DENSITY ALTITUDE MODEL assume perfect gas and constant temperature p A d nkT p=nkT h dh n is number density (number/m )dpa-nmgadh=o dnt k is boltzmann's constant nMg= M is average molecular mass n K H84km h 120km n=nexp (-h/H) h=kT/mg(scale heigh
DENSITY ALTITUDE MODEL Assume perfect gas and constant temperature n is number density (number/m 3) dpA - n m g A d h = o k is Boltzmann’s constant M is average molecular mass H ~ 8.4km h ~ 120km n = n oexp (-h/H) H { kT/mg (scale height) dh d nk T dh dp p n k T ¸ ¸ ¹ · ¨ ¨ © § dh d nk T nMg dhdp ¸ ¸ ¹ · ¨ ¨ © § dh K T Mg n dn p A dh p+dp 11
Atmos eric gases At higher altitudes o breaks down intoo by uv Primarily o from 80-90 km to 500 km Hydrogen and helium beyond 500 km Kinetic energy of o atom at 7. 8 km/s 5ev(enough to break molecular bonds -- 2ev) O is highly reactive and destructive to spacecraft Temperature at leo increases with altitude Atmosphere expands when heated by high UV(solar max) LEO densities- 108 particles/cm3
Atmospheric Gases • At higher altitudes O 2 breaks down into O by UV • Primarily O from 80 - 90 km to 500 km • Hydrogen and Helium beyond 500 km • Kinetic energy of O atom at 7.8 km/s ~ 5eV (enough to break molecular bonds ~1 - 2eV) • O is highly reactive and destructive to spacecraft • Temperature at LEO increases with altitude • Atmosphere expands when heated by high UV (solar max) • LEO densities ~ 10 8 particles/cm 3 12
ATMOSPHERIC MODEL Most common mass spectrometer and incoherent Scatter model -1986 (MSIS-1986 Based on measured data Requires ap, F1o. 7, month as input Gives average values of n, n t atomic mass as function of altitude Instantaneous values can vary by factor of 10 http:nssdc.gsfcnasagov/space/modellatmos/msis.html
ATMOSPHERIC MODEL 13 Most common Mass Spectrometer and Incoherent Scatter model - 1986 (MSIS - 1986) – Based on measured data – Requires A p, F10.7, month as input – Gives average values of n, n o, T, atomic mass as function of altitude – Instantaneous values can vary by factor of 10 http://nssdc.gsfc.nasa.gov/space/model/atmos/msis.html
AERODYNAMIC DRAG D=--PV Ov(-CDA rag 4112Cn Ballistic coefficient B=m p=density of the atmosphere=m yo oem 16x167X1027×1013=267×1013kg V=7. 8km/s "D- Drag coefficient A- Cross sectional area
AERODYNAMIC DRAG Drag Ballistic coefficient U=density of the atmosphere=m o n o =16x1.67x10-27x1013=2.67x10-13kg/m 3 V=7.8km/s C D - Drag coefficient A - Cross sectional area D 1 2 Uv x v ( v v ) CDA D m d v d t ' v 1 2 Uv 2 CDA m ª ¬ «« º¼»» 't E m CDA ª ¬ «« º ¼ »» 14
DRAG COEFFICIENTS Derived from Newtonian Aerodynamics. Depends on what air molecule does at impact Reflected CD=4 absorbed C=2 D Since f=d(mv)/dt D=-F=-d(mv)/dt 0 pv2 Adt Av. dt CD=-2(v-vi) 2 ife=o in rarefied atmosphere =4 ife=-v 15
DRAG COEFFICIENTS Derived from Newtonian Aerodynamics. Depends on what air molecule does at impact – Reflected C D = 4 – Absorbed C D = 2 Since F = d(mv)/dt D = - F = - d(mv)/dt o m = U Avidt C D = - 2 (v f - vi)/vi = 2 if v f = o in rarefied atmosphere = 4 if v f = - vi V Adt m V V V A C D i f i D 2 2 2 1 2 1 U U ¸ ¸ ¹ · ¨ ¨ © § A 15