Length Scaling in Spacecraft Dynamics A candidate spacecraft-on-chip bus is considered as a solar sail, a reentry vehicle, and a Lorentz propelled spacecraft. In each case, the magnitude of nongravitational acceleration suggests the potential for meaningful propellantless maneuvers.
Length-scaling represents a new degree of freedom for spacecraft mission design. This paper presents a method for comparing the length scales of arbitrary spacecraft and uses this approach to evaluate the relevance of 12 environmental forces and torques. Three sample spacecraft geometries are considered: a sphere, a cube, and a thin square plate, at three near-Earth altitudes: 500, 1000, and 10,000 km. This analysis offers a guide for orbit and attitude simulations of small bodies, by suggesting which effects can and cannot be neglected for a given environment and error tolerance. This approach to length scaling may enable extremely small spacecraft to exploit unfamiliar dynamic behaviors that result in solar sail maneuvers, atmospheric reentry, and Lorentz propulsion.
A candidate spacecraft-on-chip used in a preceding analysis is designed with a 1 cm characteristic length in order to enable new mission opportunities based on nongravitational accelerations.
Initials Acceleration AD Aerodynamic drag EC Eddy current drag GG Gravity gradient GR General relativity LZ Lorentz force M Magnetism MT Magnetism: torquer MR Magnetism: residual field Moon Lunar gravity OB Earth oblateness PA Planetary albedo PC Particle collisions PL Solar system planetary gravity PR Poynting–Robertson drag SP Solar pressure SR Special relativity SW Solar wind Sun Solar gravity
Very Small Solar sails
For interplanetary dust, solar radiation pressure can exceed gravity. Here, the critical radius of a particle is roughly a tenth of a micron, below which the particle can be too small to absorb or reflect the photon. Highly reflective interplanetary dust particles of this size can escape solar gravity if released from a comet near the sun.
Solar pressure can be a dominant force for flat, thin, small spacecraft at most altitudes.
The candidate spacecraft-on-chip architecture can capitalize on length scaling to achieve significant solar pressure acceleration. That is, the bus (chip) itself, by virtue of its geometry, behaves as a solar sail. The millimeter-scale design can be fabricated using IC techniques and can be readily tested in a 1 G environment. Further, by capitalizing on natural dynamics, it may be capable of avoiding the nontrivial challenges associated with solar sail control and actuation.
A common metric for solar sail designs is the lightness number which compares the solar pressure acceleration to solar gravitation. The candidate silicon spacecraft-on-chip bus achieves a lightness number of 0.01, meaning that the magnitude of solar pressure is 1% of solar gravity. Though this value is smaller than many proposed solar sail designs, there are a number of possible applications for it in geocentric, heliocentric, or three-body orbits as explored in previous research. Even thinner bodies retain the advantages of stiffness and ready deployment, and they would better compete with the lightness number of larger sails.
Sensors operating continuously through re-entry
Typical spacecraft have ballistic coefficients on the order of 10 to 100 kg/m^2. The candidate spacecraft-on-chip bus has a ballistic coefficient of 0.023 kg/m^2.
Acceleration associated with magnetic actuator torque (MT) are greater than that associated with atmospheric drag (AD). This feature suggests that a magnetic torquer could align the attitude of a plate with the magnetic field when commanded, enabling a form of controlled aerobraking or reentry. A primary challenge for spacecraft reentry maneuvers is heat management, where both the rate and total load of heat can cause catastrophic failure. Essentially, aerodynamic drag converts the spacecraft’s kinetic energy to thermal energy. A spacecraft must be capable of both decelerating and shedding heat rapidly enough to survive reentry.
Each year, thousands of metric tons of small interplanetary dust particles reach the Earth’s surface unaffected while larger meteoroids energetically ablate as meteorites. A drag and thermal model was simulated for a proposed spacecraft-on-chip architecture (a square flat plate 1 cm square and thin) from an altitude of 350 km. For the first orbit, the thin square plate is kept edge-on to the flow and drag is minimal. Once commanded, the attitude is taken to be face-on to the velocity, such that drag is maximized. The altitude rapidly drops, and the temperature increases to a peak value of only about 105 C during maximum deceleration, after which it settles to a steady state temperature driven by the Earth’s thermal radiation. This peak heating occurs in the freemolecular flow regime and results in temperatures low enough to suggest that an IC could operate throughout reentry. There may be meaningful mission opportunities for a small sensor that can sample many altitudes of the atmosphere continuously throughout the reentry process, and one that furthermore would not experience the plasma-related communications dropout of hotter reentering spacecraft.
Lorentz Force Spacecraft
A promising architecture proposed by Hoyt and Minor requires only a power source and two plasma contactors to achieve a net charge. In a vacuum, if two conductive wires are connected to the terminals of a potential source (e.g. a battery or a solar cell), each wire can be thought of as reaching a potential equal to half of the source’s potential and with opposing polarities. However, in a plasma environment, the wires’ opposite polarities generate dissimilar plasma currents, resulting in dissimilar wire potentials.
Near-Earth, the positive wire would tend to discharge almost entirely. As long as the power source can supply sufficient current, the source would maintain the potential difference and would drive the potential to the negative wire. Such a spacecraft would carry a net negative charge that may be controlled through the power source. Using this architecture, the candidate spacecraft-on-chip bus could be equipped for Lorentz propulsion using only two thin, conductive wires and a small solar-cell array. The wires act as plasma contactors and capacitors, and the solar cells produce the potential difference and current required to overcome plasma discharge currents. A previous study suggests that the candidate spacecraft-onchip bus attached with two 1mlong wires and solar cells can achieve a q/m on the order of a micro-Coulomb per kilogram. For a 500 km orbit, this q/m is sufficient to produce daily growth of roughly 400 meters of semimajor axis or 25 meters of along-track motion.
Tied to the star-chip would be a kilometer-long, micron-thin filament that would hold enough electrostatic charge to provide the Lorentz propulsion. Since there isn’t much power or capability in a single chip, Peck envisions billions of them thousands of miles apart, forming a long communications bridge to a nearby star. Any communication would have to be simple—sending the sequence of human DNA encoded in the microcircuits, perhaps, or returning a few precious close-up pictures of a distant planet.
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