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Analysis of Thruster Requirements and Capabilities for Local Satellite Clusters

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Analysis of Thruster Requirements and Capabilities for Local Satellite Clusters I I ANALYSIS OF THRUSTER REQUIREMENTS AND CAPABILITIES FOR LOCAL SATELLITE CLUSTERS G. I. Yashkot, D.E. Hastingstt I Massachusetts Institute of Technology Cambridge, Massachusetts I Abstract This paper examines the propulsive requirements necessary to maintain the relative positions of satellites orbiting in a local cluster. Formation of these large baseline arrays could allow high resolution imaging of terrestrial or I astronomical targets using techniques similar to those used for decades in radio interferometry. A key factor in the image quality is the relative positions of the individual apertures in the sparse array. The relative positions of satellites in a cluster are altered by "tidal" accelerations which are a function of the cluster baseline and orbit altitude. These accelerations must be counteracted by continuous thrusting to maintain the relative positions of the satellites. I Analysis of propulsive system requirements, limited by spacecraft power, volume, and mass constraints, indicates that specific impulses and efficiencies typical of ion engines or Hall thrusters (SPT's) are necessary to maintain large cluster baselines. In addition, required thrust to spacecraft mass ratios for reasonable size clusters are approximately I 15J..LNlkg. Finally, the ability of a proposed linear ion microthruster to meet these requirements is examined. A variation of Brophy's method is used to show that primary electron containment lengths on the order of 10 mm are I necessary to achieve those thruster characteristics. Preliminary sizing of the linear ion microthruster is given. Nomenclature IDtot = total thruster mass flow rate, kg/s 2 Ac = thruster chamber area, m2 Nc = thruster chamber width, m N = number of lifetime impulsive thruster firings b = filled aperture characteristic dimension f 3 I B = sparse aperture baseline no = chamber neutral atom density, kg/m BDV = electric field breakdown voltage, V Pin = required thruster power input, W Co = primary electron utilization factor, A-I Pslc = available spacecraft power, W da = accelerator grid spacing, m ra = along-track resolution I DtaIlk = propellant tank diameter, m R = reference satellite distance from Earth center Dslc = spacecraft diameter, m Rs = slant range e = electric charge, 1.6x10-19 C S = synthetic aperture dimension I fB = fraction of ions extracted Vo = neutral atom velocity, m1s fc = fraction of ion current produced that goes VrY!;t = net voltage across deceleration grid, V to cathode potential surfaces, m VfIJt = total voltage across acceleration grid, V Ftot = total thrust, N VD = discharge voltage, V I go = gravitational acceleration, 9.8 m1s2 Wc = thruster chamber width, m h = orbit altitude x = Displacement of cluster satellite in x y Displacement of cluster satellite in ~ = thruster chamber height, m = y IB = Impulse bit, N s z = Displacement of cluster satellite in z I Isp = spacecraft mass, s flsIc = spacecraft specific power, W/kg IB = ion beam current, A <Xpp = power plant specific power, W/kg 4 = thruster chamber width, m AV = velocity increment, m1s Ie = primary electron containment length, m £B . = average beam ion energy costs, eV life = mission life, s £p = minimum plasma ion energy costs, eV grid transparency to neutrals, m ~ = mass of propellant ion/neutral atom, kg <\>0 = IIlstc = spacecraft mass, kg 11 = thruster efficiency I mp = total propellant mass, kg 110 = propellant utilization efficiency mpp = power plant mass, kg A = sensing wavelength mi = ion mass flow rate, kg/s f = thrusting per unit of spacecraft mass, N/kg ID = propellant mass flow rate per chamber, kg/s Pp = propellant density, kg/m3 I Pslc = spacecraft density, kg/m3 t Graduate Student, Member AIAA 0 0 = total inelastic collision cross section for tt Professor of Aeronautics and Astronautics, primary electron-neutral collisions, m3 Associate Fellow, AIAA S = angular position of satellite in cluster, rad I Sr = angular resolution, radians Copyright © 1996 by the American Institute of n = satellite angular velocity I Aeronautics and Astronautics 1 I I 1. Backaround I 1.2 Interferometry I Sparse Arrays Interferometry has been used for ~ to produce images of astronomical objects in radio Another method to increase resolution is wavelengths with resolutions rivaling that of ground­ interferometry. Interferometers use separate apertures I based optical systems. I This technique, when spaced some distance apart to create a sparse aperture deployed across a cluster of satellites, may be used to as sketched in Figure 1. produce high resolution remote sensing images of I terrestrial targets from space or provide a platform above the atmosphere for space-based viewing of astronomical objects. I 1.1 Synthetic APertures The diffraction limited ground resolution of I typical filled apertures is given by2 AR I r =_'3 (1) a b' Figure 1. Ground-based Radio Interferometer Equation (1) indicates that increasing the aperture size I improves the resolving