TIGRISAT Orbital MotionSimulation and Analysis

Transcription

1 TIGRISAT Orbital MotionSimulation and Analysis Mohammed Chessab Mahdi *1 *1 Faculty of Engineering University of Kufa Iraq *1 Abstract- Satellite orbit simulation and analysis based on data collected from NASA/ North American Defense Command (NORAD) as a Two Line Elements (TLE) files is presented. General Mission Analysis Tool (GMAT) is used to simulate the orbital motion of TIGRISAT. The analysis includes orbit determination and prediction of satellite s position and velocity, satellite tracking, and command summary. Orbital path of the TIGRISAT projected onto a two-dimensional world map over some time for one and two revolution of the satellite is plotted. Keywords- Orbit Determination; Mission Planning; NORAD; TLE; SGP4; TIGRISAT; GMAT; KufaSat; Satellite Tracking I. INTRODUCTION Most satellite missions planning required tracking and orbit determination. To track satellite through space it is needed to determine the position and velocity of the satellite in the orbit now and later.satellite orbit determination estimates the position and velocity of an orbiting object from discrete observations which includes external and internal measurements, external measurements from terrestrial radar and electro-optical sensors and internal measurements from sensors and devices which are installed on the satellite itself. Finding the spacecraft position at any time is a requirement for a satellite mission planning. There are two commonly proposed solutions for finding orbital position,the first is, position estimated from a Two-Line Element (TLE) set using Simplified General Perturbations (SGP4) propagator. TLE are two lines of text data that are frequently issued to the public free of charge, and contain the latest orbital parameters of a satellite. SGP4 model predicts the effect of perturbations caused by the Earth s shape, drag, radiation, and gravitation effects from other bodies such as the sun and moon. It is mathematical model used to calculate orbital state vectors of satellites relative to the Earth-centered inertial coordinate system. The SGP4 model takes TLE as the input for the orbit prediction. The second is, Global Positioning System (GPS).In spite ofhigh power consumption of GPS receiver [1] the use of this receiver to obtain position, velocity, and time solution should therefore likely satisfy the orbital knowledge requirements for virtually any Low Earth Orbit (LEO)satellite. Accurate position determination is accomplished using a low-cost commercial GPS receiver that has been modified to work in low Earth orbit [2]. The combination of both solutions leads to a rising accuracy and reliability because if one solution fails, it can still use the information of the other system to complete the mission. The purposes of this work are, first,simulation and analysis TIGRISAT sorbitbased on data collected from NASA/ NORAD TLE files. TIGRISAT is an Iraqi 3U CubeSat built by Iraqi students at the La Sapienza University of Rome with a mission to detect dust storms over Iraq. TIGRISATLaunched in June 19, It transmits images to two ground stations, one located in Rome and another in Baghdad [3]. Secondusing the results of simulation and analysis TIGRISAT s orbitin KufaSat mission planning. Kufasat is an Iraqi student satellite project sponsored by the University of Kufa. The main tasks for Kufasat will be to imaging purposes. It is 1U cubesat with 1.5 m long gravity gradient boom, which will be used for passive attitude stabilization and will be flying in Low Earth Orbit(LEO)with 600 km altitude [4]. II. BACKGROUND Orbits are defined by a set of six elements which aremathematical parameters used to completely describe the motion of a satellite within an orbit andenable us to accurately describe orbit s shape, orbit s size, orbit s orientation, and spacecraft s location. These elements are also called Keplerian Elements. Knowingthese elements allow satellite tracking programs to calculate a satellite's position in space at a specific time.these elements are [5]: Eccentricity (e): This element defines the shape of the orbit the value of eccentricity ranges from 0 when the orbit is a perfect circle to 1 when the orbit is very flat. Semi major axis (a): This defines the size of the orbit.it is the distance between apogee and perigee divided by two. Inclination angle (i): This element defines the orientation of the orbit with respect to the Earth s equator.this element tells you what the angle is between the equator and the orbit when looking from the center of the Earth. If the orbit went exactly around the equator from left to right, then the inclination would be 0. The inclination ranges from 0 to 180 degrees. Right Ascension of Ascending Node (Ω) : This is probably one of the most difficult of the elements to describe.it defines the location of the ascending and descending orbit locations with respect to the Earth's equatorial plane. The ascending node is the place where the satellite crosses the equator while going from the Southern Hemisphere to the Northern Hemisphere. 1

