Analysis and Prediction of Tiangong-1 Reentry

ANALYSIS AND PREDICTION OF TIANGONG-1 REENTRY

IHARKA SZUCS-CSILLIK¨ Astronomical Institute of Romanian Academy, Astronomical Observatory Cluj-Napoca Str. Cires¸ilor 19, 400487 Cluj-Napoca, Romania Email: [email protected]

Abstract. Chinese officials confirmed in 2016 that they had lost control of they first space station Tiangong-1 and it would crash to Earth at the end of 2017 or in the beginning of 2018. The researchers can not say exactly the decaying data, because the artificial satellite’s motion depend from many parameters. The motion of the satellite proceeds in the field of action of various forces that are shaping its trajectory. The most important perturbation is due to the force of gravitation, then the atmospheric drag is the major enemy of the satellite. The other major perturbation to the orbit of a near satellite is the effect of the earth’s oblateness, which causes the orbital plane of the satellite to rotate about the earth’s axis. The simplest equations of motion are given to specify the evolution of the Tiangong-1 satellite orbit under the action of atmospheric drag and effect of oblateness of Earth. Numerical results presented the simulation of satellite motion till satellite collapses on Earth, emphasizing how difficult is to predict the moment and the location of the Tiangong-1 space debris fall.

Key words: space debris, space station, artiﬁcial satellite, trajectory.

1. INTRODUCTION

Tiangong-1 (”Heavenly Palace”) is China’s first prototype space station. The China National Space Administration (CNSA) designed Tiangong-1 as an 8506 kg space-laboratory module, capable of supporting the docking of manned and autono- mous spacecraft. Launched unmanned aboard a Long March 2F/G rocket from Jiuquan Satellite Launch Center, China (JSC) on 29 September 2011, it is the first operational component of the Tiangong program. In 2012 and 2013 Chinese astronauts made short visits to the station (Fig. 1). A space station is a spacecraft capable of supporting crewmembers, which is designed to remain in space for an extended period of time and for other spacecraft to dock. The first space station was Salyut-1, which was launched by the Soviet Union on April 19, 1971. Like all the early space stations, it was monolithic, intended to be constructed and launched in one piece, and then inhabited by a crew later. Unlike previous stations, the Soviet space station Mir (1986-2001) had a modu- lar design, This method allows for greater flexibility in operation, as well as removing

Romanian Astron. J. , Vol. 27, No. 3, p. 241–251, Bucharest, 2017 242 Iharka SZUCS-CSILLIK¨ 2

Fig. 1 – Tiangong-1, artist’s illustration.

Table 1 Operational ISS Satellites. Name Int’l Code NORAD ID Lunch Date Period ISS 1998-067A 25544 Nov. 20, 1998 93 Tiangong-1 2011-053A 37820 Sep. 29, 2011 90.2 Tiangong-2 2016-057A 41765 Sep. 15, 2016 92.3 the need for a single immensely powerful launch vehicle. Around the Earth currently three space stations are in orbit: the International Space Station (ISS), which is permanently inhabited, the Tiangong-2, not permanently inhabited, and the Tiangong-1 (defunct) (see Table 1). Today’s space stations are research platforms, used to study the effects of long- term space flight on the human body as well as to provide platforms for greater number and length of scientific studies than available on other space vehicles. In the space are other ”space stations”, which are modules (ex: DRAGON CRS-13, POISK, etc.) as component or spaceflights (exp: SOYUZ MS-06, SOYUZ MS-07, etc.) Tiangong-1 was initially projected to be deorbited in 2013. It remained ac- tive until March 2016, when Chinas space agency reported that the ships service had ended. In December 2017 it is in a decaying orbit. It will be replaced over the follow- ing decade by the larger Tiangong-2 and Tiangong-3 modules. The China Manned Space Engineering Office published a brief description of the larger Tiangong-2 and its successor Tiangong-3 in 2008, indicating that at least two crewed spaceships would be launched to dock with Tiangong-2. The first Chinese space laboratory module is Tiangong-1, launched on a critical test flight to demonstrate the vital docking technology required for a future space station. The Tiangong-1 space lab served as a space station module prototype for 3 Analysis and prediction of Tiangong-1 reentry 243

