Implications of Errors in Density Response Time Delay on Satellite Prediction Error Rodney L. Anderson and Christian P. Guignet October 28, 2010, NADIR MURI meeting

Introduction  Orbit prediction relies on the prediction of density from atmospheric models.  Model predictions can sometimes be inaccurate, especially during magnetic storms.  A previous study by Forbes showed a premature increase in density predicted by a model caused a as large an error as predicting no variation.  J. M. Forbes, “Low-Altitude Satellite Ephemeris Prediction”  Delays of 1-4 hours are not uncommon.  This study seeks to quantify these errors by examining time delays in the density model.

Introduction  A simple two body model was used for the spacecraft integration.  Acceleration due to drag:  Velocity relative to the atmosphere:

Introduction  Atmospheric model used: NRLMSISE-00  Model densities were computed using values provided from the CHAMP spacecraft.  Densities obtained from observations by the CHAMP satellite were used as truth.  Density data used spans 2003 through  CHAMP was in a low Earth orbit with inclination of approximately 87° and initial altitude of 457 km.

Outline  Introduction  Storms in data  Perfect model comparisons  Delays in model data  Delays in real, smoothed data

Storms in Data  Multiple storms are examined to determine possible delays between model prediction and truth density.  The model densities are computed using the CHAMP altitude and position.  A 701 point smoothing is then used to observe the peaks in the densities.

October, 2003 – 1.5 hours November, 2003 – 1.68 hours July, 2004 – 3.15 hours November, 2004 – 3.18 hours Used in delayed orbit study.

Outline  Introduction  Storms in data  Perfect model comparisons  Delays in model data  Delays in real, smoothed data

Perfect Model Comparison  A spacecraft is integrated twice:  First orbit uses model densities.  Second uses CHAMP densities.  Initial 400 km, polar orbit.  24 hour integrations are performed over years  Results are given in the Radial, In-track, and Cross-track directions.

Perfect Model Comparison  Largest differences occur in the in-track direction.  Errors are in agreement with previous study by Anderson et al.  R. L. Anderson, G. H. Born, and J. M. Forbes, “Sensitivity of Orbit Predictions to Density Variability”  Differences are largest during more active times.

Outline  Introduction  Storms in data  Perfect model comparisons  Delays in model data  Delays in real, smoothed data

Delays in Model Data  How can delays in predicting the density effect a satellite’s orbit?  Delays were introduced into the model by altering the inputs by a number of hours.  1, 2, and 3 hour delays are examined.  A spacecraft was again integrated as before:  Once using perfect model inputs.  A second time using the delayed inputs.  Simulation performed for the year 2003.

One hour delay  A delay of one hour is added to the model inputs.  Largest difference again occurs in the in-track direction  Cross-track difference is significantly less than a meter.

Two hour delay  The simulation was performed using a 2 hour delay.  Same general behavior was observed with larger magnitudes.

Three hour delay  Behavior similar to 1 and 2 hour delays.  The large spikes in the orbit differences occur during large storms.

Delays in Model Data  Very large errors can occur (thousands of meters). Time Delays (h)Radial (m)In-track (m)Cross-track (m)  Mean errors are significant as well (tens of meters). Mean values of Orbit differences

Outline  Introduction  Storms in data  Perfect model comparisons  Delays in model data  Delays in real, smoothed data

Delays in Real, Smoothed Data  Quantify the effect of the time delay on orbit prediction using real-world density fluctuations.  Perform the same simulation before using different densities:  First orbit integrated using smoothed CHAMP density.  701 point smoothing used to remove short term variations.  Second orbit integrated using same density delayed by a specified amount of time.  Simulation performed over

One hour delay

Two hour delay

Three hour delay  Orbit differences in this simulation are similar to those seen in the model simulation.  Maximum differences occur during times of high geomagnetic activity.

Delays in Real, Smoothed Data  Maximum errors can reach thousands of meters.  Mean errors are smaller but still significant. Time Delays (h)Radial (m)In-track (m)Cross-track (m) Mean values of Orbit differences

Conclusions  Model predictions of density can lag behind actual density values, especially during times of high geomagnetic activity.  Delays of several hours are possible.  Density predictions can have a significant effect on satellite orbit predictions.  Orbit errors due to density delays can reach thousands of meters.  Mean values of the orbit errors are still significant.