Flight_Dynamics

An Introduction to Astronautics Dr Simon A. Prince, City University London Dr Jai Joshi Formerly ESTEC, European Space Agency, Holland Prof. John Lagraff, Syracuse University, NY, USA 1/37 An Introduction to Astronautics Recommended Texts Fortescue, P., Stark, J., & Swinerd, G. “Spacecraft Systems Engineering” Wiley, 3rd Edition, 2004 Turner, Martin, J. L. “Rocket and Spacecraft Propulsion” Springer, 2nd Edition, 2006 Tribble, A. C. “The Space Environment” Princeton University Press, 1995. 2/37 An Introduction to Astronautics Part A: The Space Environment 3/37 Part A: The Space Environment An Introduction to Astronautics Part A: The Space Environment 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) The Earth’s Atmosphere The Earth’s Magnetic Field The Earth’s Gravitational Field The Sun and the Solar Wind The Magnetosphere The Plasma Environment and the Radiation Belts The Thermal Environment The Solar System Physical Hazards of the Near Earth Environment Human Factors of the Space Environment 4/37 Part A: The Space Environment 1. The Earths Atmosphere 5/37 Part A: The Space Environment 1. The Earths Atmosphere: Origin & Composition Nitrogen (78% @ h=0) • Produced by volcanic emission, and by denitrification of decaying organic substances. • Removed by various photochemical processes and by denitrification by microbes. Oxygen (21% @ h=0) • Produced mainly by plant photosynthesis. • Removed by oxidation processes – combustion, animal respiration. Argon (~0.9% @ h=0) • Inert gas – no significant atmospheric circulation process. Carbon Dioxide (~0.1% @ h=0) • Produced mainly by animal respiration, combustion and volcanic emission. • Removed by plant photosynthesis . Water Vapour ( ~85km • Uppermost regions of atmosphere - very low density means continuum model no longer valid (large molecular mean free path). • Kinetic Temperature (measure of average molecular kinetic energy) very high ~1000 - 2000oC. • High intensity solar & cosmic radiation causes ionization of air molecules – “Ionosphere” effective barrier to radio communication. • Exosphere ( h > ~ 500 km) region in which Space Shuttle and satellites operate in low Earth orbit – small levels of aerodynamic drag. 23/37 Part A: The Space Environment 1. The Atmosphere The Ionosphere • Ultraviolet and X-Ray wavelengths of solar radiation, as well as cosmic radiation from deep space, ionize air molecules. • Ionisation depends on molecular distribution and density through the atmosphere. 1000 900 N 800 700 600 500 400 300 200 100 0 10 6 O O 2 2 He Ar H • Different molecules are ionized at different altitudes due to change in atmospheric composition with altitude. • Different layers in the ionosphere. Altitude (km) 10 8 10 10 10 12 1014 10 16 1018 10 20 10 22 Number density (m-3) 24/37 Part A: The Space Environment 1. The Atmosphere The Ionosphere • Level of ionisation measured by electron density. • The higher the altitude, the higher the intensity of solar radiation BUT the lower the atmospheric density. Therefore low electron density. • Reducing altitude, increasing atmospheric density therefore increasing effect of solar radiation (increasing electron density), but reducing intensity of radiation due to absorption. • Eventually, as altitude reduces, intensity of solar radiation reduction begins to reduce the electron density. • A maximum in the electron density profile therefore exists. • Daily variations occur due to daytime – nighttime variation in solar radiation intensity. 25/37 Part A: The Space Environment 1. The Atmosphere The Ionosphere – The Chapman-Pedersen Electron Density Profile Pedersen (1927) and Chapman (1931) independently derived a mathematical model for the electron density profile through the ionosphere. Assumptions: • An exponential atmosphere in the ionosphere, where gas density at an altitude, z, is given (Eq 1.6) by: ρ = ρ0 e − z H where H= RT0 g (1.10) • Ionizing radiation of intensity I ∞ is incident vertically upon the atmosphere. • Ionization occurs at a rate associated with a constant ionisation coefficient: aj • Recombination occurs at a rate associated with a constant recombination coefficient: ar • Absorption occurs at a rate associated with a constant absorption coefficient: aa 26/37 Part A: The Space Environment 1. The Atmosphere The Ionosphere – The Chapman-Pedersen Electron Density Profile The absorption of radiation causes the intensity of radiation, I, to diminish according to: dI (1.11) = Iρaa dz The number of ionisation events per unit time and volume, q, is the: q = a j ρI (1.12) The rate of recombination of electrons and ions, r, is similarly: 2 r = ar ne (1.13) Combination of (1.10) and (1.11) and integration, given that I = I ∞ when z tends to infinity: (1.14) I = I e − Ha ρ e −z H ∞ a 0 27/37 Part A: The Space Environment 1. The Atmosphere The Ionosphere – The Chapman-Pedersen Electron Density Profile Combining (1.10) and (1.12) into (1.14) and since equilibrium of