China, which is the third country (after Russia and the United States) to develop the capability to launch astronauts into space and return them safely to Earth. Satellite Tiangong-1 is 10.4 m long and has a maximum diameter of 3.4 m. The spacecraft features two modules: a resource module with fuel tanks, solar panels for power, and an experiment module with an effective volume of 15 m3 (enough volume for three astronauts to live and work). Tiangong-1 was visited by a series of Shenzhou spacecraft during its two-year operational lifetime. The first of these, the unmanned Shenzhou 8, successfully docked with the module in November 2011, while the manned Shenzhou 9 mission docked in June 2012. A third and final mission to Tiangong-1, the manned Shenzhou 10, docked in June 2013. The manned missions to Tiangong-1 were notable for in- cluding China’s first female astronauts, Liu Yang and Wang Yaping, and other male taikonauts (Chinese astronauts). Amateur satellite watchers discovered in 2016 that the Tiangong-1 space station was actually out of control, it became a space debris. Last September, the Chinese conceded they hadd lost contact with it and they predicted Tiangong-1 would fall from orbit between early January and late February 2018 (David, 2017). Tiangong-1 orbits from west to east, taking about 4 minutes to cross the sky. We can see from Romania the motion of Thiangong-1 satellite (space debris). Only a few weeks longer to see it in the nighttime sky, where it can shine a little better than first magnitude on good passes (see Peat (2017)). It is big as a school bus. Some spacecraft are equipped with rockets so ground controllers can control the re-entry point, but Tiangong-1 is not. That makes it impossible to predict exactly where it will fall even shortly before reentry. In the last few decades, the amount of space debris has dramatically increased (due to the artificial satellites), and this trend is expected to continue in the near future (see Hubaux et al. (2012)). Furthermore, there is a real risk that objects in space orbiting about the Earth might collide (For example, since everything moves at thousands of miles an hour, a paperclip can smack into a satellite with more energy than a heavy machine gun round.). Therefore, the scientists works on the clean up our space junk. The simplest equations of motion are given to specify the evolution of the Tiangong-1 satellite orbit under the action of atmospheric drag and effect of oblateness of Earth. These simplified methods are shown to be very useful to understand how orbit perturbations should be exploited. Numerical results presented the simulation of satellite motion till satellite re-entry. Low Earth orbiting satellites experience orbital decay and have physical lifetimes determined almost entirely by their interaction with the atmosphere. Prediction of such lifetimes or of a re-entry date is of great interest to satellite planners, users. 244 Iharka SZUCS-CSILLIK¨ 4

2. THE DECAYING ORBIT OF THE TIANGONG-1 SATELLITE

The motion of the satellite proceeds in the field of action of various forces that are shaping its trajectory. The most important among them is the force of gravitation, which comes mainly from the attraction of Earth. For this reason, we are taking into account the terms of the Earth’s gravitational potential up to c40 for zonal harmonics and c31, s31 for tesseral harmonics. The other major perturbation for an artificial satellite near to the Earth (in our case about 300 km altitude over the Earth’s surface) is the atmospheric drag (Izsak,´ 1959). Moving in a resistance medium (atmosphere, which is not have an ideal spheroidal structure), the satellite consumes a part of its kinetic energy and loses from its velocity too. Since the greatest retardation occurs in the vicinity of the perigee (the largest velocity variations), there is producing a change in the shape and in the dimensions of the orbit (the perigee distance will have a slower variation as the apogee distance, the orbit slowly will have a circular shape). A great number of studies is devoted to the problem of atmospheric drag. In this article we will take the simplest perturbation due to the atmospheric drag. Other perturbations on the artificial satellite is the effect of the solar and lu- nar attraction, the effect of the solar radiation pressure. Other possible sources of disturbance can be the effect of the Earth’s magnetic field, the effect of the elec- trostatic field existing in the ionosphere, the effect of the radiation reflected from the Earth, the collisions with micrometeorites, the relativity effect, etc. (see Kozai (1959); Zhongolovich (1966); Roy (1988); Szucs-Csillik¨ et al. (2014)). These factors produce minimal effects in our case, and their influence on the results are insignificant (Zielinski,´ 1968; Brito et al., 2015). Let us take a coordinate system x, y, z with origin in Earth’s center. We are con- sidering perturbation due to the oblateness of Earth and to the atmospheric drag. The differential equations of satellite motion in rectangular coordinates have the form:

d2x ∂U = , (1) dt2 ∂x d2y ∂U = , dt2 ∂y d2z ∂U = , dt2 ∂z where

U = U00 + U20 + U22 + U30 + U31 + U40 + UA, (2) 5 Analysis and prediction of Tiangong-1 reentry 245 where the particular terms are respectively µ U = , (3) 00 r 1 3z2 1 U = µR2c · − , 20 2 20 r5 r3 x2 − y2 2xy U = 3µR2 c + s cos2s + 22 r5 22 r5 22 2xy x2 − y2 + c − s sin2s r5 22 r5 22 1 5z3 2z U = µR3c · − , 30 2 30 r7 r5 3 5xz2 x 5yz2 y U = µR3 − c + − s coss + 31 2 r7 r5 31 r7 r5 31 5yz2 y 5xz2 x + − c − − s sins r7 r5 31 r7 r5 31 1 35z4 30z2 3 U = µR4c · − + , 40 8 40 r9 r7 r5 1 ρC A U = − D v v , (4) A 2 m r r where µ is the gravity constant multiplied by the Earty’s mass (in our case µ = 1.4349708 Mm3/min2), r is the distance from the center of mass, R is the equa- −8 torial radius of the Earth (R = 6.378165Mm), c20 = 0.0010827, c22 = 89 · 10 , −8 −8 −8 s22 = −195 · 10 , c30 = −0.0000025, c31 = 315 · 10 , s31 = 149 · 10 , c40 = 16 · 10−7 are zonal and tesseral coefficients, s is the argument of latitude, and ρ is the atmospheric density, CD is the drag coefficient, A is the cross sectional area of the satellite perpendicular to velocity vector, m is the mass of satellite and vr is the satellite velocity vector relative to atmosphere. We consider the simple exponential atmospheric model r − r ρ = ρ exp( p ), (5) p H where ρp is the density at initial perigee point, rp is the initial distance of satellite from Earth’s surface, H is scale height. Let notate with B = m the Ballistic CDA coefficient, and we assume that the atmosphere rotates at the same angular speed as Earth. Then the relative velocity vector is

vr = v − ω × r, (6) where ω is the initial rotation vector of the Earth around z axis with ωe = 7.292115486· −5 10 rad/sec. The relative velocity vector is vr = [vx + ωey,vy − ωex,vz]. The 246 Iharka SZUCS-CSILLIK¨ 6 drag coefﬁcient depends on the satellite’s shape (see Minzner (1976); Bowman et al. (2005); Cook (1963, 1965); McLaughlin et al. (2011); Vallado (2004); Chen et al. (2010); Xu et al. (2011)). The satellite’s equations of motion, Eq. (1), explicitly can be written as dx dy dz = v , = v , = v , (7) dt x dt y dt z

dv µx µR2c 3x 15xz2 µR3c 15xz 35xz3 x = − + 20 − − 30 − − dt r3 2 r5 r7 2 r7 r9 2c x 5c x(x2 − y2) 2s y 10s x2y − 3µR2 cos2s 22 − 22 + 22 − 22 + r5 r7 r5 r7 2c y 10c x2y 2s x 5s x(x2 − y2) + sin2s 22 − 22 − 22 + 22 − r5 r7 r5 r7 3µR3 5z2 35z2x2 1 5x2 − coss c − − + + 2 31 r7 r9 r5 r7 5xy 35xyz2 5xy 35xyz2 + s − + sins c − − 31 r7 r9 31 r7 r9 5z2 35x2z2 1 5x2 µR4c 210xz2 − s − − + − 40 − 31 r7 r9 r5 r7 8 r9 4 2 2 2 1 315xz 15x ρ((v + ω y) + (v − ω x) + v ) 2 − − − x e y e z (v + ω y), r11 r7 2B x e dv µy µR2c 3y 15yz2 µR3c 15yz 35yz3 y = − + 20 − − 30 − − dt r3 2 r5 r7 2 r7 r9 2c y 5c y(x2 − y2) 2s x 10s xy2 − 3µR2 cos2s − 22 − 22 + 22 − 22 + r5 r7 r5 r7 2c x 10c xy2 2s y 5s y(x2 − y2) + sin2s 22 − 22 + 22 + 22 − r5 r7 r5 r7 3µR3 5xy 35z2xy − coss c − + 2 31 r7 r9 5z2 35y2z2 1 5y2 5xy 35xyz2 + s − − + + sins s − + − 31 r7 r9 r5 r7 31 r7 r9 5z2 35y2z2 1 5y2 µR4c 210yz2 − c − − + − 40 − 31 r7 r9 r5 r7 8 r9 4 2 2 2 1 315yz 15y ρ((v + ω y) + (v − ω x) + v ) 2 − − − x e y e z (v − ω x), r11 r7 2B y e 7 Analysis and prediction of Tiangong-1 reentry 247

