A satellite's altitude loss under atmospheric drag is found by integrating da dt = -…

PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Research software practice, verification and validation · Research software practice, verification and validation

Scientific Computing for Physicists, Ch Are they the right equations? Solution verification, benchmarks and validation

Problem

A satellite's altitude loss under atmospheric drag is found by integrating

\frac{da}{dt} = -\sqrt{\frac{\mu}{a}}\,\frac{C_dA}{m}\,\rho(a)\,a

with a verified RK4 code (order confirmed by a step-halving study), using a drag coefficient

C_d

from a preflight wind-tunnel test and a standard atmospheric density model

\rho(a)

. For a satellite orbiting near 400 km altitude, the code predicts an altitude loss over 30 days of

S = -12.4\,\mathrm{km}

. A step-halving study gives a numerical uncertainty

u_{\rm num} = 0.05\,\mathrm{km}

. Propagating the density model's stated

\pm 15\%

uncertainty at 400 km through the same code gives an input uncertainty

u_{\rm input} = 0.90\,\mathrm{km}

. Ground-based tracking of the satellite over the same 30 days gives

D = -13.1 \pm 0.4\,\mathrm{km}

. ((a)) Compute the comparison error

E = S - D

. ((b)) Combine

u_{\rm num}

u_{\rm input}

and

u_D

(independent sources) into

u_{\rm val}

. ((c)) Using

k = 2

, give the interval for

\delta_{\rm model}

and state whether the comparison is evidence of model-form error at 400 km. ((d)) The same

C_d

and density model, unchanged, are then used to predict the altitude loss of a different satellite orbiting near 250 km, where the density model's own uncertainty grows to about

\pm 40\%

because of variable atomic-oxygen composition, and where the flow regime around the satellite may differ chemically from the one in which

C_d

was measured. Is the 250 km prediction inside the validation domain established in part (c)? Justify.

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