## 2 The LEO Environment: Drag, Momentum Buildup (Aerospinning), and Meteoroids  
This section complements the technical designs of momentum transfer tethers in Section 1 with the discussion on physical specifics of the tether operations in the LEO environment. Tether lifetime and tether rotation speed stability will be quantified in the current Section. Engineers accustomed to the LEO mission design are familiar with the phenomenon of air drag. Air drag impacts much of the lifetime and requirements for propulsion for all LEO spacecrafts. However, often overlooked, is the rotation momentum imparted on the LEO tethers by air drag. The rotation momentum buildup (aerospinning) phenomenon is defined as self-sustained and self-limited prograde rotation of an object in orbit due to its interaction with the density gradient of the atmosphere. Intuitively, rotation torque appears as the lower portion of the tether encounters denser air. Therefore, the center of pressure is initially below the tether's center of mass. The diagram of forces resulting in aerospinning is shown in Figure 2. The smaller atmosphere density scale and longer tethers will result in the rotation momentum becoming significant. Such a mechanism always rotates a tether in prograde direction, resulting in the lower parts of the tether having progressively lower air velocities. As tether rotation speed increases, the center of pressure moves up until equilibrium rotation speed is reached with the center of pressure coincident with the center of mass. The unsteady process before reaching the equilibrium rotation speed may include libration and variable-speed rotation (as described by [PERSON] in [18]) and to call this \"spin-up\" is proposed by the author. The role of atmosphere in tether angular movement did not go unnoticed previously. In 1949 and 1972, [PERSON] [20] and [PERSON] [21], respectively, stated the theoretical possibility of self-sustained transverse  
Figure 2: The diagram of forces resulting in tether aerospinning. oscillations in tensioned tethers, if tangential airspeed exceeds the speed of the transverse waves in the tether. As a solution, [PERSON] [21] recommended providing separation between fundamental longitudinal and transverse frequencies to avoid large-amplitude cross-coupled oscillations induced by airflow. In 2004, [PERSON] [22] simulated the spin-up of tethers due to interaction with the planetary atmosphere, although only for transient interaction during the aero-capture. In 1997, [PERSON] [23] also demonstrated that tethers may be rotated by the transient interaction with the atmosphere. Overall, members of the research community to date have acknowledged the possibility of tether rotation initiation because of the interaction with the airflow, but failed to see the self-limiting nature of such a rotation, and the principal role of the atmospheric density gradient in initiating and sustaining a rotation. Both, air drag and air-induced torque, are dependent on the ratio between spacecraft (tether) unit mass and cross-sectional area. For unity surface divided by mass, both, drag and momentum have an associated characteristic time. These are: time to reentry for air drag, and steady angular speed divided by initial angular acceleration for air-induced momentum (called a characteristic spin-up time in Figure 5). The author has simulated normalized (1 kg weight and 1 m\({}^{2}\) ram area tethers) reentry and spin-up times using the numerical integration in conjunction with the MSISE-90 atmospheric model. The simulation results of reentry time and aerospinning steady-state tip speed are presented in Figures 3 and 4, respectively. For the lower atmosphere (below 400 km) it was found that the characteristic spin-up time to reentry time ratio is close to 1000, but tends to decrease in the upper atmosphere. Such a large \"drag-to-spin\" ratio indicates what spin-up phenomenon will manifest itself only after several orbital re-boosts, if re-boosting force is applied to the center of mass.