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Dr Mark Price ([email protected]) , Prof Mark Burchell (convener), Prof Richard Holdaway (CCLRC), Dr Vicky Fitzgerald. Spring 2011. Dr. Mark Price ◦ Room 103C ◦ E-mail: [email protected] Lectures notes will eventually be available on Moodle, but can be downloaded now from: http://astro.kent.ac.uk/~mcp2/teaching/PH508 30 hours of lectures ◦ Low Earth Orbit (4 lectures and 1 workshop – MCP) ◦ Spacecraft Systems (11 lectures and 1 workshop – MCP) ◦ Project Management (5 lectures and 1 workshop – VF) ◦ Orbital Mechanics (10 lectures and 1 workshop – RH) 4 workshops (weeks TBD) 2 class tests (weeks 18 & 24) To provide a basic understanding of the major subsystems of a spacecraft system. To provide basic frameworks for understanding of spacecraft trajectory and orbits, including interplanetary orbits, launch phase and attitude control. To provide an awareness of the basic ideas of how space is a (multi-billion dollar!) business opportunity and some of the management tools required in business. Low Earth Orbit (4 lectures) ◦ The vacuum, radiation environment and thermal environment that a spacecraft encounters in Low Earth Orbit (LEO) and that environment’s effect on the spacecraft materials (electronics, superstructure etc.). Spacecraft Systems (11 lectures) ◦ An introduction to spacecraft and their environment. Covers Spacecraft structures and materials, thermal control, power systems, attitude control systems, the rocket equation and propulsion. Project management (Dr. Vicky Fitzgerald) Orbital mechanics (Prof. Richard Holdaway) ◦ Explains the evolving framework in which world-wide public and private sector space activities are conceived, funded and implemented. ◦ Introduces the basics of business planning and management applicable to any project! ◦ Using celestial mechanics (Newton’s laws) to the real world application of satellite/spacecraft missions. ◦ Basic equations of motion are outlined in order to give an understanding of the causes and effects of orbit perturbations. ◦ Descriptions are given of different types of orbit and methods are outlined for the determination and prediction of satellite and planetary orbits ◦ Assessment of mission analysis problems such as orbital choice, ground station usage, satellite station-keeping and orbital lifetime. An understanding of the way in which space missions are configured both from the point-ofview of the constituent subsystems, mission profile (i.e., the project aims) including the influence of the space environment. Appreciate the constraints and trade-offs which led to one mission configuration over another. Appreciate space activities from a commercial viewpoint and be familiar with basic management tools for planning work (e.g., Gant charts, Pert charts etc.) Make (valid) approximations and solve problems using a mathematical approach. Spacecraft Systems Engineering by Fortescue, Stark and Swinerd (3rd edition). [*NB: No joke, this is pretty much ESSENTIAL ] Library has 6 copies (Classmark: TL875, location: Level 2 West. Also has some copies in core text collection (1 week loan?). Library has many copies (>15) of the second edition (same classmark and location) Amazon price: £37.95 Please contact me ([email protected]) if you really can’t source/afford a copy! Orbital Motion by A. Roy. (3rd edition) Library classmark: QB 355, 6 copies. Amazon price: £53.19 Space vehicle design by Griffin and French [Classmark: TL 875] Space mission analysis and design by Wertz & Larson [Classmark TL 790] Satellite Technology and its applications by Chetty [Classmark TL796] Spacecraft Attitude determination and control by Wertz [Classmark TL3260] Rocket and Spacecraft propulsion by Turner [Classmark: TL 872] Basic elements of a space mission F&S, Fig. 1.3, Page 7 Crude overview: [Read: chapter 2, F&S] 1. Ground phase (vehicle construction) 2. Pre-launch phase (payload and rocket integration) 3. Launch phase 4. Space operations phase 5. Other (planetary, asteroid belt, cometary environments, de-orbital/end of life phase) Can be sub-divided further into: Manufacture stage Assembly stage Test and checkout stage Handling stage Transportation stage Storage (prior to rocket/payload integration) Manufacture and construction stage Could be argued that this phase is the same as for any other industrial product. Incorrect! Spacecraft manufacture is very expensive, and very few spacecraft are actually made. Spacecraft (even the lowly comms satellite) are