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Rahul Sengupta / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.1049-1056 Deflection Of An Asteroid By Laser Ablation And Laser Pressure Technique Rahul Sengupta* Meghnad Saha Institute of Technology, IndiaABSTRACT The NEO deflection method employing laser ablation is an interesting and promising method to deviatethe orbit of the asteroid. This technique employs trains of solar-pumped laser pulses, from a number ofspacecrafts in specific formation, to ablate material from the asteroid surface. This process not only reduces themomentum of the asteroid by required amount but also creates a pressure in the opposite direction due tocontinuous bombardment of high pressure laser pulses. The main advantage of this technique is that it relievesthe strict constraint on the proximity to the asteroid surface, thus mitigating the effects of inhomogeneousgravity field, temperature variations and damage of the spacecraft due to regolith. The solution requires nofuturistic technology and would work on wide variety of asteroid types.NOMENCLATUREa Semi-major axis, m 𝜁 Variable used in calculation of 𝛿r(𝛿𝐤)[aI ; bI ; cI ] Radial dimensions of an ellipse, m 𝜛 Variable used in calculation of 𝛿r(𝛿𝐤)A Area, 𝑚2 𝜚 Variable used in calculation of 𝛿r(𝛿𝐤)A Matrix of Gauss planetary equationc Speed of light (299792.458 km/𝑠 2 )Cr Concentration ratio SOURCESC20;C22 Harmonic coefficients for a second For the template and the rigorous mathematical order, second degree gravity field works, I cite [1]. The plume technology has been Cineq Inequality constraint in optimisation inspirationally derived and I cite [2].d Diameter, mD Search space for a solution vector ASTEROIDS- A DISCUSSIOND Directional cosine matrix Asteroids are small rocky-icy and metallic bodies thatF; F Force, N orbit around the Sun. They are thought to be thei Inclination, rad shattered remnants of planetsimals, the bodies thatH Enthalpy of sublimation, J never became massive enough to become planets.l Length, m There are millions of these asteroids majority of themL Distance, or depth, from the orbiting in the main asteroid belt between the orbits surface of the asteroid, m of Jupiter and Mars and co-orbital with JupiterJ Objective function (Jupiter Trojans). Some other reservoirs whereK Conductivity of a material, W/m_K asteroids and comets are present are the Kuiper beltm Mass, kg (Kuiper belt objects) and the trans-Neptunian orbitM Mean anomaly, rad (Trans-Neptunians). However a significantn Mean motion, m/s or index of population of asteroids with different orbital are refraction present, some of which pass very close to the Earth’sv; v Velocity, m/s orbit. Such asteroids are known as Near-Earth 𝑣 Average velocity of particles Asteroids (NEAs) or generally Near-Earth Objects according to Maxwells distribution (NEOs). Some these NEOs actually cross the Earth’s of an ideal gas, m/s orbital path and calculations show that their 𝜃 True latitude, rad probability of impacting the Earth is significantly higher than the other asteroid groups. These asteroids*Bachelor of Technology,Electrical Engineeering are termed Potentially Hazardous Asteroids (PHAs).Department, 4th year Asteroids are classified by their characteristic spectra 𝜅 Angular in-plane component in gravity and accordingly they fall into three main categories: field, rad C-Type Asteroids:They are carbonaceous 𝜆 Wavelength, m and constitute the majority of the asteroids. 𝜇 Gravitational constant They have an albedo ranging from 0.03 to ( 𝜇⊙ =132724487690 𝑘𝑚3 /𝑠 2) 0.10. 𝑣 True anomaly, rad S-Type Asteroids: They are siliceous in 𝜉 Variable used in calculation of 𝛿r(𝛿𝐤) nature and make up 17% of the asteroids. 𝜌 Density, g/m2 1049 | P a g e
