Simulating Space Debris from a Satellite Explosion

Simulating Space Debris from a Satellite ExplosionThomas Nevins, University of Wisconsin Eau Claireworking with Dr. Paul Thomas

The Space Debris ProblemLow Earth Orbit (LEO) contains most satellites.Telecommunication, Military, ISS, Hubble, & Remote SensingAbout 200 km to 2000 km in altitude.LEO contains the most Space Junk.Objects move as fast as 20,000 mph.A chain reaction where debris from one satellite destroys another, and creates more debris is called a Kessler Cascade

Handling Space DebrisHuge amounts of the debris are due to collisions or explosions.Previous work (Springer, de Vires, NASA) has focused on:Tracking the existing debris.Predicting the change in debris population.Instead we will focus on tracking the path of a single broken satellite.

Finite DifferencingFinite Differencing Algorithm:Start with velocity and positionCalculate acceleration.Use acceleration to get new velocityUse old velocity to get new positionRepeat!Algorithm was run with MatlabPlotted in Maple

Calculate accelerationCalculate new velocity and new position. Increase time.Create starting debris: ShardsGive each shard starting velocity/positionEQs of MotionCheck timePlot

Orbital MotionIt is too difficult to handle satellites with a fixed frame, because they are already orbiting.

So we use a non-inertial frame instead to imagine the forces the satellite is feeling.

The car-ride analogy.

Perceived Force

Equations of MotionAH!!!

Red is the centrifugal forceBlue is the coriolis forceGreen is gravityWhite is air resistance

Thankfully the Computer Does the Rest!Test conditions:Original Speed: 7000 m/s Original Altitude: 2000 kmExplosion Speed: 500 m/sMass: 20,000 kgArea: 10.5 m^2

The Bad NewsThe simulation above is for about 6 hours.In 6 hours, a single point populates the entire orbit. (hundreds of thousands of kilometers cubed.)This is a relatively slow explosion (low explosion velocity, and high altitude)Only 35 points were used, many more pieces would be made normally.These points would all have the energy to destroy a satellite or a manned mission beyond Earth. If the debris problem goes untreated we could soon find LEO to be a wall of high speed space junk in a matter of hours.

The Good NewsLots of people are trying to mitigate debris.Having a simulation means we can test the mitigation before launch.After more time, some of the debris may lose enough energy that it falls out of orbit.Space debris has a strange trajectory, but a predictable one.Most debris is very small.

References and Acknowledgements Springer, H.K. et al. (2010) Satellite Collision Modeling with Physics-Based Hydrocodes: Debris Generation Predictions of the Iridium-Cosmos Collision Event and Other Impact Events. 2010 AMOS (Advanced Maui Optical and Space Surveillance) Conference Proceedings, Kihei, HI, pp. 362-372. (2) de Vires W.H., and D.W. Phillion (2010). Monte Carlo Method for Collision Probability Calculations using 3D Satellite Models. Proc. Adv. Maui Optical and Space Surveillance Technol. Conf., Wailea, Maui, HI.(3) NASA Orbital Debris Program Office, http://orbitaldebris.jsc.nasa.gov/. (Accessed April 18th, 2013).(4) Simulations were programmed and plotted using the computer algebra system Maple 14, and Matlab. (5) Special thanks to the University of Wisconsin Eau Claire Department of Physics and Astronomy for allowing us to use their computers.