power of the instrument. Interferometers were originally used in radio Aperture size is limited, however, by size and weight astronomy to distinguish discrete radio sources from constraints of the launch vehicles which place the the diffuse background. Synthesis is obtained by satellites in orbit. Synthetic Apertw'e Radar (SAR) observing separately all the interferometer pairs that I can improve resolution at RF wavelengths from Low exist within a large aperture. A chessboard with only Earth Orbit (LEO) by utilizing the Doppler shifting two chess pieces may be used as an analogy. All of signals to "synthesize" an aperture much larger combinations of the pieces on the board must be I than the satellites filled aperture. Resolutions of sampled to recreate a uniform aperture. To SAR systems are given by2 accomplish this, the receiving elements are designed to be mobile across the so-called u-v plane. As b I Ta=- (2) baselines increased, the rotation of the earth was used 2 to sweep a range of spacings with fixed antennae. Very large baselines composed of widely separated where b is again a characteristic dimension of the antennae soon made sampling the entire u-v plane I filled aperture. Although contrary to intuition, impractical. Computer calibration techniques are now . 3 equation (2) indicates that reducing the filled aperture commonly used for sparse aperture syn th eslS. size improves the resolving power of the radar. At I some point, however, aperture temperature, power The position and spacing of the elements is key to output, and gain limitations preclude the use of the quality of the image produced. The paths traced smaller apertures. Table 1 lists allowable resolutions out by the electro-magnetic waves must be carefully for a typical 10m filled aperture sensing in the controlled so that the signals may be coherently I optical, infrared (IR), or radio frequency (RF) combined. This tolerance is typically ')J20. In the wavelengths at several altitudes. case of the Space Telescope's primary mirror, this margin is a few hundredths of a micron.4 For a I Table 1. Current Achievable Resolution regularly spaced array, a pOSitional error of a few with 10m Aperture. wavelengths can cause significant sidelobes, even if Optical Infrared (IR) Radio (RF) the faulty positions are known exactly so that each I Altitude A=O.5!-l A.=10 !-lm A.=3cm element can be correctly phased.5 In cases where the m relative pOSitions of the element are not known (such tOOO kID 5cm 1m 5 m (SAR) as with random arrays), calibrations can be carried out I 10,000 kID 50cm 10m 30km to improve the quality of the images providing the 35.768 kIn 1.8 m 18 m 107km I 2 I I I relative positions do not change from one image to the next. The achievable angular resolution is diffraction I limited in accordance with the Rayleigh criteria. The size of the aperture, however, is the maximum linear distance between the individual elements. This I distance is known as the baseline, B, so thae I (3) Table 2 lists the angular resolution versus Fig. 2a. Cluster Formation Normal to sampled wavelengths for numerous existing Reference Orbit Plane I interferometers along with the baseline of each system. Although aperture synthesis is well established in the radio spectrum, imaging of I astronomical sources with multi-aperture interferometers is just beginning with the construction of the Infrared-Optical Telescope Array (IOTA) at the F .L. Whipple Observatory on Mount I Hopkins, AZ.6 Table 2. Angular resolution of existing I interferometers Int ... J~e A Ang. Resol. I VLBI 8,500 kIn 1cm-1m le-4" to le-2" VLA 35 kIn 1cm-5m 0.1" to 20" W esterbrook 3.2km 10cm-1m 5" to 100" I Merlin 135 kIn 10cm-lm 0.1" to 1" non-inertial orbit Source: Wohllenben 7 ,Pg 17 Figure 2b. Cluster Formation in Plane of Reference Orbit I 1.3 Local Satellite Clusters By coherently adding the signals received by Forming space-based sparse apertures, analogous several satellites, the cluster would, in effect, create a to the ones discussed in section 1.2, could be sparse aperture many times the size of a real aperture. I accomplished through the use of a local satellite The sparse aperture's large size could vastly increase cluster. Satellites in a local cluster orbit in the level of resolution possible. There are several formations such as those shown in Figures 2a and 2b. possible advantages of creating a sparse array cluster. I Although one or more reference satellites will be in For example: standard Keplerian (ie. inertial) orbits, maintaining 1) Extensive earth coverage could be achieved at the formation will require the other satellites to orbit GEO with a resolution similar to that of current I in planes parallel to the reference orbits. These non­ satellites in LEO. inertial orbits are characterized by either a focus which 2) By turning satellites within the cluster "on and is not located at the Earth's center of mass (Fig 2a), off' it may be possible to alter the dimensions of or orbital velocities which do not provide the proper the sparse aperture and thus zoom in on a target I centripetal acceleration to offset gravity at that detected in a broad, coarse field of view.
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