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Rahul Sengupta / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.1049-1056 They are a bit brighter than C-type with an above the threshold fluence 𝐹𝑡 (J/𝑐𝑚2 ) or ablation albedo between 0.10 to 0.22. threshold. This puts a lower limit to the fluence and M-Type Asteroids: They are metallic in the intensity of the laser pulse. The fluence would nature, most of them made up of iron. vary depending on the material and optical properties Albedo ranges from 0.1 to 0.2. of the asteroid. In general, for a successfulThe orbits of asteroids are determined through sublimation or ablation process, the laser pulsedifferent ways. Some orbitals are defined from duration must be longer than the time betweenobservational records, while some are measured electron-electron collisions and the relaxation time ofthrough the perturbations they cause in the nearby the electron-phonon coupling. If the pulse duration isobject as they pass close to it. Telescopes have also shorter than the thermalisation time, the electric fieldbeen used for identification and tracking of the of the laser pulse might exceed the threshold forasteroid orbit and now computational methods are optical breakdown and the target material isused for such kind of calculations. Whatever transformed on an ultra-fast time scale into plasma.techniques are used the orbital characteristics of an When the target area, due to ablation is convertedasteroid depends on some specific orbital elements. into plasma, the entire system may face extreme non-The numerical values of these elements for asteroid equilibrium situations resulting in orbitalApophis 99942 have been given in the table. perturbations and instability in the asteroid. These effects are not at all welcome as they tend toElement Measured Values destabilize the asteroid and might even disintegrateSemi-major axis 𝒂𝑨 0.9223 AU them which are held together by mutual gravitationalEccentricity 𝒆𝑨 0.1911 attraction. Hence, an upper limit to laser pulseInclination 𝒊𝑨 0.05814 rad duration is established and the lasers onboard theArgument of 2.2059 rad spacecraft has to operate within this region of laserperiapsis𝝎 𝑨 323.50 days fluence and intensity.Period 𝑻𝑨 2.2479x10−7 rad/s The energy that is available for ablation is anMean motion 𝒏𝑨 2.7 x 1010 kg important criterion. It depends on the laserMass 𝒎𝑨 1.8015993 x10−9 𝑘𝑚3/𝑠 2 wavelength, optical properties of the asteroid materialGravitational constant𝝁 𝑨 191m,135m,95m and also on the diameter of the illuminated spotDimensions 5.8177 x 10−5 rad/s caused by the laser. This available energy is an 𝒂 𝟏, 𝒃 𝟏, 𝒄 𝟏 interesting parameter that helps in designing the orbitRotational velocity of the spacecrafts around it. This issue has been dealt 𝒘𝑨 with later in the paper. The main importance of calculation of the amount of energy available for ablation purpose can be seen from the fact that theTable 1.Some physical values of Apophis 99942. power needed to ablate required amount of material is in direct relationship with the distance of theCONCEPT OF LASER ABLATION spacecraft from the asteroid surface. The spacecraftsLaser ablation may be defined as a sputtering process must be placed in such an orbit that would allow it toleading to the ejection of atoms, molecules and even focus optimal power necessary for deflection. It canclusters from a surface as a result from the be calculated as follows,conversion of an initial electronic or vibrational The electric field of a monochromatic, linearlyphotoexcitation into kinetic energy of nuclear motion. polarized plane wave pulse (laser pulse) in aIn laser ablation, high power laser pulses are used to homogeneous and nonabsorbent medium is given byevaporate matter from a target surface. As a result, a 2𝜋𝑧supersonic jet of particles (plume) is ejected normal 𝑬 = 𝑬0 exp [𝑖 − 𝜔𝑡]to the target surface. The plume, similar to rocket 𝜆exhaust, expands away from the target with a strong where, z is the direction of propagation of the pulse,forward directed velocity distribution of different 𝜔 is the angular frequency, 𝜆 is the wavelength of theparticles. This ejected plume, thus, provides a laser radiation.reaction force that produces a significant amount of 2𝜋 𝑐force on the target object in the direction opposite to 