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22
УДК 521.352
ТОЧНОСТЬ СОУДАРЕНИЙ ДЛЯ КОРРЕКТИРОВКИ ВРАЩЕНИЯ ПЛАНЕТ
Е. А. Морозов Научный руководитель - Л. В. Границкий Руководитель по иностранному языку - М. В. Савельева
Сибирский государственный аэрокосмический университет имени академика М. Ф. Решетнева
Российская Федерация, 660037, г. Красноярск, просп. им. газ. «Красноярский рабочий», 31
Е-mail: transserfer89@gmail.com
Погрешность траектории перемещения планетезималий для конфигураций планетарный систем, в частности корректировки вращения планет, с целью последующего полномасштабного тер-раформирования и заселения, была оценена в первом приближении. Для передвижения планетезима-лей рассматривалось только использование уже существующих технологий. Рассматривалось пять источников погрешности: время, определение координаты, скорость истечения газов, масса использованного рабочего тела, и угла поворота погрешность. Были сделаны вывод, что погрешность траектории может быть приемлема для столкновения объектов, но слишком велика для корректировки вращения планет. Таким образом, потребуется обратная связь и несколько корректировок траектории, что вероятно требует людей для управления процессом, как минимум на завершающих стадиях.
Ключевые слова: терраформирование, удары комет и астероидов, перемещение планетезима-лий, погрешность траектории, оценка точности.
ACCURACY OF COLLISIONS FOR PLANETARY ROTATION ADJUSTMENTS
Ye. А. Morozov Scientific Supervisor - L. V. Granitzkii Foreign Language Supervisor - M. V. Savelyeva
Reshetnev Siberian State Aerospace University 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation Е-mail: transserfer89@gmail.com
Trajectory error of moving planetesimals for planetary system configuration, particularly planetary rotation adjustments, for further full-scale terraforming and inhabitation, are roughly estimated. Use of only currently available technologies are considered for moving planetesimals. Five sources of trajectory error are taken into account - time, coordinate detection, jet exhaust velocity, propellant mass used, and angle errors. The research concluds that trajectory error can be enough for just merging objects, but too big for rotation adjustment. Thus feedback and several trajectory corrections are required, which is likely to require human operators to control at least last stages of the process.
Keywords: terraforming, comets and asteroids impacts, moving planetesimals, trajectory error, accuracy estimation.
Terraforming is the process of adjusting planetary properties so that a planet can sustain full-scale open growing biosphere. Before terraforming certain planets, configuration of a planetary system must be performed. Configuration of a planetary system means moving all material of significant size orbiting in the planetary system in order to achieve maximal overall carrying capacity and expansive potential. This means - forming several planets with parameters as close to optimal as possible: sizes, masses, surface chemical compounds, rotations, satellites, etc., on orbits that will be inside the habitable zone during most of mother star life cycle. This includes moving asteroids, comets, probably moons and dwarf planets, colliding them with desert planetary bodies in order to achieve above mentioned parameters. Moving the material can be done with already existing technology [1-3]. Aim of this work is to estimate accuracy of collisions available with current technological level.
Секция «Актуальные на учные проблемы в мире (глазами молодьш исследователей)»
Most accuracy in moving planetesimals is required on final adjustments of planet rotation. For the task of adjusting mass and then surface chemical compound, planetesimals might strike targeted planet on relatively low velocity - when approaching the planet, the planetesimal being currently moved is attracted to the planet center by gravity. But in order to achieve day length suitable for terrestrial life, planetesimal(s) with relatively high velocity compared to the planet must strike it strictly tangentially, to gain rotation momentum efficiently.
Let's consider up to ±5 % planetary radius trajectory error is acceptable, while planetesimal is planned to hit at 0,95±0,05 of planetary radius to provide required torque.
Is accuracy of planetesimals (objects) moving with currently available technological level enough to strike asteroid just tangentially to a planet to adjust it's rotation most effectively? And how such estimation can be done? What are the causes of possible trajectory deviations? Five sources of error can be foreseen straightforward: time error, object position detection error, jet exhaust velocity error, mass of propellant used error, and object rotation angle error.
Asteroid position detection error Ax can be about ±10 km, the method is described in [4].
Time error At is neglectful compared to other factors: we can determine switch on and off time for engine with about milliseconds accuracy. It's less then 1/3 of other errors input, thus can be neglected. But with average asteroid velocity of 25 km/s, few seconds can make significant difference.
Jet exhaust velocity error Ave can be calculated as a function of temperature/pressure or output energy control accuracy. For moving objects massive for our today scale of impact - asteroids, comets, moons and dwarf planets (planetesimals) - no economically feasible alternative of propellant then the material of the object being moved is foreseen. Most promising scheme is small ion/plasma jet robotic spacecraft delivers big nuclear thermal rocket engine [1, 5, 6] with a drilling rig and mounting it on the planetesimal planned to be moved. Most asteroids are supposed to be "rubber piles". If it's an icy comet or carbon asteroid, it's drilled crushed material (mostly ice, ammonia, and/or carbon compounds, which are most common for smaller solar system bodies [7]) is heated near the reactor to become liquid, and then - pumped through the reactor tubes, heated to about 2500 K, and exists the nozzle with exhaust velocity about 4 km/s [1].
Jet exhaust velocity must be as high as possible for decreasing material losses. It can be calculated indirectly from measuring temperature/pressure of input/output gases, or by measuring reactor energy output.
