Micro Satellite Orbital Boost by Electrodynamic Tethers

Abstract

In this manuscript, a method for maneuvering a spacecraft using electrically charged tethers is explored. The spacecraft's velocity vector can be modified by interacting with Earth's magnetic field. Through this method, a spacecraft can maintain an orbit indefinitely by reboosting without the constraint of limited propellant. The spacecraft-tether system dynamics in low Earth orbit are simulated to evaluate the effects of Lorentz force and torques on translational motion. With 500-meter tethers charged with a 1-amp current, a 100-kg spacecraft can gain 250 m of altitude in one orbit. By evaluating the combined effects of Lorenz force and the coupled effects of Lorentz torque propagation through Euler's moment equation and Newton's translational motion equations, the simulated spacecraft-tether system can orbit indefinitely at altitudes as low as 275 km. Through a rare evaluation of the nonlinear coupling of the six differential equations of motion, the one finding is that an electrodynamic tether can be used to maintain a spacecraft's orbit height indefinitely for very low Earth orbits. However, the reboost maneuver is inefficient for high inclination orbits and has high electrical power requirement. To overcome greater aerodynamic drag at lower altitudes, longer tethers with higher power draw are required.

Keywords: actuators; aerodynamic drag; and control; cubesats; dynamics; guidance; magnetic field; mini/micro satellites; navigation; orbital dynamics; spacecraft maneuvering; tether.

Figure A1

SIMULINK simulation created to validate proposals.

Figure A2

Generate Trajectory subsystem in Figure A1.

Figure A3

Actuators and Control subsystem in Figure A1.

Figure A4

Controllers subsystem in Figure A3. The * indicates optimal values.

Figure A5

Translation subsystem in Figure A1.

Figure A6

SIMULINK subsystems in Figure A1 (a) Disturbances subsystem; (b) Translation subsystem.

Figure A7

SIMULINK subsystems in Figure A1 (a) Applied Tether Force subsystem; (b) Magnitude subsystem.

Figure A8

SIMULINK subsystems in Figure A1 (a) Altitude Calculation subsystem; (b) Sensors and Observers subsystem (bypassed).

Figure A9

Kinematics subsystem in the Rotation block in Figure A1.

Figure 1

(a) Tether orientation for reboost. (b) Les Johnson, a scientist at Marshall Space Flight Center inspects nonconducting part of a tether [25].

Figure 2

Rough order-of-magnitude of environmental torques available to spacecraft as a function of altitude. These environmental torques may be used for angular momentum modification, and this manuscript focuses on such modification using only magnetic torques.

Figure 3

Comparison of quaternion normalizations (on the ordinate) for different step sizes using the Runge–Kutta solver. Standard deviations for 50 (black dashed line), 250 (green dotted line), 500 (red dot-dashed line), and 1,000 Hertz (blue solid thin line) sample rates are displayed. Time in seconds is displayed on the abscissa with quaternion normalization on ordinate.

Figure 4

Effect of electrodynamic tether reboost on a 300 km altitude orbit. (a) Trajectory. (b) Altitude change in meters on ordinate versus time on abscissa.

Figure 5

Altitude-change over one orbit with time in seconds on the abscissa and altitude change in meters on the ordinate. 200 km is blue, dash-dotted line; 250 km is red dashed line; 300 km is solid yellow line; 350 km is dotted purple line, and 500 km is green, thick dashed line: (a) Natural orbit decay from disturbances; (b) results with tether deployed.

Figure 6

Lorentz force extracted from electrodynamic tether with time in seconds on the abscissa and (a) Altitude (kilometers) on the ordinate where 200 km is blue, dash-dotted line; 250 km is red dashed line; 300 km is solid yellow line; 350 km is dotted purple line, and 500 km is green, thick dashed line; (b) Inclination (degrees) on the ordinate, respectively where 0 degrees is blue, dash-dotted line; 10 degrees is red dashed line; 30 degrees is solid yellow line; 60 degrees is dotted purple line, and 90 degrees is green, thick dashed line. (c) Lateral miss distance (meters) from orbit trajectory due to tether deflection (degrees) over one revolution on the ordinate. Zero degrees is displayed by the dashed blue; 10 degrees is displayed by the red dashed line; 20 degrees is displayed by the solid yellow line. $\hat{\mathrm{x}}$ and $\hat{\mathrm{y}}$ coordinates ($\times {10}^7$ ) on the horizontal plane with $\hat{\mathrm{z}}$ coordinates displayed vertically.