𝜆= 𝜔 𝑛that of its ejection. To apply this technique in the caseof deflection of an asteroid, the spacecrafts n is the refractive index of the medium.responsible for this operation are equipped with Analogous magnetic field is given by the similarlasing equipments that are discussed later. expression. Both the field amplitudes are related byThe process of laser ablation has an operation time of 𝑯0 = 𝑬0 𝜀0 𝑛𝑐many orders of magnitude, from the initial absorption 𝜀0 is permittivity of free space.of laser radiation to material ejection. In macroscopic Now irradiance 𝐼 is given by,level, modification occurs when the laser fluence is 𝐼 = 𝑬 𝑋 𝑯 = 𝑛𝜀0 𝑐𝑬2 0 1050 | P a g e
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Rahul Sengupta / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.1049-1056 FOCUSSING AND BEAMING SYSTEMSAverage power,𝑃𝑎𝑣𝑔 , transmitted by a laser pulse is The laser ablation of the asteroid in space is 𝑃𝑎𝑣𝑔 = 𝐼 . 𝐴𝑟𝑒𝑎 𝑠𝑝𝑜𝑡 a sophisticated issue. The laser has to produce 𝜋𝑑 2 𝑠𝑝𝑜𝑡 enough power which would sublimate the asteroid = 𝑛𝜀0 𝑐𝑬2 . 0 4 surface using the readily available resource i.e. the solar energy. The design of the spacecraft using solarEnergy of each laser pulse, 𝐸 = 𝑃𝑎𝑣𝑔 /𝑇, where T is pumped laser is a critical aspect. The spacecraft mustthe inverse of the laser frequency 𝑓. be able to concentrate a minimum power density atThus, all times which means controlling the Concentration 𝜋𝑑2 𝑠𝑝𝑜𝑡 ratio,𝐶 𝑟 . Concentration ratio of the system is the ratio 𝐸 = 𝑛𝜀0 𝑐𝑬2 𝑓 . 0 of the power density at the input to the system and 4Net energy available for ablation per pulse, the output. The attitude of the spacecraft has to be 𝐸 𝐴 = 𝐸 − 𝐸 𝑡 controlled to maintain a constant 𝐶 𝑟 . In general, each spacecraft must have the followingwhere, 𝐸 𝑡 is the threshold energy which depends on three fundamental components,the material type. Laser pulses may vary over a very 1. A power collecting unitwide range of duration (microseconds to 2. A power conversion unit picoseconds) and fluxes can be precisely controlled. 3. A power beaming unitThis is an advantage of laser ablation technique. The power collecting unit would consist ofAs a consequence of the high pressure laser pulses the solar array capable of collecting power from theapplied during the ablation process, this technique sun. These arrays will be attached to the main bodycan be used to transfer momentum to the target of the spacecraft just like a conventional satellite. Thematerial. The effect is similar to hitting the material utility of a power conversion unit is to convert thewith hammer. This mechanical force, generated when solar energy into electrical energy. This is, as wea high pressure laser pulse strikes a target, may be shall see later, because of the limits imposed by thetermed as Laser Pressure. For materials with high present day technological glitches, the direct-solarlinear thermal expansion (DL/𝐿 𝑑 , where 𝐿 𝑑 is heated pumped lasers are very lossy and would not be abledepth, DL the expansion), high Young’s to produce enough power for successful ablation.modulus(𝐸 𝑌 ), high melting point and with high oxideconcentration, significant stresses may occur due to Beaming Unit: Solar Pumped Laserlaser irradiation. As materials get ejected, thermal Lasers work by exciting electrons byshocks are generated repeatedly. Thermal shocks are simulating them with the addition of photons whichindicated by the development of thermal stress, temporarily boost them up to a higher energy state. 