- Date:03 Dec 2019
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The atmospheric drag reduces the orbital energy of the rocket bodies and. lowers the orbit until re entry occurs Lunisolar perturbations speed up or. slow down this process by changing the eccentricity of the orbit and raising or. lowering the perigee altitude which in extreme cases results in direct re entry. without drag induced decay The re entry of spent rocket bodies is desirable. because the de orbiting of these uncontrolled bodies prevents collisions with. functional spacecraft and potential generation of new space debris However. the re entry poses a risk to the Earth s population because rocket bodies. consist of components likely to survive the re entry and impact the Earth s. surface such as propellant tanks 1 Therefore to be able to mitigate any. risks due to de orbiting the re entry of rocket bodies needs to be predicted. The major source of error in orbit prediction is the computation of the. atmospheric drag 2 The perturbing acceleration due to drag r drag depends. on the spacecraft s drag coefficient Cd area to mass ratio A m velocity. with respect to the atmosphere v and the atmospheric density. r drag Cd v 2 1, The drag coefficient and the effective area to mass ratio depend on the ob. ject s attitude which is generally uncertain The local atmospheric density. on the other hand depends on the solar and geomagnetic activity for which. future values are unknown 3 4 In addition the drag calculation is subject. to inaccuracies in the atmospheric density model and possible mis modeling. of the drag coefficient 1 Finally the velocity with respect to the atmosphere. is uncertain because the local wind speed is unknown. For state of the art re entry prediction the accuracy of atmospheric den. sity calculations can be improved by calibrating the density models using. near real time satellite tracking data 5 6 7 In addition the effective area. can be computed by performing six degrees of freedom 6DoF propagation. to calculate the attitude of the rocket body 8 Moreover using the attitude. and a physical model of the rocket body the drag coefficient can be computed. 8 9 Furthermore a wind model can be used to compute the horizontal. wind speeds in the atmosphere 10, When density correction models and 6DoF propagation techniques are not. available e g because the object details are unknown or the measurements. necessary for density corrections are unavailable the drag coefficient Cd. and area to mass ratio A m can be combined into one parameter called the. ballistic coefficient BC Cd A m that can be estimated from orbital data. Such an estimated BC depends on the actual Cd and area to mass ratio but. also soaks up atmospheric density model errors and possibly other errors e g. orbital data inaccuracies More accurate orbital data and dynamical models. therefore result in estimated BCs that are closer to the true BC 6. The application of highly accurate models and orbital data is required for. accurately predicting the impact point of re entering objects Sufficiently. accurate orbital data is however often not available and Two Line Element. sets TLEs provided by the United States Strategic Command are the only. available data to perform re entry prediction The accuracy of TLE data. is however limited due to the application of simplified perturbation models. SGP4 and SDP4 11 12 especially for objects in GTOs 13 14 and in. orbits with high energy dissipation rates 15, In this paper the re entry prediction of rocket bodies in eccentric orbits. based on only TLE data is assessed Because attitude and density correction. data are not directly available from TLEs the predictions are carried out us. ing 3DOF propagation and a standard empirical atmospheric density model. Different methods have been developed in the past to improve TLE based re. entry prediction by preprocessing TLE data and by estimating the BC solar. radiation pressure coefficient SRPC object state vector or a combination. of these In this paper re entry predictions using only an estimate for the. BC are investigated This approach is straightforward and can be used to. obtain a first order guess of the re entry date several weeks or months before. re entry when accurate prediction of the impact point is not feasible due to. uncertainties in future space weather predictions In addition re entry pre. dictions using only BC estimates can easily be automated to perform daily. predictions for many objects Within this assumption only BC estimation. the goal of this paper is to provide guidelines on how to estimate the BC to. obtain the most accurate re entry predictions, Ballistic coefficient estimation For the estimation of the BC based on. TLEs several methods have been developed 16 17 18 19 20 Saunders et. al 17 and Sang et al 18 estimate the BC by comparing the change in. semi major axis according to TLE data with the change in semi major axis. due to drag computed by propagation using an initial state from TLEs This. method is straightforward and uses semi major axis data from TLEs which. are generally accurate The methods by Saunders and Sang are almost equiv. alent the main difference is that Sang computes a single BC estimate directly. where Saunders finds improved estimates by iteration Gupta and Anilkumar. 20 on the other hand estimate the BC by minimizing the difference be. tween apogee and perigee altitudes according to TLEs and propagation This. method is said to perform well for re entry prediction during the last phase. of orbital decay It is however more complex and requires the use of the. eccentricity from TLEs which is generally less accurate than semi major axis. data A method for estimating both the BC and initial eccentricity was de. veloped by Sharma et al 16 to improve re entry prediction of upper stages. in GTO 21 22 23 Here the eccentricity and BC are estimated by fitting. the apogee altitude according to propagation to TLE apogee data using the. response surface methodology Finally Dolado Perez et al 19 developed a. method for estimating the BC and SRPC simultaneously This is carried out. by comparing the rate of change of the semi major axis and eccentricity ac. cording to TLE data and propagation The method assumes that the change. in semi major axis is due to both drag and SRP which should improve the. BC estimate However again less accurate eccentricity data from TLEs are. used for the estimation In addition because the eccentricity is strongly af. fected by lunisolar perturbations the changes in eccentricity due to drag and. SRP are hard to observe Finally the methods by Sharma et al 16 and. Gupta and Anilkumar 20 estimate a single BC that is used for the purpose. of re entry prediction Saunders Sang and Dolado Perez on the other hand. estimate multiple BCs and subsequently take a statistical measure of the set. as final estimate, It should be noted that all these methods estimate a single i e fixed.

