1. NADIR workshop - October 25-26, 2011page 1 / 15 Drag coefficients Sean Bruinsma CNES Marcin Pilinski CU Boulder

2. NADIR workshop - October 25-26, 2011page 2 / 15 The drag coefficient, C D, 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: i.e., the drag coefficient scales density inferred from perturbation analysis or accelerometer data directly. But C D is not modelled according to standards… The problem

3. NADIR workshop - October 25-26, 2011page 3 / 15 GOCE: drag Simplest macro-model: Frontal area A = 0.70 m 2 Mass = 1038 kg Optical properties: ‘GRACE’ Drag coefficient C D = 2.65 (Accommodated diffuse=2.01 Specular: 0.64) Using these values resulted in the densities to the right

4. NADIR workshop - October 25-26, 2011page 4 / 15 GOCE: drag However, more realistic values appear to be: - A = 1.10 m 2 - C D = 3.65 - Densities are 32% smaller when using the larger frontal area - Densities are 37% smaller when using the larger C D - Densities are 69% smaller when using larger frontal area and C D Difference with JB2008 increases!

5. NADIR workshop - October 25-26, 2011page 5 / 15 GOCE: satellite model

6. NADIR workshop - October 25-26, 2011page 6 / 15 GOCE: drag coefficient NB: ESOC uses C D =3.7, and this gave good station acquisition results Computed speed ratio: 9.0 – 10.3 C D =3.5-3.6

7. NADIR workshop - October 25-26, 2011page 7 / 15 Satellite: Stella Launched: 26 September 1993 Mean altitude: 800 - 835 km Eccentricity: 0.02 Inclination: 98.6° Diameter: 24 cm Mass: 48 kg Drag coefficient: high altitude We selected an easy object for the study: a sphere

8. NADIR workshop - October 25-26, 2011page 8 / 15 Previous Work Harrison and Swinerd 1995: estimated C D based on multi-satellite analysis quasi-specular model C D =2.52 Pardini et al. 2006: Estimated based on literature review, some adsorption considerations, and Cook’s model diffuse model C D =2.2 - 2.8 [Pardini et al. 2006] Drag coefficient: high altitude

9. NADIR workshop - October 25-26, 2011page 9 / 15 Diffuse Reflection With Incomplete Accommodation Drag coefficient: high altitude

10. NADIR workshop - October 25-26, 2011page 10 / 15 Quasi-Specular Reflection and Goodman’s Model of Accommodation cosine reflection Adapted from Gregory and Peters 1987 ν =2.215 Drag coefficient: high altitude

11. NADIR workshop - October 25-26, 2011page 11 / 15 Semi-Empirical Satellite Accommodation Model (SESAM) [Pilinski, 2011] Drag coefficient: high altitude

12. NADIR workshop - October 25-26, 2011page 12 / 15 Model bias estimated by Bowman and Moe (2005) Drag coefficient: high altitude

13. NADIR workshop - October 25-26, 2011page 13 / 15 Harrison and Swinerd, 1995 Drag coefficient: high altitude

14. NADIR workshop - October 25-26, 2011page 14 / 15 Pardini et al., 2006 Drag coefficient: high altitude

15. NADIR workshop - October 25-26, 2011page 15 / 15 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 C D 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 C D at altitudes around 800 km. Therefore a value of 2.2 is likely to be too low. Drag coefficient: high altitude