𝑠 𝑡 = 𝐸 𝑌 DL/𝐿 𝑑 This continues until a population inversion exists. Where there are more electrons at a higher energyThese thermal shocks pressurize the layer beneath the state the electrons drop back to their original groundablated layer and when integrated over a cylindrical state releasing photons that produce emissions havingvolume with height is the diameter of the asteroid and the same spectral properties of the stimulatingradius is the radius of the thermal shock front, it radiation which makes it highly coherent. The energyaccounts for a significant amount of force. This force that is not released as output emission manifests asis termed as laser pressure. It must be noted that laser heat. This implies that the heat must be dissipated bypressure is a consequence of the ablation process by large radiators attached to the spacecraft as shown inlasers. figure 1.This technique has been discussed in this paper as a There are two methods of powering the laser in spacepossible and effective method for the deflection of an using solar energy:earth-bound NEO. The plume produced by the 1. Indirect Pumping: Indirect-pumped solarablation process would produce a thrust on the NEO, lasers convert the solar energy first intowhich would decrease its momentum creating a force electrical energy which is then used toopposite its direction of flow. Also another force power the laser. Photovoltaic cells are thehave been introduced here called the Laser Pressure, best options for space applications. Thewhich is a single stake force that has the capability to drawback of this process is the addition ofpush the asteroid off its present course given enough an electrical power generator which will addtime is available. At the end of the paper possible to the mass, size and power requirements ofimprovements have been discussed which could help our spacecraft. This problem can solved byin improving the overall effectiveness and make it using high efficiency solar arrays inmore feasible economically. conjunction with solid-state lasers. Solid state lasers pumped with electric power can currently have 60% efficiency. If the solar 1051 | P a g e
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Rahul Sengupta / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.1049-1056 arrays give us 30% efficiency, we can have CONCEPTUAL OPERATION DESIGN an overall 18% efficiency. The navigation strategy of the entire 2. Direct Pumping: In direct solar-pumped operation is designed on the basis of the attitude lasers, the laser is directly energized using measurements of the spacecrafts and the 2D image solar radiation. Due to mismatch between from the onboard camera. Since a single spacecraft the wide-band emissions of the sun with would mean a single point failure of the whole narrow absorption band of the lasers, the mission and lesser power to attack the asteroid, a efficiency is very less. Hence this method of mission with an optimal number of spacecrafts in a laser pumping is still not feasible. Further specific formation is conceived. Each spacecraft in research into this method can make this the formation should be able to measure its attitude method very suitable for this sort of with a star tracker and stay in position with respect to missions. the entire formation. Once the formation is deployedLasing Materials from a mother ship, a leader spacecraft searches forThe lasing materials that can be used for a solar the programmed location of the asteroid until it is inpumped solid state laser include the field view of the camera. The centroid of the Nd:YAG with chromium doping which image is determined by simple geometry and aligned contains neodymium ions (𝑁𝑑3+ ) in yttrium with the camera’s boresight. The pointing vector is aluminum garnet (𝑌2 𝐴𝑙5 𝑂12 ). It is relatively relayed to the entire formation. When the entire cheap to produce and readily available, and formation is fed with the position of the centre of the more importantly, has good thermal NEO, the range of spacecraft and asteroid is resistance, durability and lifetime. triangulated as the spacecrafts align themselves in the Nd:Cr:GSCG which has a host of plane containing the centroid of the image of the Gadolinium Scandium Gallium Garnet. It is asteroid. The feed of the relative positioning of the highly efficient. spacecrafts is used to direct the laser beams on a single point on the asteroid. The employed formation Nd:YLF where the host material is Yttrium is deliberately not aligned in line with the sun and the Lithium Fluoride (YLi𝐹4 ). asteroid to overcome the factors that come into play when the solar arrays are shadowed by the asteroid. This is shown in figure 3. For the spacecrafts to hover at a fixed distance from the asteroid, the solar arrays are so designed that the solar radiation pressure and the force due to the asteroid gravity field are in equilibrium. These static points are called Artificial Equilibrium Points (AEP). These points are not fixed in space and the spacecrafts hovering around these points cannot remain indefinitely in any AEP. This is due to the dynamic forces that work continuously here. The position of these equilibrium points over the full orbit of the Apophis is shown in figure 4.Figure 1. A model spacecraft with solar laser system For a spherical and homogenous gravity field of the asteroid, the dynamics of the arrays is governed by the following set of equations, 𝑟𝐴 𝜇⊙ 𝜇⊙ 𝑥 = 2𝑣 𝑦 − 𝑦 + 𝑥𝑣 2 + 2 − 3 𝑟 𝐴 + 𝑥 𝑟𝐴 𝑟𝐴 𝛿𝑟 𝜇𝐴 𝐹𝑠 𝑥 (𝑥, 𝑦, 𝑧) 𝐹𝑢 − 3 𝑥+ + 𝑥 𝛿𝑟 𝑚 𝑠𝑐 𝑚 𝑠𝑐 𝑟𝐴 𝜇⨀ 𝜇𝐴 𝑦 = −2𝑣 𝑥 − 𝑥 + 𝑦𝑣 2 − 3 𝑦 − 3 𝑦 𝑟𝐴 𝑟𝑠𝑐 𝛿𝑟 𝐹𝑠 𝑦 (𝑥, 𝑦, 𝑧) 𝐹𝑢 𝑦 + + 𝑚 𝑠𝑐 𝑚 𝑠𝑐 𝜇⨀ 𝑧 𝜇𝐴 𝐹𝑠 𝑧 (𝑥, 𝑦, 𝑧) 𝐹𝑢 𝑧=− 3 − 3 𝑧+ + 𝑧 𝑟𝑠𝑐 𝛿𝑟 𝑚 𝑠𝑐 𝑚 𝑠𝑐 where, 𝑚 𝑠𝑐 is the estimated mass of the spacecraft, 𝑭 𝑆𝑅𝑃 = [𝐹𝑠 𝑥 , 𝐹𝑠 𝑦 , 𝐹𝑠 𝑧 ] is the solar force, 𝑭 𝑢 = Figure 2.Radiator area vs Radiator temperature [𝐹𝑢 𝑥 , 𝐹𝑢 𝑦 , 𝐹𝑢 𝑧 ] is control force. 1052 | P a g e
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Rahul Sengupta / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.1049-1056To fulfill the objective of the mission, an optimalnumber of spacecrafts must be deployed around theasteroid as justified earlier. For spacecrafts flying information with the asteroid orbiting in tandem aroundthe sun, their orbits must be designed as such so thatthey can maintain a constant power density of laseron the asteroid surface and also avoid the irregulargravity field of the asteroid and the plume of debrisejecting from the surface. Figure 4.Position of the equilibrium points over a full orbit of the asteroid Apophis. The formation orbit can be thought of as an orbit around the Sun with a small offset in the initial position 𝛿𝑟0 and velocity 𝛿𝑣0 . This offset can also be expressed as the difference between the orbital parameters of the chief (e.g. the asteroid) and the formation. As long as there is no difference in semi- major axes, the two orbits will remain periodic. 𝛿k =𝒌 𝑠𝑐 -𝒌 𝐴 = [𝛿a 𝛿e 𝛿i 𝛿Ω 𝛿𝜔 𝛿M] As the mean anomaly is a function of the semi-major axis, the difference in mean anomaly will remain Figure 3. Operation design using formation of constant throughout the orbit so long as 𝛿a = 0. spacecrafts. If the optimal thrust direction that maximizes theTo design the formation orbits, we use the orbital deviation is along the unperturbed velocity vector ofelement difference between a chief orbit (which can the asteroid, then the exhaust gases will flow alongbe virtual, and is located at the origin of the Hill the y-axis of the local Hill reference frame.reference frame)and a spacecraft in the formation. Therefore, the size of the formation orbits projected 𝑟𝐴 𝜇⨀ 𝜇⨀ in the x-z plane should be maximal. All the 𝑥 𝑡 = 2𝑣 𝑦 − 𝑦 + 𝑥𝑣 2 + 2 − 3 (𝑟 𝐴 + 𝑥) requirements on the on the formation orbits can be 𝑟𝐴 𝑟𝐴 𝑟𝑠𝑐 𝑟𝐴 𝜇⨀ formulated in mathematical terms as a multi- 𝑦 𝑡 = −2𝑣 𝑥 − 𝑥 + 𝑦𝑣 2 − 3 𝑦 objective optimization problem, 𝑟𝐴 𝑟𝑠𝑐 𝜇⨀ 𝑚𝑖𝑛 min 𝐽1 𝑧 𝑡 = 3 𝑧 = 𝛿𝑟 𝑟𝑠𝑐 𝛿𝒌 𝜖 𝐷 𝑣with, 𝒓 𝑠𝑐 = 𝒓 𝐴 + 𝛿𝒓, 𝑟𝑠𝑐 = (𝑥 + 𝑟 𝐴 )2 +𝑦 2 + 𝑧 2 𝑚𝑖𝑛 min 𝐽2 = − 𝑥2 + 𝑦 2where, 𝒓 𝑠𝑐 𝑎𝑛𝑑 𝒓 𝐴 are vectors from the sun to the 𝛿𝒌 𝜖 𝐷 𝑣formation spacecraft and the asteroid respectively, 𝑣is the angular rate of change of the solar orbit. subject to constraints:This is a first approximation of the spacecraft motionneglecting the gravity field of the asteroid and the 𝐶 𝑖𝑛 𝑒𝑞 = min(𝛿𝑟 𝑣 − 𝑟 𝐿𝐼𝑀 ) > 0solar pressure but suffices our requirements. 𝑣 where, 𝑟 𝐿𝐼𝑀 is the minimum radius sphere imposed to avoid the non-linearity in the asteroid gravity field and D is the search space for the solution vector 𝛿𝒌; 𝐽1 , 𝐽2 being objective functions. Solving the problem by a hybrid-stochastic- deterministic approach based on multiagent search tool combined with a decomposition of the search space, results in several groupings of formation orbits. The existence of families can be seen, for example, through 𝛿𝜔 and 𝛿Ω, where for a given input value there are multiple values for the objective functions 𝐽1 and 𝐽2 . 1053 | P a g e