ballistic coefficient In reality the BC however varies over time due to e g. rotation of the object or changes in Cd due to altering atmospheric conditions. Efforts can be made to predict the future variation of the BC 24 or assume. a relation between the drag coefficient and the orbital regime 25 but this. is beyond the scope of this paper, State estimation To obtain an accurate state of the object for re entry. prediction state estimation can be carried out by orbit determination using. pseudo observations derived from TLE data This approach is widely used. and is described by e g Levit and Marshall 26 Vallado et al 14 and. Dolado Perez et al 19 In this paper state estimation will only be utilized. for comparison, TLE preprocessing TLE data is used for estimating the BC and state. of an object however the quality of TLEs associated with an object is not. homogeneous sometimes low quality or even wrong TLEs are distributed. For this reason preprocessing of TLEs is needed to identify outliers and. TLEs of poor quality 27, TLE based re entry prediction approach The goal of this paper is to. obtain accurate re entry predictions of decaying GTO rocket bodies using. only an estimate for the BC and irrespective of TLE quality and availability. This is achieved by TLE preprocessing see Lidtke et al 27 and enhancing. the BC estimation for the purpose of re entry prediction The main contri. butions of this work are, The estimation of the BC is tailored for re entry predictions by compar. ing the decay of the mean semi major axis according to TLE data and. according to a high fidelity propagator considering all perturbations. The impact of the initial state used for BC estimation on the re entry. prediction is shown, The performance of the method is assessed and improved based on.

predicting the re entry dates of 101 upper stages in highly eccentric. orbits all initially in GTO and the sources of inaccurate predictions. are analyzed, The good performance of using a single BC estimate versus the use of. a median BC estimate and versus BC and state estimation is shown. Because the considered rocket bodies are in highly eccentric orbits all rele. vant perturbations geopotential lunisolar drag and SRP are always con. sidered during orbit propagation, The methods used in this approach are discussed in the following section. After that the BC estimation and re entry prediction results using a single. and multiple BC estimates is discussed, The orbital propagator and BC and state estimation and TLE preprocessing. methods used for TLE based re entry prediction are discussed in the follow. 2 1 Propagation method, The orbital propagator used in this study is the Accurate Integrator for. Debris Analysis AIDA a high precision numerical propagator tailored for. the analysis of space debris dynamics using up to date perturbation models. AIDA includes the following force models 28 geopotential acceleration com. puted using the EGM2008 model 10x10 atmospheric drag modeled using. the NRLMSISE 00 air density model solar radiation pressure with dual cone. shadow model and third body perturbations from Sun and Moon. NASA s SPICE toolbox1 is used both for Moon and Sun ephemerides. DE405 kernels and for reference frame and time transformations ITRF93. and J2000 reference frames and leap seconds kernel Solar and geomagnetic. activity data F10 7 and Ap indexes are obtained from CelesTrak2 and Earth. orientation parameters from IERS3 A wind model is not used because the. effect of wind generally cancels out over one orbital revolution 29 and the. impact of neglecting wind is small compared to the effect of inaccuracies in. atmospheric density modeling,2 2 Ballistic coefficient estimation method.

The approach used for the estimation of the BC is based on the method. for deriving accurate satellite BCs from TLEs proposed by Saunders et al. 17 Several modifications were made to improve the method for the re. entry prediction purpose The BC estimation algorithm uses the data of. two TLEs The BC is estimated by comparing the change in semi major. axis according to two TLEs to the change in semi major axis due to drag. computed by accurate orbit propagation using an initial state derived from. the first TLE4 Since short periodic changes are removed from TLE data the. change in semi major axis according to TLEs can be assumed to be purely. the secular change caused by atmospheric drag5 Therefore any difference. between the change in semi major axis according to TLE data and due to. https naif jpl nasa gov naif index html,http www celestrak com SpaceData sw19571001 txt. ftp ftp iers org products eop rapid standard finals data. If not stated otherwise states are obtained from TLEs using SGP4 to convert the. TLE to an osculating state at the desired epoch and subsequently converting the state. from the TEME to J2000 reference frame, Long periodic variation of semi major axis due to gravitational terms and SRP may. be included in TLE data but are generally small compared to changes due to drag 30. drag computed by orbit propagation can be assumed to be caused by a wrong. guess for the BC The BC that gives the correct change in semi major axis. is obtained as follows, 1 Compute the change in semi major axis between the two TLEs aTLE. using the mean mean motion no available in a TLE,aTLE aTLE2 aTLE1 3. 2 Take guess for value of the BC, 3 Propagate the orbit with the full dynamical model between the two.

TLE epochs and simultaneously compute,2 frdrag e sin ftdrag 4. dt drag p r, where p is the semi latus rectum the true anomaly and frdrag and. ftdrag the acceleration due to drag in radial and transverse direction. respectively,4 Integrate da, over time to obtain the change in semi major axis due. to drag only aPROP,aPROP dt 5,TLE1 dt drag, 5 Update the BC estimate value using the Secant method. BCn 1 BCn 2,BCn BCn 1 aDIFF BCn 1,aDIFF BCn 1 aDIFF BCn 2.

where BCn is the nth BC estimate and aDIFF aTLE aPROP. 6 Repeat the procedure from step 3 until convergence is reached. The first guess BC1 for this method is taken from the B of the first TLE. The B parameter in TLEs is an SGP4 drag like coefficient and a BC value. can be recovered from it BC 12 741621 B 31 The second guess BC2. needed for the Secant method is computed by performing one propagation. using the first guess and assuming a linear relation between the BC and. The convergence criterion is met when aDIFF is less than 10 4 km

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