dv µz µR2c 9z 15z3 µR3c 30z2 35z4 3 z = − + 20 − − 30 − − + dt r3 2 r5 r7 2 r7 r9 r5 5c z(x2 − y2) 10s xyz 10c xyz + 3µR2 cos2s 22 − 22 + sin2s − 22 + r7 r7 r7 5s z(x2 − y2) 3µR3 15xz 35z3x + 22 − coss c − + r7 2 31 r7 r9 15yz 35z3y 35yz3 15yz + s − + sins c − + − 31 r7 r9 31 r9 r7 15xz 35xz3 µR4c 350z3 315z5 75z − s − − 40 − − − 31 r7 r9 8 r9 r11 r7 2 2 2 1 ρ((v + ω y) + (v − ω x) + v ) 2 − x e y e z v , 2B z where p r = x2 + y2 + z2. Using the two line elements (a = 6.663 km - semi-major axis, e = 0.0019523 - eccentricity, i = 42◦.7542 - inclination, Ω = 114◦.7038 - right ascension of the ascending node, ω = 348◦.1819 - argument of perigee, M = 110◦.8534 - mean anomaly) from December 22th (12:28:36 UT), 2017 (see Kelso (2017)), we numer- ically investigated the trajectory of Tiangong-1 satellite for 80000 minutes (see Fig. 2).

Fig. 2 – Tiangong-1 orbit (three dimensional) for 60000 minutes and before the re-entry.

The check of orbital data shows that Tiangong-1 has been slowly dropping from its roughly 360 kilometer altitude at the beginning of 2017 to roughly 300 kilometers 248 Iharka SZUCS-CSILLIK¨ 8 at the end of 2017 (see Kelso (2017)). The ﬁgures 3 report decay predictions and altitude (both perigee and apogee).

Fig. 3 – Tiangong-1 perigee and apogee value (www.satﬂare.com).

According to the analysis of the orbital elements gathered during the last months, the re-enter may accour in February 2018 (20%), in March 2018 (60%) on in April 2018 (20%) (see Fig. 4).

Fig. 4 – Tiangong-1 decay predictions (www.satﬂare.com).

Using two-line element (TLE) data, and the numerical integration of the presented equations of motion we can say that the reentry possible occur around the end of February 2018, after about 80000 minute from January 1, 2018. In Fig. 5 one can see the variation of perigee and apogee distance in megameter versus time (minutes), the perigee distance decreases from roughly 275 km in January at 180 km at the end of February. Investigations of other satellite reentry shows that 9 Analysis and prediction of Tiangong-1 reentry 249 for satellite reentry the perigee altitude target is approximately 100-150 km. When a satellite reaches this target altitude, then after 600-1000 seconds, it will collide with Earth (see Colombo et al. (2014); Brito et al. (2015)). The moment depends from local circumstances (atmosphere, elevation of terrain, etc.) too.

Fig. 5 – Tiangong-1 re-entry (estimated perigee-apogee distance)

Consequently, the location area of the collaps can not be estimated now, even- tually few days before, because a very small perturbation can change the trajectory of the satellite.

3. CONCLUSIONS

The Tiangong-1 space station (space debris) reentry can not be predicted exactly. What is known is that the vehicle will reenter somewhere between 43◦ North and 43◦ South latitude. Using two-line element (TLE) data, and our numerical integrator we can say that the Tiangong-1 reentry can occur around late of February 2018. Atmospheric drag play a role in speeding up or slowing down reentry for satellites in low-Earth orbit. The space station is set to burn up in Earth’s atmosphere during its fall from orbit. Due to the relatively large size of the object, it is expected that there will be many pieces reentering together, some of which may survive reentry and land on the Earths surface. 250 Iharka SZUCS-CSILLIK¨ 10

Acknowledgements. The author thank colleagues Dr. Vlad Turcu and Dr. Tiberiu Oproiu for their comments and useful suggestions. I also thank Dr. T.S. Kelso to provide information on satellite tracking and orbital elements. This work was supported by a grant of the Ministry of National Education and Scientiﬁc Re- search, RDI Programe for Space Technology and Avanced Research - STAR, project number 513.

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Received on 8 January 2018