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Rahul Sengupta / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.1049-1056ASTEROID DEFLECTION MODELA very general set of formulas with no approximation 𝜇 where, mean motion, n= 𝑎3is discussed here. The deviation distance is definedhere as the difference in 𝑟 𝐴 between the original The thrust produced by the deflection method is aundeviated orbit and deviated orbit at 𝑡 𝑀𝑂𝐼𝐷 where direct function of the expelled surface matter 𝑚 𝑒𝑥𝑝MOID is minimum orbital intersection distance. Non- Therefore,linear equations were derived for determining thedifference in 𝑟 𝐴 are expressed as a function of the 𝑑 𝑚 𝑒𝑥𝑝 𝑦 𝑚𝑎𝑥 𝑡 𝑜𝑢𝑡 1 1ephemeris in the Hill reference frame 𝒜 centered on = 2𝑣 𝑟𝑜𝑡 𝑦0 𝑡 𝑖𝑛 𝑃𝑖𝑛 − 𝑄 𝑟𝑎𝑑 − 𝑄 𝑐𝑜𝑛𝑑 𝑑𝑡 𝑑𝑦 𝑑𝑡 𝐻 𝑡the asteroid with ∆𝒌 giving the difference inKeplerian parameters between the undeviated and where, [𝑡 𝑖𝑛 , 𝑡 𝑜𝑢𝑡 ] is the duration of lasing on thedeviated orbit. point, [𝑦0 , 𝑦 𝑚𝑎𝑥 ] are the limits of the vertical illuminated surface, H is the enthalpy of sublimation, 𝑃𝑖𝑛 is input power due to solar arrays, 𝑄 𝑟𝑎𝑑 is the heat loss due to black-body radiation and 𝑄 𝑐𝑜𝑛𝑑 is conduction loss. Figure 5.Ellipsoid model of an asteroid with radial dimensions.We define, 𝜚 cos 𝜃 + 𝜁 sin 𝜃 ∆𝒓 = −𝜁 cos 𝜃 + 𝜚 sin 𝜃 − cos(Δ𝜃 − 𝜃) sin ΔΩ sin 𝑖 + 𝜛 sin(Δ𝜃 − 𝜃) Figure 6. Definition of relative reference frameswhere, 𝒜 is centered on the asteroid 𝜛 = cos 𝑖 sin(Δ𝑖 − 𝑖) + cos ΔΩ cos(Δ𝑖 − 𝑖) sin 𝑖 𝒮 𝑖𝑠 centered on the spacecraft.𝜚 = − cos ΔΩ cos(Δ𝜃 − 𝜃) + cos(Δ𝑖 − 𝑖) sin ΔΩ sin(Δ𝜃 − 𝜃) The magnitude of induced acceleration is then given𝜁 = cos 𝑖 cos(Δ𝜃 − 𝜃) sin ΔΩ + 𝜉 sin(Δ𝜃 − 𝜃) by𝜉 = cos ΔΩ cos(Δ𝑖 − 𝑖) cos 𝑖 − sin(Δ𝑖 − 𝑖) sin 𝑖 𝚲𝑣 𝑚 𝑒𝑥𝑝In the remaining paper Δ𝒓 is used to compute both 𝒖 𝑑𝑒𝑣 = . 𝒗𝐴 𝑚 𝐴𝑖relative position of the spacecraft with respect to theasteroid and the deflection at the Earth.By definition of the coordinate system, where, 𝒗 𝐴 is the direction of velocity vector. 2 𝒓 𝑨 = [𝑟 𝐴 , 0,0] 𝑇 𝚲≅ 𝜋 is scattering factor assuming debris plume isThe change in the orbital parameters are calculated uniformly distributed over half a sphere.by numerically integrating the Gauss planetary 𝑣 is the average velocity of the debris particleequations using tangential thrust vector 𝒖 𝑑𝑒𝑣 induced according to Maxwell distribution of an ideal gas.by the sublimation method. 𝑚 𝐴 𝑖 is the remaining mass of the asteroid. 𝑡1 Apart from the thrust produced by the ejection of 𝑑𝑘 (𝒖 𝑑𝑒𝑣 ) debris plume, the high pressure pulsed laser would Δ𝑘 = 𝑑𝑡 𝑡0 𝑑𝑡 produce a pressure on the asteroid. The transfer ofThe change in angular location calculated at the momentum by the laser pulses accumulated over aMOID is: significant interval of time is capable of changing the momentum of the asteroid by a desired amount. This 𝑡1 change of momentum plays a very significant role in 𝑑𝑀Δ𝑀 = 𝑑𝑡 + 𝑛 𝐴0 𝑡0 − 𝑡 𝑀𝑂𝐼𝐷 + 𝑛 𝐴 𝑖 (𝑡 𝑀𝑂𝐼𝐷 − 𝑡 𝑖 ) the design of asteroid deflection procedures. 𝑡0 𝑑𝑡 Using general vector notation, 1054 | P a g e
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Rahul Sengupta / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.1049-1056Momentum of the asteroid, 𝑴 𝑎 . deflection mechanism. Based on the model of Kahle,Momentum transferred by a single laser pulse be 𝑴 𝑙 . the sublimation process is comparable to theResultant momentum due to a single pulse, generation of jets in comet tail and the plume 𝑴 𝑅 = 𝑴 𝑎 − 𝑴𝑙 expansion is similar to a rocket exhaust through aNet momentum shift required, nozzle. The density of the gas can be computed 𝑴 𝑎 − 𝑴 𝑅 = 𝑚 𝑎 (𝒗 𝑎 − 𝒗 𝑅 ) analytically as,where, 𝑚 𝑎 is the asteroid mass, 𝑣 𝑎 is the asteroid 𝑑2 𝑠𝑝𝑜𝑡 𝜋Θ 2velocity and 𝑣 𝑅 is the resultant velocity of the 𝜌 𝑟, Θ = 𝜌 ∗ 𝑗 𝑐 2 (cos( )) 𝑘−1 2𝑟 + 𝑑 𝑠𝑝𝑜𝑡 2Θ 𝑚𝑎𝑥asteroid.From literature, an earth-bound NEO would require 1 where, r is the distance from the spot on the surfacecm/sec of velocity change to increase its MOID. of the asteroid, 𝑑 𝑠𝑝𝑜𝑡 is the illuminated spot diameter,Thus, 𝒗𝑎 − 𝒗𝑅 = 1 Θ is the elevation angle of the spacecraft with respectTherefore, to the asteroid Hill reference frame 𝒜, 𝑗 𝑐 is jet 𝑴𝑎 − 𝑴𝑅 = 𝑚𝑎 constant, Θ 𝑚𝑎𝑥 maximum expansion angle, 𝜌 ∗ is theTaking only magnitude of the vectors, density at the sublimation point. 