2 Argument of Perigee (ω): Since an orbit usually has an elliptical shape, the satellite will be closer to the Earth at one point than at another. The point where the satellite is the closest to the Earth is called the perigee and the furthest from the Earth is called the apogee. Argument of perigee defines where the low point, perigee, of the orbit is with respect to the Earth's surface. True mean anomaly (v):the mean anomaly tells you where the satellite is in its orbital path. The mean anomaly ranges from 0 to 360 degrees. The mean anomaly is referenced to the perigee. If the satellite were at the perigee, the mean anomaly would be 0. The Keplerian orbitis ideal since it assumes that the earth is a uniform spherical mass. Actually the Earth is not a sphere but rather an oblate spheroid in which the radius at the equator is about 21km greater than at the poles. Earth s asymmetrical mass causes a non-central gravitational pull. Satellites orbiting in near-earth are subject to a lot of disturbing forces. These forces can be divided into three categories: the gravitational forces, the non-gravitational forces, and empirical forces.the equation of motion of a near-earth satellite can be described in an inertial reference frame as follows [6]: Where: r = a g + a ng + a emp (1) ris the position vector of the center of mass of the satellite,a g is the sum of the gravitational forces acting on the satellite including Earth s geopotential, solid earth tides, ocean tides, planetary third-body perturbations, and relativistic accelerations,a ng is the sum of the non-gravitational forces acting on the surfaces of the satellite including drag, solar radiation pressure, earth radiation pressure, and thermal radiation acceleration, anda emp is the unmodeled forces which act on the satellite due to either a functionally incorrect orincomplete description of the various forces acting on the spacecraft or inaccurate values for the constant parameters which appear in the force model.another way to determine the orbit is the orbital state vectors which are Cartesian vectors of position (r) and velocity (v) that together with their epoch time (t) uniquely determine the trajectory of the orbiting body in space. The position vector describes the position of the body in the specific frame of reference, while the velocity vector describes its velocity in the same frame at the same time. III. TWO-LINE ELEMENT A two-line element (TLE) is a special form of mean classical orbital elements that describe the orbit of an earth satellite. TLEs are generated with an orbit determination process based on observations by the United States Space Surveillance Network (SSN), which comprises a number of radar and electro-optical sensors [7]. These elements are periodically updated so as to maintain a reasonable prediction capability on all space objects. The TLE is in a format specified by North American Aerospace Defense Command (NORAD) and used by NORAD and NASA. The TLE can be used directly by all Simplified perturbations models (SGP, SGP4, SDP4, SGP8 and SDP8) which used to calculate orbital state vectors of satellites and space debris relative to the Earth-centered inertial coordinate system. Orbital elements are determined for many thousands of space objects by NORAD and are freely distributed on the Internet in the form of TLEs.Data for each satellite consists of three lines in the format shown in Figure (1) Fig. 1TIGRISAT Two Line Element Line 0 is a twenty-four character name (to be consistent with the name length in the NORAD Satellite Catalog SATCAT). Lines 1 and 2 are the standard Two-Line Orbital Element Set Format identical to that used by NORAD and NASA. The format description is as shown in Figure (2). Fig. 2TLE Parameters Explanation 2

