A Parametric Study of Interplanetary Mission Using Solar Sail Harijono Djojodihardjo * Professor and corresponding author, Aerospace Engineering Department, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia; email: harijono@djojodihardjo.com Ali Yousefian Research Assistnant , Aerospace Engineering Department, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia; H.DJOJODIHARDJO & A. Yousefian

Assumptions Only the gravitational field of the Central body is considered as a two body problem In all the solar sail configurations considered, they are ideal photon reflectors, in the sense that all photons are perfectly reflected. H.DJOJODIHARDJO & A. Yousefian 2

Spherical Polar Coordinate Coordinate System Spherical Polar Coordinate Heliocentric coordinate system with the origin at the center of the Sun H.DJOJODIHARDJO & A. Yousefian 3

Introduction Flat Solar Sail (FSS) The concept behind solar sailing is utilizing the vanishingly small momentum of solar photons in space. This can be compared to sail boats that use earth wind vessels to achieve high velocities using sun light as propulsion Uses a simple extremely large flat surface to reflect and utilize the momentum of solar photons. The entire surface in generating thrust H.DJOJODIHARDJO & A. Yousefian 4

IKAROS Only successfully deployed solar sail so far Achieved a successful flyby to Venus in 2010 With sail area of 200 m2 and a sail thickness of 7 μm (thickness of a human hair is about 20 μm ) H.DJOJODIHARDJO & A. Yousefian 5

Orbital Dynamics of FSS H.DJOJODIHARDJO & A. Yousefian 6

Orbital Dynamics of FSS Dynamic Analysis of FSS Orbital Dynamics of FSS H.DJOJODIHARDJO & A. Yousefian 7

Orbital Dynamics of FSS Solar radiation force acting on a solar sail can be calculated as follows: H.DJOJODIHARDJO & A. Yousefian 8

Orbital Dynamics of FSS Where and are the unit vectors along the sunline and its reflection respectively Total radiation force would be : Which can be rewritten as : H.DJOJODIHARDJO & A. Yousefian 9

Orbital Dynamics of FSS Where effective pressure is solar radiation pressure for a perfectly reflecting solar sail at 1 AU distance from the sun which is : H.DJOJODIHARDJO & A. Yousefian 10

Orbital Dynamics of FSS Characteristic acceleration can also be written in terms of solar gravitational acceleration : Here β is called the sail loading parameter also known as lightness number which is a dimensionless constant described as the ratio of solar radiation acceleration to solar gravitational acceleration. H.DJOJODIHARDJO & A. Yousefian 11

Logarithmic Spiral Trajectories Dynamic Analysis FSS Logarithmic Spiral Trajectories Logarithmic Spiral Trajectories are one attractive option for interplanetary travel which requires the spacecraft to utilize a continuous low thrust propulsion system and to have an inverse square variation with distance(Reference 1). H.DJOJODIHARDJO & A. Yousefian 12

Logarithmic Spiral Trajectories for FSS The equation of motion for a perfectly reflecting Flat Solar Sail can be defined as: where and since m << it can be assumed that . H.DJOJODIHARDJO & A. Yousefian 13

Logarithmic Spiral Trajectories for FSS The transverse and radial components of solar sail velocity vector are derived as follows H.DJOJODIHARDJO & A. Yousefian 14

Logarithmic Spiral Trajectories for FSS By integrating the equation for the radial velocity , transfer time can be obtained from an initial orbit radius r0 to a distance r H.DJOJODIHARDJO & A. Yousefian 15

Logarithmic Spiral Trajectories for FSS A sample interplanetary trajectory of a Flat Solar Sail to Mars and Venus with a sail lightness number of 0.06. H.DJOJODIHARDJO & A. Yousefian 16

Results and Discussions The transfer time of the vehicle is a function of spacecraft lightness number β and sail pitch angle α. β is a design parameter which depends entirely on spacecrafts mass and dimensions α is sail pitch angle, which can be controlled H.DJOJODIHARDJO & A. Yousefian 17

Results and Discussions Influence of α 0.1 0.125 0.15 α*[degrees] 35.68 35.53 35.37 T [days] 430.9629≈ 431 343.2159≈342 283.0221≈283 With a known lightness number β the transfer time between two orbits depends entirely on sail pitch angle α By finding the optimum sail pitch angle α* a minimum transfer time can be achieved H.DJOJODIHARDJO & A. Yousefian 18

Results and Discussions Influence of α A spacecraft with the lightness number of 0.1 Earth-Mars Logarithmic Spiral Trajectory with a sail pitch angle of 79 degrees (left), 70 degrees (middle) and optimum angle (right) H.DJOJODIHARDJO & A. Yousefian 19

Results and Discussions Influence of β   WSF MIT JHU CCL sail area [m2] 3000 1000 22700 60000 sail mass [Kg] 139 15 180 300 σ [gm-2] 46.3 7.9 5 achar[mms-2] 0.17 0.52 0.98 1.55 0.0287 0.0877 0.1652 0.2613 Mars mission Transfer time [days] 1532.6 493.2 255.8 156.7 Sail lightness number is a design parameter which varies with sail area and spacecraft mass Spacecrafts designed during 1980’s for the 1992 Mars race will be considered Table shows that the sail lightness number has an effective impact on transfer time and trajectory H.DJOJODIHARDJO & A. Yousefian 20

Results and Discussions Influence of β Figure exhibits the trajectories of these spacecrafts. It is obvious that higher sail lightness number would lead to higher characteristic acceleration and therefore shorter transfer orbits H.DJOJODIHARDJO & A. Yousefian 21

Conclusion FSS Advantages It is propellantless efficient propulsion system By using the optimum sail pitch angle a minimum transfer time can be achieved Disadvantages Problems in handling and deployment since it is extremely sensitive H.DJOJODIHARDJO & A. Yousefian 22

References C.McInnes, Solar Sailing: Technology, Dynamics, and Mission Applications, Springer-Praxis, 1999. Japan Aerospace Exploration Agency;http://www.jaxa.jp/projects/sat/ikaros/index_e.html, accessed 16 February 2014. A.D.Guerman,G.V.Smirnov,and M.C.Pereira, Orbital Dynamics of a Simple Solar Photon Thruster, Mathematical Problems in Engineering, Volume 2009, Article ID 537256, 11 pages B.Dachwald, and W.Seboldt, Solar Sails For Near-Term Advanced Scientific Deep Space Missions , June 2002,German Aerospace Center (DLR), Institute of Space Simulation, Cologne, Germany K.Howell, Solar Sailing, www.insightcruises.com/pdf/sa07_slides/Solar_Sailing.pdf, accessed 16 February 2014. H.Djojodihardjo, A.Yousefian, Comparative Study of FSS and SPT for Interplanetary Solar Sail Propulsion, Proc. 2nd IAA-AAS DyCoSS, Rome, March 2014. H.DJOJODIHARDJO & A.S.M.HARITHUDDIN

Further Work H.Djojodihardjo and A.Yousefian, Comparative Study of FSS and SPT for Interplanetary Solar Sail Propulsion, paper IAA-AAS-DyCoSS2-14-11-03, Proceedings, 2nd IAA-AAS Conference on Dynamics and Control of Space System, Rome, 25-27 March, (2014). H.Djojodihardjo and A.Yousefian, Comparative Study of FSS and SPT Comparative Study of Solar and Electric Sailing Simple Maneuver Strategies, proceedings, 14th International Space Conference of Pacific-basin Societies (ISCOPS), 27-29 May, (2014). H.DJOJODIHARDJO & A.S.M.HARITHUDDIN

Thank You A. Yousefian 25