The units of measurement JSAC is second instead of day and grav of 1 au3/a2 instead of kilogram.
Then the Solar mass is exactly equal to 4n2 grav, and the Earth mass is equal to 118.57 micrograv with a relative error of 4-10-9 due to the accuracy of astronomical observations,
This choice of measurement units is useful for modeling long-distance space
travel.
Earth day (SAC), important for ground-based astronomical observations in deep space useless. At the same time, the Julian year is a natural scale of the orbital periods of the celestial bodies and spacecrafts.
SI system, as well as the SAC, focused on terrestrial realities. For example, a unit rate of 1 m/s is a walking pace. JSAC similar manner designed for the realities of deep space. For example, a velocity unit 1 av = 1 au/a ~ 4740 m/s, is equal to the specific impulse of the oxygen-hydrogen rocket engine. The specific impulse of the engine RD-180 is equal to 0,7 av. The orbital velocities of the planets vary in the range from 1 av (Neptune) to 10 av (Mercury). The average speed of the Earth's orbital motion is exactly equal to 2n av.
The specific energy unit is defined as the magnitude of gravity potential of one grav to a distance of one astronomical unit. It is equal to 1 se = 1 grav/au = = 1 au Va2, and corresponds to a value 22.47 MJ/kg.
A body moving on the Earth's orbit, has a total specific energy of -2n2 se, potential specific energy of -4n2 se and kinetic potential specific energy of +2n2 se.
The escape velocity from Earth corresponds to the specific energy equal to 2.77 se ~ 62.24 MJ/kg. The specific heat of kerosene combustion equal to 2 se, hydrogen of 5.4 se.
According to the SAC astronomical unit accurately expressed in metres (1 au = 149 597 870 700 m), and the Julian year - in seconds (1 a = 31,557,600 s).
In turn, under the International System of Units the second has been defined as the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
The metre is defined as the distance travelled by light in vacuum in 1/299792458 second. It equal to 30.6633189884984 periods of cesium radiation.
Thus, the grav is not dependent on the value of a kilogram and exactly expressed through the metre, second, and ultimately through the number of cesium radiation periods:
1 grav = 1 au3/a2 = 3361772358500740000 m3/s2 = 1146.9541498532 Tcs.
This pursuit of precision is necessary because the mass in kilograms of the celestial bodies and the gravitational constant can be known only to a relative error of 10-4. At the same time gravitational parameter of the celestial body, equal to the product of its mass in kilograms by the gravitational constant, obtained from astronomical observations with a relative error of 10-10. This is the accuracy of the mass of celestial bodies in terms of grav. It corresponds to the accuracy of the board device used in determining the pseudorange.
The prototype of this device was a marine chronometer retain exact time of the prime meridian, which made it possible to determine longitude. Accordingly, in
those days, it was presented extremely high demands on accuracy of a chronometer. Requirements for exactness in deep space navigation will be most stringent, as the numerical solution of the spacecraft flight control tasks in real time would require the use of iterative algorithms with possible roundoff accumulation.
5. Coordinate system
Terrestrial prototypes of the considered infrastructure (GPS and GLONASS) use the geocentric coordinate system, respectively WGS84 and PZ-90.
To determine the coordinates of celestial bodies in outer space problems should be based on the International System of ICRS astronomical coordinates [14], approved by the International Astronomical Union as a reference for all astronomical measurements.
Its origin is at the barycenter of the Solar System, with axes that are intended to be fixed with respect to space. ICRS axes tied to several hundred quasars from the catalog FK5.
To calculate the ephemeris of the celestial bodies is carried out in the mobile GCRS geocentric coordinate system, which is adequate to the terrestrial astronomical observations. For the purposes of the spacecraft navigation system it is preferable to use a fixed ICRS system in all calculations.
Spherical coordinates ICRS of the celestial body include the following
items:
- the radius vector R, which connects the barycenter of the solar system with the body,
- its declination (latitude) /, measured from the plane of the equator ICRS,
- its right ascension (longitude) X, measured from the plane perpendicular to the equator and a line passing through the Earth's orbital nodes.