ionisation and recombination ( q = r ) gives the electron density: aj ne =  ρ0 e − z H I ∞ e − Ha ρ e  ar  a 0 −z H  2    1 (1.15) This relationship can then be simplified if it is rearranged by the substitution of a non-dimensional altitude: (1.16) ξ = z − ze max Then: ne = ne max 1 (1−ξ H −e −ξ H ) e2 (1.17) 28/37 Part A: The Space Environment 1. The Atmosphere The Ionosphere – The Chapman-Pedersen Electron Density Profile 9 8 7 6 /H Dimensionless altitude, 5 4 3 2 1 n e /n emax 0 -1 -2 -3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 29/37 Part A: The Space Environment 1. The Atmosphere The Ionosphere – daytime electron concentration profile 1000 900 800 700 600 500 400 300 200 100 D 0 2 1.E+02 10 10 1.E+03 3 Solar Maximum Solar Minimum Altitude (km) F2 F1 E 10 1.E+04 4 10 1.E+05 5 10 1.E+06 6 10 1.E+07 7 Daytime electron concentration (cm -3) 30/37 Part A: The Space Environment 1. The Atmosphere The Ionosphere – night-time electron concentration profile 1000 900 800 700 600 500 400 F 300 200 100 0 2 10 E Solar Minimum Solar Maximum Altitude (km) 1.E+02 1.E+03 10 3 10 1.E+04 4 10 1.E+05 5 10 1.E+06 6 10 1.E+07 7 Night-time electron concentration (cm -3) 31/37 Part A: The Space Environment 1. The Atmosphere The Ionosphere Layer Altitude (km) Night-time electron density (cm-3) Daytime electron density (cm3) Ion species Cause of Ionisation 2 2 D 60 - 85 < 102 103 NO+ O2+ Lyman α (1215 Å) E 85 - 140 ~2 x 103 1 – 2 x 105 NO+ O2+ Lyman β (1025 Å) X-Rays F1 140 - 200 2 – 5 x 105 NO+ O2+ O+ UV F2 200 - 1500 2 – 5 x 105 0.5 – 2 x 106 O+ He+ H+ UV The Ionospheric levels • A “C” – layer can sometimes form at the lowest level of the D layer, due to increased intensity of cosmic radiation. • Most of the D, E and F1 layers disappear at night. 32/37 Part A: The Space Environment 1. The Atmosphere The Ionosphere – Ground-satellite radio communication • Ionosphere represents an effective shield to certain frequencies / wavelength of radio waves. • Dependent on the natural frequencies within the ionosphere plasma such as: • Electron gyro frequency • Ion gyro frequency • Collision frequency of electrons • Low frequency radio waves absorbed by the F-layer. • Need to employ following bands for radio communication between ground and space: Ultra-High Frequency (UHF): 300MHz – 3GHz (1m – 10cm wavelength) Super-High Frequency (SHF): 3GHz – 30GHz (10cm – 1cm wavelength) Extremely-High Frequency (EHF): 30GHz – 300Gz (1cm – 1mm wavelength) 33/37 Part A: The Space Environment 1. The Atmosphere Effects of the tenuous atmosphere in low Earth orbit Atmospheric molecules / ions that exist as a rarefied plasma in low Earth orbit are still capable of exerting an aerodynamic effect on spacecraft. Given the speed of orbiting spacecraft, each impact by an atmospheric particle can be considered to transfer momentum to the spacecraft – aerodynamic drag. The resulting drag may be small, but over time this can act to decelerate the spacecraft into a lower orbit and, eventually, into re-entry and destruction in the Earth’s atmosphere. Sputnik 1 (1957) re-entered the Earth’s atmosphere After only 3 months in orbit. 34/37 Part A: The Space Environment 1. The Atmosphere Effects of the tenuous atmosphere in low Earth orbit Atmospheric molecules which impact spacecraft in low Earth orbit, with relatively high energies, can cause the chemical bonds keeping atoms on the surface material of the spacecraft to break. This causes surface damage to the spacecraft material, including ablation whereby the material is gradually eroded away. This effect is called Sputtering. The average impact energies of various constituent atoms / molecules is given at a number of orbital altitudes in table below: Altitude (km) 200 400 600 800 Velocity (km/s) 7.8 7.7 7.6 7.4 H 0.3 0.3 0.3 0.3 Species Average Energy (eV / particle) He 1.3 1.2 1.2 1.1 O 5.0 4.9 4.7 4.5 N2 8.8 8.6 8.3 7.9 O2 10.1 9.8 9.5 9.0 Ar 12.6 12.2 11.8 11.2 35/37 Part A: The Space Environment 1. The Atmosphere Effects of the tenuous atmosphere in low Earth orbit For sputtering to occur, the impact energy must exceed a certain threshold value (dependent on the strength of chemical bond in the particular material concerned). This threshold energy can be estimated by: m  Eth = 8U  t  m   i −1 3 for mt/mi < 3 (1.18) for mt/mi > 3.  4mt mi   1 − 4mt mi 2  Eth = U  2    (mt + mi )  (mt + mi )    where: U is the binding energy of a surface atom, mi is the mass of the impacting particle mt is the mass of the target atoms 36/37 Part A: The Space Environment 1. The Atmosphere Effects of the tenuous atmosphere in low Earth orbit The sputtering energy thresholds for several materials and incident species are given in table below. Target material Ag Al Au C Cu Fe Ni Si O 12 23 19 65 15 20 20 31 Sputtering Threshold Average Energy (eV / particle) O2 14 29 15 82 22 28 29 39 N2 13 27 15 79 21 27 27 37 Ar 17 31 15 88 24 31 31 42 He 25 14 53 40 20 23 24 18 H 83 28 192 36 60 66 72 40 37/37