very complicated with many subassemblies and built-in redundant systems. Operational constraints mean that each spacecraft (or rocket) is only used once (slight exception is the space shuttle) and cannot be ‘test driven’. It has to work, and it has to work first time! [Q: Approximate cost of comms./science satellites?] Manufacture and construction stage (continued) The end user environment (see later in course) imposes unusual constraints in terms of mass, volume, power, allowable materials, reliability, technology etc. over conventional manufacturing. All this pushes up the cost, construction time and complexity of the end product (spacecraft or rocket). Need to impose the highest standards of quality control to guarantee the manufactured end assembly. Test and checkout stage A time-consuming and therefore expensive process. Remember: it has to work, and it has to work first time! ◦ Example: A chip fails during a PCB test. What do you do? ◦ Answer: Replace ALL chips from the same manufacturer on all PCBs. ◦ Example: A solar panel generates insufficient power for the end user requirement. What do you do? ◦ Answer: Rebuild panel, delaying the mission by 6 months. ◦ HST mirror! Handling stage To be ‘space qualified’ all components and assemblies have to handled in a clean environment. Human operatives have to wear paper coveralls, gloves, hairnets, facemasks. All handling of sub-assemblies is documented meticulously (do not drop a spanner onto the spacecraft, or one of the flight detectors on the floor!) Transportation stage: Manufacture and checkout facility may be a long distance (>1000 km) from the launch site (end user requirement, depends on the required orbit) Vibration and shocks are monitored during transport by gauges. Transported in a sealed environment to prevent ingress of dust, moisture and temperature extremes. Just moving a spacecraft is expensive! Storage: Missions get delayed, sometimes for years. Estimated cost of HST storage was $500M - $1Bn! ‘Ground Phase’ duration can last years. Time to build a typical Spacecraft ~3 years, longer for scientific payloads. Recent attempts have been made to try and ‘production line’ the process particularly for telecommunication satellites due to commercial pressures. ‘Ground Phase’ environment: ‘one-g’, standard temperature and pressure, in a clean room. [Aside: clean rooms are quantified by the number of particles per cubic foot (US). A class ‘1000’ being dirtier than a class ‘100’. Spacecraft and scientific payload assembly is normally done in a class ‘100’ or ‘1000’] Spacecraft is delivered to the launch site for integration with rocket. The whole assembly is then moved to the launch-pad. This period can last days, but delays can (and do) occur. Environment: ‘one-g’ gravity, temperature and pressure that of the launch site, cool dry air can be flowed over the spacecraft to give a certain degree of environmental control. Duration: typically ~1000 seconds, from ground to orbit. Environment: Vibration/noise, acceleration shock (‘g-force’), mechanical shock (vibration), thermal changes (ground – space), pressure change (1 atmosphere – vacuum). Vibration/noise caused by: ◦ Burning of fuel ◦ Operation of pumps, compressors, turbines etc. ◦ Aerodynamic buffeting Vibration/noise environment Two modes of transport to payload 1. Vibration through payload mounting structure 2. Acoustically through the atmosphere At its worst (peak intensity) at launch (from reflections off ground, main firing of rocket) and during transonic flight through the atmosphere. Uneven air flow over the rocket causes buffeting/shearing forces. Dr Mark Price ([email protected]) , Prof Mark Burchell (convener), Prof Richard Holdaway (CCLRC), Dr Vicky Fitzgerald. Spring 2011. Typical Ariane 4 & 5 noise spectrum Definition of noise intensity, I P I 20 log 10 5 2 10 I has units of decibels, ‘dB’. P is the overpressure (i.e., a ‘relative’ pressure) referenced to 20 millipascals (at 1kHz). Vibration is given by spectral density, units of g2/ Hz (g = acceleration) Ariane 4 vibration Spectrum (F&S, Fig 2.2). Actual shape is rocket and payload dependent. Both vibration and noise can damage a payload. Designers/engineers do ‘destruction’ tests on engineering/flight spare components to make sure the flight model Spacecraft will survive. The fairing (the detachable cover over the Spacecraft) vibrates. Due to weight constraints, the fairing has to be lightweight and thus is prone to vibration. Acceleration (‘g force’ – normalised to Earth standard gravity) Acceleration is not constant. Has several peaks and troughs during the launch phase. These peaks and troughs happen as various stages ignite and drop-off and during jettisoning of the payload fairing. Early ‘brute force’ rockets had high values of ‘g’. Early Mercury rockets peaked at ~6.7g. Space shuttle has a ~3g sustained peak. A sustained thrust reduces the peak g experienced. Note: starts at 1g (ground) ends at 0g (free-fall). Ariane 4 acceleration profile (F&S – Fig. 2.3) If –gz (ie., ‘up’) is > 5g blood supply to brain stops (heart is pumping against 5g). Leads to unconsciousness. Can survive front-back motions at higher g as limitation is the squashing/tearing of soft tissue in the lungs. During an uncontrolled descent, some Russian cosmonauts survived >18g! (Soyuz 18 + others?) For very short time periods (<msec) accelerations can be very much higher (~hundreds of g) as fairings detach etc. Heat experienced by payload is not due to the radiative/conductive heat from the rocket motor. Payload is well insulated from this The payload fairing is forcing its way through the atmosphere and gets hot (think inverse heat shield). Atmospheric frictional heating occurs and this heat can be conducted to the payload or radiatively from the fairing’s inner surface. Effect decreases with altitude due to decreasing atmospheric density. Total energy input, E, into payload can be calculated via: E F dx Where dx is each interval of distance travelled F is the drag force experienced travelling dx The drag force, F, is defined as: 1 2 F C D Av 2 CD is the drag coefficient - a function of atmospheric density, ρ. Typical values are between 0.5 – 2. Also a function of altitude A is the cross-sectional area of the spacecraft in line of flight v is the velocity. Emery equation difficult to solve exactly as some terms are altitude dependent. Main points: ◦ Energy input is large ◦ Dominated at low altitude by increasing velocity (acceleration through thick atmosphere). ◦ Decreases at high altitude at ρ decreases. But this is energy input. The temperature is a function of the heat capacity of the fairing and the way it dissipates heat and how that heats the payload. Fairing temperature: ◦ Atmospheric frictional heating ◦ Specific heat capacity ◦ Radiative, conductive and convective heat loss Payload temperature determined by: ◦ Radiative and conductive thermal pathways from fairing. ◦ Then direct radiative input after fairing is jettisoned from space environment. Jettison occurs at an altitude of ~100 km. ◦ Heat input into Ariane V is typically 500 W m-2 with a peak of 1135 W m-2. Atmospheric pressure/density Affects heating of fairing and thus payload Affects the noise/vibration environment Affects the final velocity achieved Thus is very important! As the atmospheric pressure drops, the pressure in the payload bay drops. The depends on the venting through the fairing. Need good venting paths to avoid sudden pressure drops and large pressure differentials across the payload (‘pop!’). ◦ For Ariane rockets pressure venting is ~10 mBar s-1. ◦ For the Space Shuttle, the venting pressure rate is controllable. How does the atmospheric pressure change with density? However, the absolute pressure varies not just with altitude, but with the Sun! Due to fluctuating energy input from the Sun, weather, time-of-day, solar cycle. COSPAR Int. Ref. Atmosphere (1972) Different species concentration as function of altitude (US Standard atmospheric Model). Things to ‘take home’ ◦ The design and implementation of a space mission is a complicated and expensive task. ◦ Each separate phase has to implement the highest possible level of quality control. It has to work, and it has to work first time! ◦ Many different things to consider when designing a mission: power requirements, weight, thermal control, mechanical robustness, system redundancy, etc. [Will crop up again in PH608, and probably PH711] Can be broadly categorised into: ◦ Near Earth Environment ◦ Deep Space ◦ Other ‘local’ environment (planetary orbits, asteroid belt, cometary etc.). As ‘Near Earth’ is local space we’ll start with the general case: deep space. Deep Space: gravity “Zero gravity” . Not true. You are always subject to gravity, but in a freefall state (or coasting) you appear to have ‘Zero gee’. ‘Zero gee’ is now going out of fashion to be replaced with the more correct term: “microgravity (μg)”. Spacecraft vibrations can shake the structure giving