MASTER'S THESIS Venus Thermosphere Densities as Revealed by Venus Express Torque and Accelerometer Data Moa Persson 2015 Master of Science in Engineering Technology Space Engineering Luleå University of Technology Department of Computer Science, Electrical and Space Engineering Lule˚a University of Technology Master Thesis VENUS THERMOSPHERIC DENSITIES AS REVEALED BY VENUS EXPRESS TORQUE AND ACCELEROMETER DATA Supervisor: Author: Dr. Colin Wilson Moa Persson Examiner: Dr. Victoria Barabash A thesis submitted in fulfilment of the requirements for the degree of Master of Science in Space Engineering at Division of Space Technology Department of Computer Science, Electrical and Space Engineering September 2015 Abstract The Venus Express spacecraft is the most recent spacecraft to orbit around the planet Venus. During the years 2008 to 2014 it made several successful campaigns in which it was submerged into the upper atmosphere. By using the force exerted on the space- craft during these campaigns of different pericentre altitudes three data sets were obtained: the so called radio tracking, torque and accelerometry. These three data sets have been used to calculate the density and its variations, in the altitude range 130-200 km, in order to understand more about the Venusian atmosphere. In this project the densities from the torque method have been calculated and used, together with the previously calculated ac- celerometry data, in order to determine the mean atmospheric state and the variabilities. The previously calculated tracking densities have been used as a validation method. These results have inferred a mean state with 40 % lower densities in the polar atmosphere com- pared to the Hedin model predictions and a factor of two stronger solar zenith angle (SZA) dependence for higher altitudes than was previously modelled in the Hedin model. A high rate of variability was found, a factor of 7 between maximum and minimum of the ob- served densities once height and SZA dependence have been consid- ered, in the upper atmosphere which is currently unexplained. This project therefore gives many suggestions for further work in order to give a better understanding and improve the results achieved. i Sammanfattning Venus Express var den senaste satelliten som hade sin omlopps- bana kring planeten Venus. Under ˚aren2008 till 2014 gjorde den flera framg˚angsrika kampanjer d¨arsatelliten var helt neds¨ankti den ¨ovreatmosf¨aren. Genom att anv¨andakraften som ut¨ovades p˚asatelliten av atmosf¨arenunder dessa kampanjer med olika peri- centerh¨ojderlyckades den m¨atadensiteten mellan 130-200 km ¨over ytan genom att anv¨andatre olika metoder: sp˚arning,vridmoment och luftbromsning. Dessa tre m¨atningsmetoder anv¨andessedan f¨or att ber¨aknadensiteten och dess variationer f¨oratt kunna f¨orst˚amer om den Venusiska atmosf¨aren. I det h¨arprojektet har densiteten fr˚anvridmomentsmetoden ber¨aknatsoch anv¨ants, tillsammans med tidigare utr¨aknadedata fr˚anluftbromsningsmetoden, f¨oratt kunna best¨ammaatmosf¨arens medeltillst˚andoch variationer. Den tidigare ber¨aknadedensiteten fr˚ansp˚arningsmetoden har anv¨ants f¨oratt validera ber¨akningarna. Resultaten har frambringat ett medeltillst˚andmed 40 % l¨agreden- siteter i den pol¨araatmosf¨arenoch ett tv˚ag˚angerh¨ogreberoende av solzenitvinkeln f¨orh¨ogrealtituder, ¨anvad som tidigare har mod- ellerats. En h¨ogvariation, med en faktor p˚asju mellan maximum och minimum efter exkludering av beroenden p˚asolzenitvinkeln och h¨ojd,har ocks˚auppt¨ackts i den ¨ovreatmosf¨arenmen detta st˚ar fortfarande of¨orklarat.Detta projekt ger d¨armedm˚angaf¨orslagp˚a fortsatta arbeten med dessa data f¨oratt ge en b¨attref¨orst˚aelsef¨or och f¨orb¨attrade uppn˚addaresultaten. iii Acknowledgements First of all I would like to thank Dr. Colin Wilson for giving me this amazing opportunity to do my master thesis for him at the well renowned Oxford Univer- sity. With your help, support, and never ending stream of ideas for further work and improvements this work gave me both a project with interesting results and a good start to hopefully my future career as a researcher. I want to thank the different science teams, including Sean Bruinsma et al. and Pascal Rosenblatt et al. that have given their allowance for us to use their calculated data in my work to be able to receive the results we have. I would also like to thank Emmanuel Grotheer for allowing me to use and refine his pipeline for calculating the torque densities, to Ingo Mueller-Wodarg for his support and help with understanding the physics behind the results and to Sanjay Limaye who has been a bit of a mentor through the time period of this work, by his support and helping words when work have been difficult and to others who have helped with theory and understanding of the subject. Thank you Dr. Victoria Barabash for your feedback and helpful advice throughout the course of the thesis. Last of all I want to thank my family and friends for believing in me and helping me through the good and the bad, without you I would never have reached this far! v Contents Abstract i Sammanfattning iii Acknowledgements v Contents viii List of Figures ix List of Tables x Abbreviations xi Physical Constants xi Symbols xii 1 Introduction 1 1.1 Objectives . 