# Performance Estimate of a Spin-Stabilized Drag Sail for Spacecraft Deorbiting
## 1 Introduction  
The number of satellites in geocentric orbit has grown continuously since the dawn of the space exploration era. This growth has further strengthened over the past two decades as, in addition to traditional large spacecraft, small and medium-sized satellites have become increasingly numerous, mainly due to significant technological advances in miniaturization and component integration [1, 2, 3]. The employment of small satellites provides significant cost reductions, mainly due to the use of standardized commercial components and the ability to be launched as a secondary payload, which has allowed nations with limited technical and financial resources and even universities access to space [4, 5, 6, 7], thus significantly increasing the number of launches [8, 9, 10]. [PERSON] and [PERSON] [11] were the first to highlight the problem of space crowding and to estimate the risk of impact with space debris in low Earth orbit (LEO). A possible cascading effect due to the creation of new uncontrolled debris with each collision was also hypothesized, and this scenario is now known as the \"[PERSON] syndrome\". Subsequent and more in-depth analyses confirmed that this problem needs to be addressed appropriately [12, 13, 14]. The first strategy to be adopted is debris mitigation, which means to avoid creating new debris by properly disposing of satellites that are no longer operational. To better address this issue, a special Inter-Agency Space Debris coordination Committee (IADC) was created, which proposed a guideline according to which a satellite should be able to deorbit (or fit into a graveyard orbit) within 25 years after the end of its operationalphase [15; 16]. However, the IADC guidelines are not mandatory, and even if they were universally adopted, the problem of space crowding would still require further actions [17]. In this regard, ESA's Space Safety Program (former Space Situational Awareness program) has been proposed to prevent collisions between working satellites [13; 18] and facilitate active debris removal to reduce its density in the most crowded orbital belts [19; 20; 21; 22]. In addition to this, some agencies are currently proposing stricter guidelines for end-of-life spacecraft disposal. Notably, the U.S. Federal Communication Commission has reduced the 25-year limit of IADC to only 5 years. As part of this problem, systems that can enable a spacecraft to rapidly decay from LEO orbits are receiving increasing attention. In particular, due to the large number of small and medium-sized spacecraft that are not equipped with a propulsion system or do not have enough propellant to deorbit by conventional methods, propellantless deorbiting systems are becoming very attractive [23; 24]. Among them, it is worth mentioning electrodynamic tethers [25], which exploit the interaction between an electric current and the Earth's magnetic field to generate a drag force, and plasma brake systems [26; 27], which exploit the electrostatic interaction between a negatively charged tether and charged particles in the ionosphere and which will be tested in the near future [28; 29]. An additional class of deorbiting systems that do not exploit any propellant are drag-enhancing devices [30; 31; 32], whose principle of operation is to increase the area-to-mass ratio of the spacecraft, thereby generating more atmospheric drag which reduces its altitude until reentry into the atmosphere. The most representative sample of this class is the drag sail. The latter consists of a thin membrane that is deployed by a spacecraft after the conclusion of its operational life, with the objective of exposing a large surface area to atmospheric particle flux, thereby reducing the satellite's orbital velocity. A significant advantage of drag sails lies in the fact that they are similar, in architecture, structural elements, and deployment mechanisms, to solar sails.