rise to a μg environment. Deep space: μg Advantages: Disadvantages: ◦ Small forces -> light structures can be employed ◦ Cheap to launch (but objects still have mass and inertia!). ◦ Low self-damping -> vibration prone (rigidity more important than strength, determines limiting mass). ◦ Difficult to test material behaviour on the ground ◦ Fluid flow problems in μg environment (‘bubbles’) ◦ Need active pumping/circulation system (no gravity feed) ◦ Humans? Sleeping, eating, respiration etc. all affected by μg environment. Deep space: pressure (or lack of!) At Geostationary Earth Orbit (GEO, altitude ~36,000 km) pressure ~10-15 Pa! At altitudes >120 km don’t really use pressure units, but a ‘number density’ (number per cubic metre, m-3). The molecules of a gas are too separated to interact, so can treat as separate species. Different species concentration as function of altitude (US Standard atmospheric Model). [F&S, Pg. 22] At an altitude of ~400 km the number density is approximately 1012 – 1014 atoms per m3 depending on the species and solar activity. Typical number density at low altitude inside the atmosphere ~1024 m-3. The result of such a low pressure is outgassing. Solids give off materials contained within them when the ambient pressure ~ vapour pressure (10-11 – 10-4 Pa) Outgassing examples: ◦ Metals → adsorbed/absorbed gases and water on surface. ◦ Polymers →volatile components (normally organic) which are part of their matrix material. ◦ Composite →absorbed water. This process starts immediately the pressure drops and can last months until all trapped molecules are released. Outgassing consequences: ◦ Polymers: loss of organic components leads to chemical changes and thus to mechanical and electrical changes (they become brittle, and their electrical conductivity changes). ◦ Composites: loss of water leads to mechanical shrinkage and thus distortion. Outgassed material can condense onto nearby surfaces – normally the coldest. This could be a telescope mirror and lead to frosting/degrading of the surface. The camera on NASA’s Stardust mission to visit a comet acquired a layer of ‘goo’ (technical term) during launch and lead to blurred images. Solutions: Careful material selection before construction. Vacuum bake out preflight, then coat the surface to seal it. Sublimation: (solid → gas phase) ◦ Metals: happens at very low rate but does occur (see Table next slide). ◦ Plastics/polymers: also occurs at low rate ◦ Lubricants: very high rate A potential problem if a thin film is involved, or if exposure is very long. Sublimation of metals can lead to short/open circuits in PCBs Sublimation of polymers & lubricants can lead to recondensing of material somewhere else, and probably somewhere unwanted! Solution: careful material selection. Use low volatility oils and solid lubricants (graphite powder). Note: very low rate for metals, but non-zero! [F&S, Table 2.8, Pg. 40] Whisker growth: Exacerbated by vacuum. Fibre-like monocrystalline filaments grow under vacuum conditions. Some metals more prone than others. E.g., Mo, W, Zn, Cd, Al, Sn, Ag. These conducting whiskers can lead to electrical shorting of PCB and ICs and arcing within the spacecraft (non-desirable!). Example: in the 1990s Hughes built satellites which are now starting to fail. Supposed reason for failure is they used tin (Sn) coatings on relays and whisker growth now probably occurring. Material strength & fatigue Generally enhanced in vacuum by approximately an order of magnitude Possible reasons: ◦ Retardation of crack propagation? ◦ Material sublimation ◦ Thermal ‘hotspots’ (for non-conductive polymers, no convective cooling). Electromagnetic radiation environment: Dominated by the Sun Yellow dwarf star: class G2 Spectral peak ~440 nm (‘yellow’). Spectrum approximated by a ~5800 K blackbody Has enhanced UV and X-ray output over a blackbody spectrum. ◦ Energy output ~3.85 x 1026 Watts (equivalent to the energy output of burning all the Earth’s fossil fuels for 50 milliseconds!). ◦ Radiation intensity falls off as 1/r2 ◦ ◦ ◦ ◦ Slight aside: the Sun’s radiation density at the Earth. ◦ Assume Earth – Sun distance = 149.6 million km = 1.49 x 1011 metres. ◦ Surface area of sphere at that distance (4πr2) = 2.81 x 1023 m2. ◦ Solar output = 3.85 x 1026 Watts ◦ Radiation density at earth’s surface = 3.85 x 1026/ 2.81 x 1023 = 1369 Watts m-2 (ignoring attenuation from atmosphere etc.) – generally referred to as the ‘solar constant’. 