1 1.2 Structure of the report . 2 2 Background 3 2.1 Previous missions to Venus . 3 2.2 Venus' upper atmosphere . 4 2.2.1 Composition . 4 2.2.2 Temperature . 4 2.2.3 Winds . 5 2.2.4 Gravity waves . 5 2.2.5 Density . 6 2.3 Previous models of Venus atmosphere . 6 3 Density derivations 9 3.1 VEx Atmospheric Drag Experiment . 9 3.1.1 Radio tracking . 10 3.1.2 Torque . 10 3.1.3 Validation of torque against tracking results . 15 3.2 Accelerometry . 16 4 Analysis & Results 18 4.1 Preparing the data . 18 4.2 Height dependence . 18 4.3 Solar zenith angle dependence . 20 4.4 Morning/Evening terminator differences . 21 4.5 Day-to-day variability . 23 4.6 Temperature . 23 4.7 Waves . 25 vii 5 Discussion 27 5.1 Calculated densities . 27 5.2 Mean atmospheric density . 27 5.3 Temperature . 28 5.4 Variability . 29 5.5 Waves . 30 6 Conclusions & Future Directions 33 References 34 viii List of Figures 1 Venus Express torque experiment. 11 2 Gravity gradient torque reduction . 12 3 Hyper-thermal free-molecular flow . 14 4 Torque validation against tracking . 15 5 Density results from torque measurements and calculations . 17 6 Density data used for empirical fit to height dependence . 19 7 Densities from torque and accelerometry data sets with empirical fit ................................... 19 8 SZA dependence in torque data . 21 9 SZA dependence in both torque and accelerometry data sets . 22 10 Comparison between the morning and evening terminator densities. 24 11 Day-to-day variability in the torque densities . 24 12 Temperature profiles from density calculations . 25 13 Wave patterns . 26 14 Comparison of empirical fit and data to Hedin model densities . 29 15 Normalisation to SZA 90 degrees for torque data . 32 ix List of Tables 1 Previous missions to Venus . 4 2 Time periods for VExADE and accelerometry . 9 3 Systematic uncertainties in torque densities . 16 x Abbreviations CNES Centre National d'Etudes Spatiales ESA European Space Agency EUV Extreme Ultraviolet GW Gravity Waves LST Local Solar Time POD Precise Orbit Determination PV Polar Vortex RW Reaction Wheel SNR Signal-to-Noise SZA Solar Zenith Angle VEx Venus Express VExADE Venus Express Atmospheric Drag Experiment Physical Constants µ Standard gravitational parameter 324 859 km3 s−2 g Acceleration of gravity (at surface) 8.87 m s−2 k Boltzmann's constant 1.38 ·10−23 m2 kg s−2 K−1 xi Symbols A Area m2 CD Drag coefficient CL Lift coefficient H Scale height km I Spacecraft total inertia tensor in spacecraft frame kg m2 L Angular momentum kg m2 s−1 M Mean molecular mass g mol−1 Q Rotation matrix between reference and spacecraft frame T Temperature K α Accommodation coefficient ! Angular rate rad s−1 ρ Density kg m−3 F~AD Aerodynamic force N S~ Sensitivity m5 s−2 T~g Gravity gradient torque Nm T~s Solar radiation torque Nm T~AD Aerodynamic torque Nm ~i Reference frame direction ~j Reference frame direction ~n Normal vector ~r Spacecraft centre of mass in reference frame m ~rCoM Centre of mass position in reference frame m ~rC Centroid position in reference frame m ~rV Venus centre of mass in reference frame m ~v Incident molecular flow in reference frame m s−1 ~z Reference frame direction f SZA dependence h Altitude above surface m xii 1 Introduction The exploration of the planetary atmospheres in our Solar System is a crucial step towards better understanding of both our own planet and the space around us. By investigating these atmospheres we will not only be able to interpret the past, present and future of Earth, but also learn more about what might be possible when developing new methods and ideas for sending spacecraft and even people to these other worlds. [13] Through studying the densities and their variations in different atmospheres it will be conceivable to understand the possibilities to use aerobraking, i.e. the drag from the upper atmospheric particles, in order to change the orbital parameters of an orbiter or lander. This could not only decrease the amount of propellant needed to be brought but also lower the cost and thereby help with sending out more explorations in the future. [17] Venus has a very dense atmosphere with a structure not too unlike Earth. This planet has therefore been subject to extensive research, where one of the latest exploration missions was by the Venus Express (VEx) spacecraft, which had a polar orbit around the planet during 2006-2014.