𝑀𝑎 − 𝑀𝑅 = 𝑚𝑎 𝑚 𝑒𝑥𝑝 𝜌∗ = ⟹ 𝑀𝑅 = 𝑀𝑎 − 𝑚𝑎 (𝐴 𝑠𝑝𝑜𝑡 𝑣 𝑔𝑎𝑠 )If the mass of the asteroid is roughly 10 million tonesand its velocity 56 km/sec, where, 𝐴 𝑠𝑝𝑜𝑡 is the area of the spot and 𝑣 𝑔𝑎𝑠 is theThen, velocity of the exhaust gas. 𝑀 𝑅 ≃ 5.59999 x 𝟏𝟎 𝟏𝟔 kg-cm/sec Putting this in the previous equation, 4𝑚 𝑒𝑥𝑝 1 𝜋Θ 2So a slight change in momentum is required to 𝜌 𝑟, Θ = 𝑗𝑐 2 (cos( )) 𝑘−1 𝜋𝑣 𝑔𝑎𝑠 2𝑟 + 𝑑 𝑠𝑝𝑜𝑡 2Θ 𝑚𝑎𝑥deviate the asteroid. Since this method is an additiveprocess where both the forces act in the same This model predicts that the density at a distance rdirection, the deflection would be more than any weakly depends on the size and spot geometry. In aother method in the same time interval thus nutshell, the maximum expansion angle is not aconstituting a force that is stronger than any other function of the spot geometry which is a bit undermethod available. This is shown in the figure 7. justified. For a massive extended object, much bigger than the spot, the expansion cone may be a little different. Hence there is an utter need for a better plume dynamics modeling. The direct solar-pumped laser is another genre in which significant improvement is required. Due to mismatch between emission band of the sunlight and absorption band of the laser, a highly efficient system is yet to be developed. Although recent studies with ceramic laser currently reported a 40% efficiency with pseudo solar light, its effect for space-based application is yet to be tested. Another region of possible improvement is the solar array technology. Solar arrays currently do not yield as much power as would be desired for this method. A very effective prospect could be to use a Figure 7. A Diagram showing Laser ablation and conglomeration of solar arrays where each array is Laser pressure forces acting in the same direction connected parallel to each other so that maximum amount of input solar power is available every time for pumping the laser and each array can produce itsPOSSIBLE IMPROVEMENTS maximum output. Also it must be made sure that inThe technique discussed in this paper is an overall case of indirect solar-pumped lasers, the electricconcept of deflection of an asteroid. It is worth power generator consumes as much less power asmentioning that for a very successful NEO mitigation possible.to occur, all the process mentioned here wouldrequire an optimization re-evaluation to increase theeffect produced by this technique. DISCUSSIONOne of the major areas of improvement is the plume In near future there is an ample probability ofdynamics modeling. This plume dynamics is very asteroids either impacting the Earth or passing veryimportant as it forms the soul of our asteroid close to it. In both cases, a massive destruction will 1055 | P a g e
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Rahul Sengupta / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.1049-1056be the outcome and the face of the Earth would not asteroid to avoid damaging of the mirror orremain as beautiful as it is today. So to mitigate this its reflectivity due to debris plume.problem, a number of techniques have been Push time of this technique is independentproposed. Some of them include – of mirror lifetime and the method works 1) Impulsive change in the linear momentum until technical glitches arise. of the asteroid by nuclear interceptors. Also this method has advantages over all the other 2) Producing continuous gravitational tugs on methods