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Presentation transcript:

Rosetta_CD\PR\what_is_RS.ppt, :26AM, 1 Mars Express Radio Science Experiment MaRS MaRS Radio Science Data: Level 3 & 4 Basics S.Tellmann, M.Pätzold ESAC June 2008

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 2 Overview LEVEL 3: The Bending Angle & the Rayparameter The Refractive Index/Refractivity & Radius LEVEL 4: The Neutral Atmosphere Density Temperature Pressure The Ionosphere The Electron Density The Twoway Problem

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 3 Earth Occultations Ionosphere Mars Neutral Atmosphere f rec w/o f = f +  f rec w/o send MEX dop MEX f : signal transmitted from MEX f : signal received w/o atmosphere  f : classical Doppler shift MEX send w/o rec dop

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 4 Earth Occultations Ionosphere Mars Neutral Atmosphere f rec w/o f = f +  f rec w/o send MEX dop MEX f : signal transmitted from MEX f : signal received w/o atmosphere  f : classical Doppler shift f : signal received with atmosphere  f : frequency shift from atmosphere MEX send w/o rec dop rec with f = f +  f +  f +  f rec with MEX send dopiono atm rec with f atm   bending angle Ray Asymptote

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 5 Bending Angle & Rayparameter Retrieval based on geometrical optics [Fjeldbo et al., 1971]  : bending angle a : rayparameter

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 6 Bending Angle & Rayparameter [Fjeldbo et al., 1971] Basic Idea: Input: Position of Spacecraft, Groundstation & Mars Velocity of Spacecraft, Groundstation & Mars

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 7 Doppler Effect For v Earth << v S/C :

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 8 The Refractivity Calculation of Refractive index from bending angle and rayparameter Reconstruction of a two-dimensional radial symmetric distribution f(r) from its projection g(y) inverse Abeltransform The twodimensional function is given by: [Pretzler et al., 1992] [Jenkins, 1992] Abel transform: Inverse Abel transform:

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 9 The Refractivity Inverse Abeltransform: Integration of bending angle and rayparameter over all layers already traversed Refractive Index: n1n1 n2n2 n3n3 n4n4

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 10 The Radius (ray peripasis) r : radius a : rayparameter n : refractive index

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 11 Refractivity Ionosphere: Negative Refractivity higher than ~ 80 km altitude approx km radius Transition Region: no significant bending approx. 60 km – 80 km altitude approx km – 3480 km Neutral Atmosphere: Positive Refractivity up to approx. 50 km altitude up to approx km radius Neutral Atmosphere Ionosphere Ionopause Transition Region Refractivity

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 12 Retrieval of atmospheric parameter f 0 : Radio link frequency N e : electron density C 1, C 3 : atm. constants k : Boltzman constant n: neutral number density Neutral AtmosphereIonosphere Refractivity  (h):

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 13 The Ionosphere f 0 : Radio link frequency N e : electron density C 3 : atm. constant Neutral AtmosphereIonosphere Refractivity  (h) in Ionosphere (h>60km):

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 14 The Electron Density f 0 : Radio link frequency N e : electron density C 3 = m 3 /s 2 refractivity is ~1/ f 2 S-band is more sensitive to electron density than X-band

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 15 The Neutral Atmosphere Neutral AtmosphereIonosphere Refractivity  (h) in neutral atmosphere (h<50km): Second term << first term C 1 : atm. constants k : Boltzman constant n: neutral number density

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 16 Neutral Number Density: Pressure (assuming hydrostatic equilibrium): Temperature: ideal gaslaw Neutral Atmosphere

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 17 The Twoway Problem

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 18 Ionosphere Mars Neutral Atmosphere f rec w/o f = f +  f rec w/o send MEX dop MEX f : signal transmitted from MEX f : signal received w/o atmosphere  f : classical Doppler shift f : signal received with atmosphere  f : frequency shift from atmosphere MEX send w/o rec dop rec with f = f +  f +  f +  f rec with MEX send dopiono atm rec with f atm   bending angle So far assumed: Oneway

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 19 But in Realty: Twoway Radio Link Ionosphere Mars Neutral Atmosphere f f = f +  f recsend Earth MEX up Earth send Up: X-band: 7.1 GHz

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 20 Ionosphäre Mars Neutralatmosphäre f f = f +  f recsend Earth MEX up f = { f +  f }· k MEX send Earth send up f · k MEX rec The Twoway Problem Up: X-band: 7.1 GHz

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 21 Ionosphere  Mars Neutral Atmosphere f f = f +  f recsend Earth MEX f = k· f + k·  f +  f Earth rec Earth send updown f Earth rec MEXup f = { f +  f }· k MEX send Earth send up The Twoway Problem Up: X-band: 7.1 GHz Down: X-band: 8.4 GHz S-band: 2.3 GHz

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 22 The Twoway Problem Bending of Radio link on Uplink & Downlink Difficult to seperate effects from Uplink & Downlink Different dependency on Radio frequency in Ionosphere and Neutral atmosphere Neutral Atmosphere: Independent of frequency Ionosphere:  ~ 1/ f 2

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 23 The Twoway Problem Different frequencies on Uplink and Downlink Ionospheric Bending is ~ 1/f 2 Different bending on Uplink & Downlink Bending in Neutral Atmosphere independent of frequency Retrieval of bending angle and rayparameter is exclusively dependent on measurement geometry!!!! No frequency dependeny taken into account! Solution: Retrieve Ionosphere and Neutral Atmosphere separately

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 24 Twoway Problem: The Ionosphere Best Solution: Use Differential Doppler (~ pure Oneway S-band Downlink) All effects ~ f are subtracted due to the use of to coherent frequencies Other solution: Make an iterative solution: solve for „mean Ionosphere“ Calculate electron density refractivity for Uplink & Downlink Make Raytracing: calculate bending in this „assumed“ atmosphere Compare solution of ray tracing with true residual……

Rosetta_CD\PR\what_is_RS_v4.ppt, :26AM, 25 Twoway Problem: Neutral Atmosphere Treat Uplink and Downlink explicitely with basic formulas from Oneway Solve Uplink & Downlink in the way already described Literature: Lipa, B. and Tyler, G.L., „Statistical and Computational Uncertainties in Atmospheric Profiles from Radio Occultation: Mariner 10 at Venus“, Icarus 39, 192 – 208. Jenkins et al., „Radio Occultation Studies of the Venus Atmosphere with the Magellan Spacecraft“, Icarus 110, 79 – 49.