3 IV. SIMPLIFIED GENERAL PERTURBATIONS4 ALGORITHM Simplified General Perturbations Satellite Orbit Model 4(SGP4) is a NASA/NORAD algorithm of calculating near earth satellites. Any satellite with an orbital period of less than 225 minutes should use this algorithm. Satellites with orbital periods greater than 225 minutes should use thesimplified Deep Space Perturbations (SDP4) or (SDP8) algorithms [8]. The required input for SGP4 is a two line elements which are published by NORAD at regular time intervals. SGP4 uses a closed form series of equations in order to calculate the satellite s position at a future epoch.tle data older than 30 days is considerably inaccurate due to perturbations in the orbit.sgp4 computes satellite coordinates in the mean equinox true equator coordinate system based on the epoch of the specified TLE which was used as input to the SGP4 propagator. The TLE information is a set of mean orbital elements that are suitable to the SGP4 propagator only. In this work TLE s of TIGRISATwhich available through a web link ( have been used for input to the SGP4 propagator. V. SATELLITE TRACKING FROM GROUND STATION Figure(3)andFigure (4) show two graphical views of satellite ground track from General Mission Analysis Tool (GMAT). General Mission Analysis Tool is an open-source space mission design tool which is designed to model and optimize spacecraft trajectories. It is developed by a team of NASA, and is used for real-world engineering studies, as a tool for education and public engagement [9]. Fig. 3TIGRISAT ground track for one revolution Fig. 4 TIGRISAT ground track for two revolutions Figure (3) shows the orbital path of the TIGRISAT projected onto a two-dimensional world map over some time for one revolution of the satellite. As a result of the Earth s rotation the LEO satellite, can be observed by a ground stations for three to four consecutive passes, after whichthe satellite will be out of reach of theground station for many hours. In Figure (4), a ground track of two future revolutions of the satellite is shown, where the westward ground track movement in time is clearly noticeable. 3

4 VI. ORBIT SIMULATION AND ANALYSIS Satellite orbit simulation and analysis based on data collected from NASA/ NORAD TLE files.the analysis will be includes orbit determination and prediction of satellite position and velocity, satellite tracking, and command summary.general Mission Analysis Tool (GMAT) is used to simulate the orbital motion of TIGRISAT.The spacecraft epoch and six Keplerian orbital elements required to inputto GMAT. 26 Aug :59: is used as TIGRISAT epoch and the Keplerian orbital elements areused as shown in Table (1). The TLE set contains some of these elements (ECC, INC, AOP, RAAN), and the remainder can be determined using the TLE provided elements. TABLE (1)KEPLERIAN ORBITAL ELEMENTS OF TIGRISAT Field Value Unit Semi-Major Axis (SMA) km Eccentricity (ECC) Inclination (INC) deg Argument of Perigee (AOP) deg Right Ascension of the Ascending Node (RAAN) deg True Anomaly (TA) deg UTC Gregorian Epoch format and EarthMJ2000Eq coordinate system are used in simulation.force model with RSSStep error control, Earth as a central body, JachiaRoberts atmosphere model and JGM-2 gravity model were used to evaluate the drag on the TIGRISAT. The Gravitational bodies include the Sun and Moon. Many of other bodies have such a small effect on the orbit of TIGRISAT so they can be neglected. Other non-gravitational forces included in the propagation, these are drag and solar radiation pressure (SRP).RungeKutta89 with 60 sec initial step size, sec mini step size, 2700 sec max step size, and 9.99e-12 accuracy are used as integrator in simulation. Figure 5: shows Keplerian elements as calculated by GMAT plotted with NORAD tracking data. The plotted NORAD data shows that Semi-Major Axis changes with the eccentricitychange,figure(5a, 5b), it changes about 0.3% of its value. The plotted NORAD data also shows sinusoidal variations in the orbital inclination that are predicted by GMAT Fig(5c). Fig(5d) shows that Ascension of the Ascending Node changes from zerodeg to 131deg in Elapsed Days.Fig (5e) shows that Argument of Perigee error ± 2deg about its value 350 deg. Figure (5f) shows true anomaly which represents the position of TIGRISAT in the orbit plane, measured from the perigee position to the satellite. (a)semi-major Axis (SMA) (b)eccentricity (ECC) 4

