ORBITAL DECAY ANALYSIS FOR DEBRIS DEORBITING CUBESATS IN LEO: A CASE STUDY FOR THE VELOX-II DEORBIT MISSION Sarat Chandra Nagavarapu(1), Amal Chandran(1), and Daniel E. Hastings(2) (1)Satellite Research Centre (SaRC), Nanyang Technological University, Singapore, 639798, Email: [email protected], [email protected] (2)Aeronautics & Astronautics Department, MIT, Cambridge, MA, USA, 02139, Email: [email protected] ABSTRACT Keywords: Space debris; LEO; orbital decay; debris re- moval; VELOX-II; CubeSat. Since the launch of Sputnik 1 into space in 1957, hu- mans have sent thousands of rockets and more than ten thousand satellites into Earth’s orbit. With hundreds of 1. INTRODUCTION more launched every year, in-space collisions and the creation of high-speed debris fragments are becoming in- creasingly likely, threatening future space missions. The Space debris is any man-made object in orbit about the term orbital debris comprises defunct satellites, spent up- Earth that no longer serves a useful function. The Earth per stages, fragments resulted from collisions, etc., which orbit is in serious danger caused by millions of these pose a significant threat to many other operational satel- space debris. Since the beginning of the space age, more lites in their vicinity. With the advent of satellite mega- than 10,680 satellites have been placed into orbit [1]. Out constellations in low Earth orbit (LEO), the LEO envi- of which 6,250 are still in the orbit and only 3,700 are op- ronment is becoming extremely crowded. In addition to erational, leaving an astonishing 2550 dead satellites in the government space organizations, several private space the orbit. Furthermore, more than 28,210 objects are cur- agencies are also investing heavily in space launches in rently being tracked and classified by the Space Surveil- LEO. Due to all these, the low earth orbits are getting lance Network (SSN). overpopulated, increasing the risk of collisions, which might set off a collision chain. Thus, it is necessary to There are over 34,000 pieces of space debris larger than monitor and remove space debris for the existence of fu- 10cm and more than 128 million pieces smaller than 1 ture space operations. From a commercial deployment cm in size. Furthermore, close to a million bits of de- and economic point of view, it is viable to use small bris between 1 cm and 10 cm are estimated to be orbiting satellites, especially CubeSats to perform this task, when the Earth [1]. The space objects in LEO travel at speeds compared to the deployment of large satellites. As the greater than 7 kilometers per second. At that speed, a orbital speeds in LEO are far greater than that of the little fleck of paint packs an equivalent punch of a 250- speeds in GEO, at more than 7 km/s, it is indeed essen- kilogram object travelling at 100 kilometers per hour. tial to track the debris and remove them. In this paper, Such impact damages critical components such as pres- we present the orbital decay analysis for a debris deorbit- surized items and solar cells besides creating new pieces ing CubeSat from LEO. We also aim to present the life- of potentially threatening debris. time analysis for 6U, 12U, and 27U CubeSats removing space debris under the effect of solar radiation flux F10.7 Thus, debris removal and collision avoidance are signif- cm, variable drag cross-sectional area, and drag coeffi- icant to ensure safe space exploration. A few methods cient. We also present a case study on the VELOX-II have been proposed to capture and remove space debris deorbit mission using a CubeSat equipped with a passive in the past decade. Ground and parabolic flight experi- deorbit device, a drag sail. VELOX-II is a 6U CubeSat ments are ongoing to test the efficiency of these methods. launched into a near-equatorial orbit at an altitude of 550 As humans launch more and more objects, these num- km, designed to demonstrate inter-satellite communica- bers are further going up and turning Earth’s orbits into a tion between a LEO and a GEO satellites, data downlink dangerous and crowded junkyard. To regulate space op- anywhere any time in orbit without passing the ground erations, all space organizations & industries are directed station, and precision navigation and fault-tolerant elec- to follow the 25-year safety lifetime standard for space- tronics. As VELOX-II is still orbiting the Earth post its craft, which states that all the satellites that are functional intended mission life, it is recommended to deorbit this in LEO, should lower their orbit and re-enter the Earth’s satellite within 25 years. Therefore, we explore and anal- atmosphere within 25 years of mission completion [2]. yse the