A well-known formula of exhaust velocity dependence on temperature and pressure for Laval nozzle is:
Y-1
TR 2y 1 - f Л Y
M y-1 I P
(1)
ve =
where ve = exhaust velocity at nozzle exit; T = absolute temperature of inlet gas; R = universal gas law constant; M = the gas molecular mass (also known as the molecular weight); y = cp/cv = isentropic expansion factor; (cp and cv are specific heats of the gas at constant pressure and constant volume respectively); pe = absolute pressure of exhaust gas at nozzle exit; p = absolute pressure of inlet gas.
Temperature and pressure control system for thermo-nuclear rocket engine within ±0,5 % accuracy is described in [8]. For two variables, it's geometric sum of relative errors, Ave ~ ±0,7 %.
Mass of propellant used error Amp can be estimated by today's drilling technology. Material flow rate error, with unpredicted density of drilled ice and rubble rocks, is suggested to be ±10 % in [9]. If storage of crushed material organized, shredder can deliver it to the heated area with ±1 % rate error.
Angle error Aar of planetesimal rotation can be measured rather accurately if observed during several cycles from at least two points far enough to measure rotation axis angle. It can be within ±1 % angle error.
Thus, deviation from estimated trajectory error Ad can be calculated as:
Ad = ^Ax2 + At2 + Ave2 + Am2p + Aar2 (2)
1 AU is about 1,5*10n m, on this scale Ax error is neglectful. Even for planet radius of 3000-7000 km, ±10 km is less then 0,3 % (less then 1/3 of other considered errors).
Thus, deviation from estimated trajectory error is about ^0,0072 + 0,012 + 0,012 « 0,016
For main belt asteroid distance 2 AU from Venus being moved to adjust it's rotation [1, 2], ±1,6 % error is 0,016 • (1,5 • 108) km = ±4,8 • 106 km, which is about 3 orders of magnitude more then planetary radius.
According to universal gravity law, an object with mass m2 orbiting object with mass mi is balanced
m • m m • v2 mostly by two forces: gravity Fg = G 1 2 2 and centrifugal acceleration Fc = G—1-. If object is in
r2 r
JG • m1 lG • m1 steady state (orbit change is neglectful), Fg=Fc, radius r = —-and velocity v = J-1 are derived.
v \ r
If asteroid from main belt (2,8 AU, 17,8 km/s) is moved to Mars (1,5 AU, 24,1 km/s), velocity change Av is 6,3 km/s, with error ±0,016 • 6,3 km/s = ± 0,1 km/s.
For the asteroid to collide with Mars, condition must be performed:
mm m
G am >
•Av2
(3)
r
r
ma
sa
where G = gravitational constant (6.674 • 10-11 N • (m/kg)2); ma = mass of the asteroid; mm = mass of Mars; Avsa = error of the asteroid velocity related to Sun; rsa = distance from Sun to the asteroid; rma = distance from Mars to the asteroid.
Thus, to collide Mars, the asteroid must approach it closer then:
r <
ma
Av.
m • r Ul »1 '
(4)
From widely published facts [10], we can derive rma < 3,13 • 107 km.
To sum up, estimated accuracy can be enough to just merge planetesimal with targeted planet cause planetary gravity can do the rest for collision, while the direction of the force vector is from the planetesimal mass center to the planet's mass center; while for rotation correction, several trajectory corrections required while the planetesimal approaches the planet rather closely, as well as final acceleration before collision occurs to be also required.
For feedback on planetesimal move and trajectory corrections during the object travel to destination, human operators are likely to be required for observation and several trajectory correction decision being estimated and arrived at.
References
1. Robert Zubrin, Christopher McKay. "Technological requirements for terraforming Mars". AIAA, SAE, ASME, ASEE Joint Propulsion Conference and Exhibition, 29, Monterey, June 28-30, 1993. 14 p.
2. Paul Birch, "Terraforming Venus Quickly". Journal of British Interplanetary Society, 1991. Vol. 44, pp. 157-167.
3. Pollack J., Sagan C. "Planetary Engineering", in Resources of Near Earth Space, J. Lewis and M. Mathews, eds, Univ. of Arizona Press, Tucson, Arizona, 1993.
4. Guo P. Ocenka tochnosti opredelenia parametrov dvizhenia asteroida Apofis po izmereniam kompleksa "Nebosvod". Molodezhnyi nauchno-technicheskii vestnik MGTU im. Baumana. 2015. Vol. 4/
5. Site from 10.03.2016 http://www.daviddarling.info/encyclopedia/N/NERVA.html.
6. Robbins W. H., Finger H. B. An Historical Perspective of the NERVA Nuclear Rocket Engine Technology Program. NASA Contractor Report 187154/AIAA-91-3451, NASA Lewis Research Center, NASA. 1991.
7. Site from 10.03.2016: http://www.esa.int/Our_Activities/Space_Science/Asteroids_Structure_and_ composition_of_asteroids/
8. Yuri B. Shtessel. "Sliding Mode Control of the Space Nuclear Reactor System". IEEE transactions on aerospace and electronic systems Vol. 34, No. 2 April 1998.
9. Site from 10.03.2016: https://www.slb.com/~/media/Files/resources/oilfield_review/ors08/aut08/ meeting_the_subsalt_challenge.pdf
10. Site from 10.03.2016: http://solarsystem.nasa.gov/planets/mars/facts.
© Морозов Е. А, 2016
