Propagation and Collision of Orbital Debris in GEO

Disposal Orbits

Benjamin Polzine

Graduate Seminar

Presentation Outline

Need – Approach - BenefitGEO Debris

Continuation of Previous WorkPropagation Methods

Modified Equinoctial ElementsPerturbations

CollisionsBreakup Model

Completed WorkWhat’s Left

Need – Approach - Benefit• Need

– GEO is a high-activity, valuable regime

– Debris remains here for a much longer period of time

– Debris behavior in the nearby graveyard orbit is not yet fully understood

• Approach– Create a high-accuracy propagator that takes into account

major perturbations in this regime

– Verify propagator for accuracy by propagating real TLE’s and comparing outcomes to observed outcomes

– Simulate collisions within and outside the regime

• Benefit– An understanding of debris behavior and danger to GEO

GEO Debris• Decommissioned GEO Satellites are generally

pushed into a Graveyard Orbit– >200 km above GEO

• Earth gravity perturbations– Results in “geopotential wells” that capture satellites

– Operational satellites use East-West station keeping to combat this effect

– Wells have unknown effect on debris population• Do they act as sinks?

Continuation of Previous Work• Continuing the work of Christina Diaz

– Study of collisional evolution of debris in Geopotential Wells and GEO Disposal Orbits

• Modeled in Fortran, Visualized in MATLAB

• Propagation with Cowell’s Method

• Perturbations include: – 16x16 Geopotential, Lunar/Solar Gravity, SRP

• Simulated East/West geopotential wells– Could not catch East-West trapped objects

• Had a suspect upward longitudinal drift

Propagation Methods

• Cowell’s Method– Summary: Direct integration of position and velocity

– Pros: Easy to understand, quick to code

– Cons: Not as accurate as VoP, runs slowly

• Variation of Parameters (VoP)– Summary: Break perturbative force down into changes

of each orbital element over time

– Pros: Accurate

– Cons: Hard to find errors, non-intuitive, breaks down at zero inclination if using COE element set

Modified Equinoctial Elements• A VoP element set

• Seeks to address singularity issues with more common VoP element sets

• Pros– Non-singular for any orbit

– High accuracy (as a VoP method)

• Cons– Non-intuitive elements

– Posigrade/Retrograde must be known

Perturbations• Earth’s Oblateness

– The oblateness of the Earth results in a non-constant gravitational force

– Earth analyzed as a checkerboard of different gravitational effects

– Strongest effects for GEO at J2, J22

Φ , 1 , sin ∗ , cos , sin

Φ ,

Perturbations• Earth’s Oblateness

Verified Propagation My J2+J22 Propagation

Perturbations• 3rd-Body Gravitation

– Pull of non-Earth bodies effect satellite’s orbit

– Strongest sources on an Earth satellite are Sun and Moon

– Dependent on vector between S/C and body

Lunar PerturbationSolar Perturbation

Perturbations• 3rd-Body Gravitation (Sun)

Verified Propagation

My Sun Gravity Propagation

Perturbations• 3rd-Body Gravitation (Moon)

Verified Propagation

My Lunar Gravity Propagation

Perturbations• Solar Radiation Pressure

– Photons expelled from the sun exert pressure on S/C

– Dependent on shape of S/C, orientation, mass distribution, and reflectivity

– Assumptions made• Constant Solar Flux @ 1367 W/m2

• 0 < CR < 2

• Spherical spacecraft model

• A/m ratio

P C Am r

Perturbations• Solar Radiation Pressure

Verified Propagation My SRP Propagation

Collisions• Collisions result in massive fragmentation that

can snowball in size– Adversely effects safety of satellites in GEO regime

– Very long time until deorbit is possible

• Low impact velocity (~1.5 km/s)– Typically same orbit, same direction, low orbit speed

• Use Hanada’s experimental scaling of NASA Standard Breakup Model for GEO regime

Hanada’s Breakup Model• NASA Standard Breakup Model describes a high-

speed collision model for LEO

• Hanada gives modification for low-speed GEO breakups

• Steps– Describe size distribution of breakup (LC)

– Determine A/m distribution

– Fragment dV distribution

• Fragment distribution favors low-mass, low-speed fragmentation

Completed Work• MATLAB Modified Equinoctial Propagator

– High accuracy for the following perturbations:• Earth’s Oblateness (J2, J22)

• Sun Gravity

– Need to be adjusted:• Moon Gravity

• SRP Perturbation

• Collection of GEO Debris TLE data

• Breakup model ~75% complete

What’s Left• MATLAB Modified Equinoctial Propagator

– Address perturbation issues

– Verification vs. TLEs

• Completion of Breakup Model– Verification against Hanada’s output

• Collision Simulation– Collision conditions

– # of fragments to propagate

– Verification of orbital well entrapment

– Behavior analysis

Questions?