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 be- ginning 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 com- ponent 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 perma- nently 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 num- ber 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 oblate- ness of Earth. These simplified methods are shown to be very useful to understand how orbit perturbations should be exploited. Numerical results presented the simula- tion of satellite motion till satellite re-entry. Low Earth orbiting satellites experience orbital decay and have physical life- times 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