With high accuracy ICRS equatorial plane coincides with the plane of Earth's equator and the pole ICRS with the pole of the world.
Coordinates of the object in deep space, as well as a global positioning calculated by measuring its pseudoranges relatively few beacons.
The velocity vector is determined from the Doppler frequency shift of the signal with respect to a few beacons.
In addition, it can be used telescopic observations in the optical and radio wavelengths, active sensing radar and laser means.
6. Architecture
The deep-space beacons it is advisable to arrange a circular heliocentric orbit of radius 1 au in the ICRS equatorial plane.
In this case, the motion of the beacon only changes its longitude X on a simple sawtooth law, and the velocity vector rotates uniformly in the equatorial plane of the ICRS. This simplifies the calculations of the coordinates and velocities of the celestial bodies and spacecrafts.
It should also be noted, more efficient triangulation of spacecrafts and celestial bodies that move near the ecliptic plane.
The plane in which beacons are moving, inclined at 23° to the ecliptic plane and coplanar with the plane in which geostationary satellites move.
It should be placed on the equatorial heliocentric orbit six beacons forming a regular hexagon. Then the distance between adjacent beacons is exactly equal to 1 au.
To eliminate the gravitational perturbations of the Earth at the time of the vernal equinox longitude beacons must be equal to n/6-(2k + 1), k = 0.. .5.
Then the nearest beacons is at a distance of 0.26 au from Earth, it is equal to the distance from Earth to Venus at its inferior conjunction.
Since the orbital velocity of the Earth and the beacon are equal, it will be for the terrestrial observer moving along the celestial equator at the same angular distance from the Sun.
To improve the accuracy of triangulation should be added the ecliptic beacons, located in the vicinity of the Earth's orbit at points with longitudes kn/3, k = 0.5.
Four of them (k = 0, 1, 3, 5) are respectively Lagrange point L2 (L1), L4, L3, L5 of the Earth-Sun system.
The proposed architecture of the beacon system allows to transmit data at a fixed direction that simplifies the design of radiators.
In the asteroid belt should also be provided regularly spaced beacons.
Unlike the Global Positioning System navigation calculations, due to their complexity, must be carried out as beacons, not consumers navigators. Therefore, the primary signal should come not from the beacon to the consumer, but from the consumer to the beacon.
The signal contains users ID and the time of sending by the onboard clock signal. After processing the signals received by several beacons, the control signal is generated to adjust the spacecraft trajectory.
Natural celestial bodies can be equipped with transmitters and retroreflectors to facilitate their sensing. In this case, only the processed data stored in the dangerous objects base but a control signal is not generated.
Calculations of trajectories of objects are carried out in real-time mode, so their results can be continuously corrected observation data and recalculated the beam paths in the solution of the variational problems.
To do this for each item should be kept in a database of its computational beam paths from the last implemented correct its trajectory.
The set of beacons and ground stations formed a peer-to-peer computer network, which implements the consolidation of the results of calculations and the databases content.
Conclusion
The described infrastructure, as well as any large system can be established only if there is actual relevant tasks.
Currently, these are the only problem is the identification of dangerous space debris and meteoroids, their sensing for exploration of resources, and their cataloging.
Near-Earth means can not quickly find the body moving on the sunny side (Chelyabinsk meteorite as example). Need a remote observation point, preferably outside the Ecliptic plane.
There is also a fundamental problem that must be solved in advance, before the creation of the beacons system.
They are
- improving the methods of celestial mechanics and computational mathematics,
- development of software,
- improvement and miniaturization of computing devices.
Список литературы
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Самков Леонид Михайлович
кандидат технических наук, доцент, лаборатория сетевых информационных технологий,
Югорский научно-исследовательский институт информационных технологий E-mail: parzefal@gmail.com
Samkov Leonid Michaylovich
candidate of technical sciences,
associate professor,
laboratory of network information
technologies,
Ugra research institute
of information technologies
УДК 629.786 Samkov, L. M.
The forecasting project of the deep space sensing-positioning-communication infrastructure / L. M. Samkov // Модели, системы, сети в экономике, технике, природе и обществе. - 2016. - № 2 (18). - C. 97-105.