feasibility of the CubeSat-based debris deorbit Therefore, removing or burning up this debris by deor- mission. For VELOX-II, orbital decay for various drag biting them is an essential task to facilitate future space surface area increments is analysed. missions. Proc. 8th European Conference on Space Debris (virtual), Darmstadt, Germany, 20–23 April 2021, published by the ESA Space Debris Office Ed. T. Flohrer, S. Lemmens & F. Schmitz, (http://conference.sdo.esoc.esa.int, May 2021) The remainder of the paper is organized as follows: Sec- Where D is the drag force, ρ is the atmospheric density, tion 2 briefly discusses the orbital decay analysis using v is the speed of the satellite in the orbit, A is its cross- the drag equation and the orbital period decay expres- sectional area perpendicular to the direction of motion, sion. It also analyses the effect of variation in solar flux, and Cd is the surface drag coefficient. By substituting drag surface area, and drag coefficient on LEO CubeSats. this drag force in Newton’s second law together with or- Section 3 presents the VELOX-II deorbit mission and the bital energy equations, we can derive an expression for design details of a deobiter CubeSat. This section also the change in the orbital period of the satellite with time. presents the orbital decay results obtained for the deor- The expression for the decay in orbital period ∆P due to biter CubeSat using various drag sails. Conclusions are atmospheric drag is given by: provided in Section 4. ∆P = −3 π h ρ (ACd=ms) ∆t: (2) Where P is the orbital period, h is the semi-major axis, 2. ORBITAL DECAY ANALYSIS FOR CUBESATS ∆t is the time step increment used for the simulation, and IN LEO ms is the mass of the satellite respectively. The MSISE- 00 [5] empirical model has been used to obtain the at- mospheric density in LEO, to compute the orbital decay. The lifetime or orbital decay of space debris depends on MSISE-00 is an empirical, global reference atmospheric three major parameters, namely solar radiation flux F10.7 model of the Earth from ground to space. was developed cm, the drag coefficient of the surface, and the drag sur- by Mike Picone, Alan Hedin, and Doug Drob [5]. face area. Therefore, for a satellite commissioned to deor- bit space debris, these parameters define its lifetime dur- The following sections emphasise the effects of the vari- ing reentry. Out of all the regions of space, low Earth or- ation in solar flux F10.7 cm, drag surface area, and drag bit (LEO) has higher debris density. With the increase in coefficient on satellite lifetime. Throughout this paper, day-to-day launches, the debris density is further grow- the term satellite lifetime refers to the lifetime of the satel- ing and eventually making some orbits unusable. Be- lite deorbiting with the captured debris object. sides, the in-orbit collisions might initiate a chain reac- tion and damage all the operating satellites in their vicin- ity. Therefore, debris removal from LEO using satellites 2.2. Effects of Solar Radiation Flux F10.7cm has become one of the important space missions nnowa- days To perform this prime task, it is recommended to use The solar radio flux at 10.7 cm is an important indicator smaller satellites than choosing larger satellites, to reduce of solar activity at a given time. Often called the F10.7 the design and launch costs. index, it is one of the longest-running records of solar activity by the NOAA, USA [6]. These radio emissions To address this issue, a miniature satellite design has been originate high in the chromosphere and low in the corona proposed in 1999, called a CubeSat [3]. CubeSats are of the solar atmosphere. The F10.7 correlates well with miniature satellites that have been used extensively in the sunspot number as well as a number of UltraViolet LEO for the last two decades. The CubeSat standard (UV) and visible solar irradiance records. It has proven and design was first proposed in 1999 by Jordi Puig- to be very valuable in specifying and forecasting space Suari of California Polytechnic State University and Bob weather. From the atmospheric drag model equations, an Twiggs of Stanford University, as primarily training tools increase in the F10.7 flux readings show an exponential for students to get acquainted with flight hardware de- decay in the satellite lifetime for a non-varying drag coef- sign, building, testing, and operations. They are built to ficient and drag surface area values. The F10.7 radiation standard dimensions of 10 cm x 10 cm x 10 cm, defined varies w.r.t. the Sun’s solar activity as per the 11-year as one U or a unit [40]. They can be 1U, 3U, 6U, 9U, 27U solar cycle, which is continuous with time.