of asteroid deflection. It is insensitive to the the asteroid by thrusters attached to the asteroid morphology unlike gravity tractors. It is spacecrafts. applicable for asteroids that are made up of chunks of 3) Producing a passive low thrust on the rocks held together by mutual gravitational attraction. asteroid by an induced change in its thermo- It also does not involve landing or going very near to optical properties. the asteroid thus cancelling the effects of non-linear 4) Driving the asteroid by an electric solar sail gravity fields. attached to it. This technique mentioned in this paper has been 5) Producing controlled thrust on the asteroid discussed as deeply as possible within the limited by ablation of its surface (through laser scope. The concept of laser ablation and the available pulses or solar mirrors) energy for ablation has been discussed with theThese are some of the legitimate methods available to introduction of the laser pressure concept. Theus for deflecting the asteroids. Hence, a thorough dynamics and navigational strategy of the operationinvestigation is required to select an optimal has also been presented. Although it would require atechnique or even a number of techniques clubbed high initial investment for the space-basedtogether and their actions divided into various stages. application of this process, subsequent running cost isA study conducted by the Space Advanced Research low. The research and development of betterTeam, University of Glasgow, made a thorough technologies might solve the problem of initialcomparison of the deflection methods based on investment in near future.certain criteria – miss distance at the Earth, warningtime available and mass into orbit. The result from ACKNOWLEDGEMENTthe study reported the sublimation method to be the I would like to take this opportunity to thank Dr.most effective and safe. Debiprosad Duari, Director, Research andBut this sublimation can be done by laser or by Academics, M.P.Birla Institute of Fundamentalmirrors. A technique using laser ablation, applied by Research, for his enthusiastic involvement in thisa number of spacecrafts in formation have been project and for the thoughtful insights he gave fordiscussed here and have advantages over the developing this paper.sublimation technique using mirrors. Theseadvantages are as follows: REFERENCES It requires lesser payload as no large mirrors 1) C.A. Maddock, C.McInnes, G.Radice, are required to place in orbits. M.Vasile, “NEO deflection through a multi- It requires lesser control elements as no mirror system,FinalReport”, ESA, , 9 June control element is required to control the 2009,Contract no.-21665/08/NL/CB. position of the mirrors. 2) “Interaction Laser Radiation Matter. Laser ablation is effective even at large Mechanisms of Laser Ablation”,MMendes distance from the sun, provided enough Tech, 2010. power is available for laser pumping, but 3) http://www.wikipedia.org power for sublimation will be significantly 4) K.Imasaki, T.Saiki, D.Li, S.Taniguchi, reduced in case of solar mirrors. S.Motokosi and M.Nakatsuka, “Solar This technique has an advantage of the pumped laser and its application to availability of an extra force (laser pressure) hydrogen production”,ILT, 5 June 2007, acting along the line of action of the thrust Turkey. due to ablation. 5) Leslie S. Coleman, “Introduction: Rocket In case of solar mirror method continuous Science ain’t all Rocket Science”, Frosty beaming of concentrated solar energy will Dew Observatory. heat up the asteroid which may cause 6) http://www.physorg.com thermal instability and even 7) http://www.tuk.fi/Units/Ats/projects/prlaser/ defragmentation. This consequence is not ablation.htm present in laser ablation process as very less 8) Asteroid Fact Sheet, Dr. David R. Williams, heat is dissipated on the asteroid by the laser NASA pulses. No extra effort is required to place the spacecrafts strategically or further from the 1056 | P a g e
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