1) Assuming the power output from the Sun is 3.85 x 1026 Watts what is the radiation density at the surface of? ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto (1369 W m-2, 100% of Earth’s solar constant) And what percentage is that density compared to the Earth’s solar constant? 2) 130 decibels is defined as the pain threshold of hearing (at 1 kHz). What pressure does this correspond to? Calculate the pressure for 120 dB (permanent hearing damage), 85 dB (safe working limit) and 50 dB (standard conversation level). Show ALL working, and state where you obtained your mean Sun-planet distance from please! (Wikipedia isn’t always correct!). PIGEON HOLESON SECOND FLOOR PLEASE BY 5PM TUESDAY 25 th JAN. Electromagnetic radiation environment So, if you put a Spacecraft into space its temperature will stabilise as a function of: ◦ ◦ ◦ ◦ ◦ Radiation incident on structure Radiation reflected from structure Radiative heat loss (its emissivity) Its distance from the Sun Solar activity levels Fundamental to a lot of physics, Space physics and Astrophysics! Solar spectrum showing blackbody fit and UV, X-ray excess [F&S, Fig. 2.7, Pg. 18] Thermal considerations: acceptable temperature values ◦ Spacecraft structure: -100 → +100° C (approx.) ◦ Electronics: -10 →+40° C Problem: ◦ Inner solar system will be too hot, so need reflective surfaces, shades and passive cooling (radiators). ◦ Out solar system will be too cold, so need heaters (power hungry) and insulation. Ultra-violet radiation Problems: Solution: ◦ causes material degradation and embrittlement (particularly of plastics and polymers). ◦ Also changes the resistivity of some materials (again, mostly polymers and plastics). ◦ Leads to deterioration of plastics, paints, adhesives, epoxy resins etc. ◦ Use protective coatings (UV absorbing paint) and metal films to protect vulnerable materials. X-rays and gamma-ray radiation cause similar problems but have much lower flux (and also much harder to protect against!). The charged particle environment. Solar wind – outward flow from Sun. Mainly protons driven outward by radiation pressure. At Earth, these protons have a velocity of 450 km s-1 (a kinetic temperature, Tk ~105) At Earth, number density ~9 cm-3. Solar flares give an enhanced flux and a higher energy (30 MeV, factor of several thousand higher than normal). After a solar flare the Earth sees two events: ◦ The first approximately 20 minutes after the flare ◦ The second ~1 day later with an enhanced solar wind and a velocity of ~1000 km s-1. Cosmic rays (a misnomer, actually particles) Originate outside the Solar System from supernovae, neutron stars, black holes etc. Mostly highly energetic (MeV – TeV) H+, He++, Cn+, On+ and Fen+ ions. Problems: ◦ Organic materials suffer. ◦ Electronics suffer single event upsets (SEUs) and (eventual) degradations. Especially semi-conductors. ◦ Degradation due to disruption of crystalline lattice. ◦ SEUs cause bit errors in CPU and subsequent software malfunction and latch-up etc. Cosmic rays (continued) Solutions (partial) ◦ Shielding (normally Ti foil). Partially effective but can produce secondary ‘showers’ of lower energy particles with shorter stopping distances. May make things worse! ◦ Use ‘radiation hard’ components. Some technologies more resilient than others. Generally a trade-off between active area and disruption (large ICs have big active volume, but one event may only cause one bit error, a small SMT IC may suffer thousands of bit errors!). ◦ Software error detection and correction algorithms and coincidence detection. Now look at the differences between a ‘generic’ deep space environment and the local space around the Earth – the NEO environment. Thermal effects: Albedo and “Earth Shine” (the Earth reradiates some energy back into space). Radiation density ~ 200 W m-2. Eclipses (Earth passes between Spacecraft and Sun). ◦ ◦ ◦ ◦ ◦ Spacecraft cools Solar cells inoperative 35 minutes per orbit (~hours) for LEO 1.2 hours per orbit (1 day) for GEO Well understood effect, and thus can be accounted for in design and operation and is not a problem. Meteoroids (small, natural) and debris (man-made) The Earth enhances the number density and flux of interplanetary particles via: ◦ Gravitational focussing (particles are gravitationally attracted) ◦ Atmospheric focussing (particles interact with upper atmosphere, slow down, and get captured). ◦ Aero capture Total enhancement over interplanetary space environment is ~ a factor of 10. Man-made debris – now a major concern Created by: ◦ ◦ ◦ ◦ ◦ Dead satellites Old upper stages of rockets Fragments from exploded rockets/stages Flecks of paint Aluminium oxide spheres (microns in size) from solid rocket burns. 