Transcript Sean Bruinsma: Drag coefficient modeling for the Stella

Drag coefficients
Sean Bruinsma
CNES
Marcin Pilinski
CU Boulder
NADIR workshop - October 25-26, 2011
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The problem
The drag coefficient, CD, quantifies the atmospheric drag of an
object. It depends on surface material, speed, temperature,
atmospheric temperature and mean mass.
The drag acceleration of a spacecraft is computed as follows:
adrag
A
2
1
  2 CD v
m
2adrag m
 
2
CD Av
i.e., the drag coefficient scales density inferred from perturbation
analysis or accelerometer data directly.

But CD is not modelled
according to standards…
NADIR workshop - October 25-26, 2011
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GOCE: drag
Simplest macro-model:
Frontal area A = 0.70 m2
Mass = 1038 kg
Optical properties: ‘GRACE’
Drag coefficient CD = 2.65
(Accommodated diffuse=2.01
Specular: 0.64)
Using these values resulted
in the densities to the right
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GOCE: drag
However, more realistic values appear to be:
- A = 1.10 m2
- CD = 3.65
Difference with
JB2008 increases!
- Densities are 32% smaller when using the larger frontal area
- Densities are 37% smaller when using the larger CD
- Densities are 69% smaller when using larger frontal area and CD
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GOCE: satellite model
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GOCE: drag coefficient
CD=3.5-3.6
Computed speed ratio:
9.0 – 10.3
NB: ESOC uses CD=3.7, and this gave good station acquisition results
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Drag coefficient: high altitude
We selected an easy object for the study: a sphere
Satellite: Stella
Launched: 26 September 1993
Mean altitude: 800 - 835 km
Eccentricity: 0.02
Inclination: 98.6°
Diameter: 24 cm
Mass: 48 kg
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Drag coefficient: high altitude
Previous Work
Harrison and Swinerd 1995: estimated CD based on multi-satellite analysis
quasi-specular model
CD=2.52
Pardini et al. 2006: Estimated based
on literature review, some
adsorption considerations,
and Cook’s model
diffuse model
CD=2.2 - 2.8
[Pardini et al. 2006]
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Drag coefficient: high altitude
Diffuse Reflection With Incomplete Accommodation
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Drag coefficient: high altitude
Quasi-Specular Reflection and Goodman’s Model of Accommodation
Adapted from
Gregory and Peters
1987
cosine reflection
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ν=2.215
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Drag coefficient: high altitude
Semi-Empirical Satellite Accommodation Model (SESAM)
[Pilinski, 2011]
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Drag coefficient: high altitude
Model bias estimated by Bowman and Moe (2005)
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Drag coefficient: high altitude
Harrison and Swinerd, 1995
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Drag coefficient: high altitude
Pardini et al., 2006
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Drag coefficient: high altitude
Conclusions
Due to the large uncertainty in model inputs (i.e. accommodation coefficient),
lack of surface reflection data, and the significant differences in model results
(±15%), one could state that the problem of physical drag coefficients at 800
km remains largely unsolved
Fitted ballistic coefficients corrected for model bias result in a CD between 2.3
to 2.7
SESAM predicts a CD between 2.8 and 3.0
Accommodation values of 0.9 or higher will probably result in incorrect CD at
altitudes around 800 km. Therefore a value of 2.2 is likely to be too low.
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