5 (c)inclination (INC) (d)right Ascension of the Ascending Node (RAAN) (e)argument of Perigee (AOP) (f)true Anomaly (TA) Fig. 5Six Keplerian Elements (a) Semi-Major Axis(b) Eccentricity(c) Inclination(d) Right Ascension of the Ascending Node(e) Argument of Perigee (f) True Anomaly Figure (6)shows Planetodetic properties, Altitude, Latitude, and Longitude. Fig 7 shows TIGRISAT properties which is the coefficient of drag (Cd) used to compute the acceleration due to drag, the coefficient of reflectivity (Cr) used to compute the 5

6 acceleration due to solar radiation pressure (SRP), and SRP area.figure (8) and Figure (9) show the three components of the TIGRISAT position and velocity with respect to the coordinate system. Fig. 6Altitude, Latitude, and Longitude Fig. 7Coefficient of drag (Cd), Coefficient of reflectivity (Cr), and SRP Area Fig. 8 X, Y, Z components of the TIGRISAT position with respect to the coordinate system Fig. 9X, Y, Z components of the TIGRISAT velocity with respect to the coordinate system 6

7 The Command Summary is a summary of orbit and spacecraft state information after execution of a commandfigure (10). Propagate command summary contains spacecraft state information, time information, planetodetic properties, and other orbit data after propagation is performed. Fig. 10Command Summary VII. CONCLUSION In order to achieve any mission it is essential to determine and predict an accurate orbit of the satellite. To effective satellite mission planning, it is required to understand how satellite lifetime is related to orbital parameters and how disturbing forces effect on satellites orbits. In this study orbital motion simulation and analysis for TIGRISAT is presented. This simulation provides support for model development and integration and gives a visual insight into satellite orbits, by producing the orbital path of the TIGRISAT projected onto a two-dimensional world map over some time. As a starting point for the simulation of 7

8 future, using the parameters of KufaSat instead of TIGRISAT gives ability to observe the effects on shape and position of the orbit which lets a better understanding of the KufaSat orbit. REFERENCES [1] Mechael.R.Greene, Robert E. Zee Increasing Accuracy of Orbital Position Information from NORAD SGP4 Using Intermittent GPS Readings, 23rd Annual AIAA/USU Conference on Small Satellite. [2] Mohammed Chessab Mahdi et al, Attitude Determination and Control System design of KufaSat International Journal of Current Engineering and Technology, Vol.4, No.4 (Aug 2014) [3] REAL TIME SATELLITE TRACKING AND PREDICTIONS [4] Mohammed Chessab Mahdi et al, Direct Fuzzy Logic Controller for Nano-Satellite Journal of Control Engineering and Technology, Vol.4, No.3 (July, 2014) [5] Wikipedia Orbital elements. [6] H. J. Rim, B. E. Schutz, PRECISION ORBIT DETERMINATION (POD), Center for Space Research The University of Texas at Austin, October [7] James MASON, Development of a MATLAB/STK TLE Accuracy Assessment Tool, in Support of the NASA Ames Space Traffic Management Project, Master Thesis, International Space University, August, [8] Hujsak, R.S. and Hoots, F.R. (1982), Deep Space Perturbations Ephemeris Generation, Aerospace Defense Command, Peterson AFB, CO. [9] GMAT, General Mission Analysis Tool. BIOGRAPHY Mohammed Chessab Mahdireceived his B.Sc. degree in control & systems engineering from University of Technology Baghdad in 1984 and received his M.Sc. Degree in space technology from University of Kufa in He is full time lecture in Technical Institute of Kufa Al-Furat Al-Awsat Technical University Iraq and member of KufaSat team - Space Researchs Unit-Faculty of Engineering University of Kufa. He has good skills in the design and modeling of attitude determination and control systems using Matlab program. He has been published more than 9 researches. 8