1 burn generates 1020 such spheres. When any of this debris hits something get a cloud of smaller ejected debris. The process is self propagating! (‘going viral’!). [F&S, Fig. 2.21, Pg. 35 Probably out of date!] Impact damage on Endeavour (STS-118) and Challenger window (STS-7) Microgravity Gravity gradient varies 10-3 – 10-11 g. Depends on spacecraft size, configuration, altitude. Accelerations (μg) due to attitude control, internal movement (mechanisms, pumps, astronauts). Difference from “zero gee” is important for some applications, experiments involving crystal growth etc., but not for the majority. Partial vacuum At orbital altitudes (few hundred km) vacuum is hard, but not total. This causes a drag force, slows the Spacecraft down and its orbit drops. Therefore need a altitude control mechanism. The ISS needs regular reboosts during its life to maintain its orbit. Also get low density plasmas and subsequent arcing between points at different electrical potential. Solutions: ◦ Good design (as always!) ◦ A ‘wake shield’. Fly Spacecraft behind a big shield. The vacuum behind the shield is improved. Atomic oxygen (not an obvious problem!) Atomic O recombines on Spacecraft surfaces, giving off a blue glow. This glow can interfere with scientific observations (optical astronomy). Atomic O also erodes some materials (e.g., kapton thermal blankets) chemically and physically (encounter velocity ~8 km s-1). Erosion rates ~1 μm/day at altitude of 250 – 300 km. Alters the reflective/emissive properties of materials thus degrading thermal control. Affects other materials, many plastics, silver etc. Magnetic field Earth’s magnetic field influences charged particles. ◦ Reflects some charged particles to give partial protection in LEO ◦ Traps others (Van Allen belts – has a confinement period of years). Regions of trapped particles may be unavoidable The South Atlantic Anomaly (SAA) is a particular problem as hard to avoid (altitude of a few hundred km). Spacecraft charging Caused by exposure to plasma and/or ionising radiation. Particularly bad at geosynchronous altitudes Clouds of trapped low energy (~keV) electrons formed by magnetic disturbances Interact with Spacecraft ◦ ◦ ◦ ◦ ◦ Charging of dielectrics Build-up of large potential differences Electrical arcing Physical damage Disruption of electronics Spacecraft charging (continued) Solution: provide conductive paths to prevent large potential differences. E.g., coat glass solar cells with indium oxide (indium oxide is conducting, but transparent). Protection ◦ Shielding ◦ Careful orbit selection ◦ De-orbit old spacecraft upper stages or push into a higher ‘graveyard’ orbit. Planets ◦ Thermal. Changes with distance from Sun. ◦ Magnetic fields Strong: Jupiter (severe problems), Saturn, Uranus and Neptune. Weak: Mercury, Venus and Mars ◦ No debris, but can get more natural dust (i.e., Saturn’s rings) but usually tenuous. Asteroid belt Comets ◦ Low number density ◦ Dust (?) ◦ Charged gas/plasma near nucleus ◦ Random loss of material at high speed ◦ ‘Dusty’ environment Summary – you should now have an understanding of the various environments that a spacecraft could encounter: ◦ ◦ ◦ ◦ ◦ Gravity Vacuum Thermal Radiation Debris, etc. Also an understanding of how these environments affect the Spacecraft and its subsystems ◦ General case of deep space ◦ Specific case of NEO and the differences between the two. ◦ Other areas around Solar System bodies. Conceptually The various phases of a space mission from ‘concept’ through to ‘end-of-life’ phase. An appreciation of some of the details of each of these phases and how financial, engineering and science constraints etc. affect mission design. How a spacecraft’s environment changes from ground level, near earth orbit and deep space. How these environments (radiation, thermal, dust etc.) feedback into the final mission design. Mathematically Understand how to use the drag equation to work out the force on a body as it travels through the atmosphere Calculate the solar constant for Earth and (other bodies) making justifiable assumptions. Derive the escape velocity of a body. Dr. Mark Price ◦ Room 103C ◦ E-mail: [email protected] Lectures notes will eventually be available on Moodle, but can be downloaded now from: http://astro.kent.ac.uk/~mcp2/teaching/PH508