Drag

The drag force model accounts for the deceleration experienced by a spacecraft due to atmospheric resistance. As a spacecraft orbits Earth, it encounters atmospheric particles that exert a retarding force opposite to the spacecraft's velocity vector. This force is particularly significant for low Earth orbit (LEO) satellites, where atmospheric density is higher.

Physical Description

Atmospheric drag arises from the collision of atmospheric molecules with the spacecraft's surface. The magnitude of the drag force depends on several factors:

• Atmospheric density: Varies with altitude, solar activity, and geomagnetic conditions
• Spacecraft cross-sectional area: The effective area presented to the velocity vector
• Ballistic coefficient: A measure combining spacecraft mass, drag coefficient, and cross-sectional area
• Relative velocity: The speed of the spacecraft relative to the atmosphere

The drag acceleration is given by:

a_drag = -0.5 * ρ * (v_rel · v_rel) * (A/m) * C_D * (v_rel / |v_rel|)

Where:

• ρ is atmospheric density
• v_rel is the spacecraft velocity relative to the atmosphere
• A is the cross-sectional area
• m is the spacecraft mass
• C_D is the drag coefficient

Components

The drag force model in AstroForceModels consists of several key components:

DragAstroModel

The main struct that encapsulates all drag-related parameters:

• satellitedragmodel: Defines the spacecraft's physical properties (area, drag coefficient, mass)
• atmosphere_model: Specifies which atmospheric model to use for density calculations
• eop_data: Earth Orientation Parameters for accurate atmospheric modeling

Satellite Shape Models

Different representations of spacecraft geometry:

• CannonballFixedDrag: Simplified spherical model with constant drag coefficient

Atmospheric Models

AstroForceModels supports seven different atmospheric models for calculating atmospheric density:

JB2008 - Jacchia-Bowman 2008

• Type: Semi-empirical thermospheric model
• Altitude Range: Surface to 1,000 km
• Features:
  • Includes solar activity effects (F10.7, Ap index)
  • Temperature and density variations
  • Based on satellite drag data
  • High accuracy for thermospheric modeling
• Primary Use: LEO satellites, precise orbit determination
• Data Sources: Satellite drag measurements, solar indices

JR1971 - Jacchia-Roberts 1971

• Type: Static diffusion model with empirical temperature profiles
• Altitude Range: 90 to 2,500 km
• Features:
  • Includes latitudinal, seasonal, geomagnetic, and solar effects
  • Statistical accuracy of ~15%
  • Assumption of rigid body rotation with Earth
  • Temperature-dependent composition
• Primary Use: General orbital mechanics, extended altitude range
• Data Sources: Spacecraft drag data, atmospheric measurements

MSIS2000 - NRL MSIS 2000

• Type: Empirical global reference atmospheric model
• Altitude Range: Surface to 1,000 km
• Features:
  • Mass spectrometer and incoherent scatter radar data
  • Comprehensive species composition (N₂, O₂, O, He, H, Ar, N)
  • Solar and geomagnetic activity dependence
  • International standard for space research
• Primary Use: High-precision applications, research
• Data Sources: Mass spectrometer, incoherent scatter radar, satellite data

ExpAtmo - Exponential Atmosphere

• Type: Simple exponential decay model
• Altitude Range: All altitudes (no upper limit)
• Features:
  • Assumes constant temperature with altitude
  • Exponential pressure/density decay: ρ = ρ₀ × e^(-h/H)
  • Scale height H ≈ 8.42 km
  • Very fast computation
• Primary Use: Quick analysis, initial estimates, educational purposes
• Mathematical Form: ρ(h) = ρ₀ × exp(-h/8420) where h is in meters

HarrisPriester - Harris-Priester

• Type: Semi-empirical thermospheric model with diurnal density variation
• Altitude Range: 100 to 1,000 km
• Features:
  • Cosine power law for diurnal density bulge (configurable exponent n, default 4)
  • Static density table for mean solar activity conditions
  • No space weather indices required
  • Fast computation
• Primary Use: General LEO analysis, cases where space weather data is unavailable
• Configuration: HarrisPriester(; n=4) where n controls bulge sharpness (2=smooth, 6=sharp)

HarrisPriesterModified - Modified Harris-Priester (Hatten & Russell 2017)

• Type: Improved semi-empirical thermospheric model
• Altitude Range: 100 to 1,000 km
• Features:
  • C³ continuous density profiles across altitude boundaries
  • Cubic dependency on 81-day centered average F10.7 solar flux
  • Eliminates singularities present in the classic model
  • Requires SpaceIndices.init() for F10.7 data
• Primary Use: Higher-fidelity LEO analysis where smooth derivatives are needed (e.g., optimization, AD)
• Reference: Hatten, N. & Russell, R. P. (2017). Advances in Space Research, 59(2), 571-586.
• Configuration: HarrisPriesterModified(; n=4) where n controls bulge sharpness

NoAtmosphere - No Atmosphere

• Type: Vacuum model
• Altitude Range: All altitudes
• Features:
  • Returns zero atmospheric density
  • Eliminates drag effects entirely
  • Useful for comparative studies
• Primary Use: High-altitude missions, interplanetary trajectories, model comparison

Model Selection Guidelines

Choosing the Right Atmospheric Model

The choice of atmospheric model depends on your mission requirements:

For High-Precision LEO Missions (< 600 km altitude):

• Recommended: JB2008 or MSIS2000
• Rationale: Most accurate for thermospheric conditions
• Applications: ISS, precise orbit determination, collision avoidance

For General LEO Applications (200-1000 km altitude):

• Recommended: JB2008 or JR1971
• Rationale: Good balance of accuracy and computational efficiency
• Applications: CubeSats, standard orbital propagation

For Extended Altitude Range (up to 2500 km):

• Recommended: JR1971
• Rationale: Only model extending beyond 1000 km altitude
• Applications: HEO missions, Molniya orbits, disposal orbits

For Rapid Analysis or Educational Use:

• Recommended: ExpAtmo
• Rationale: Fastest computation, simple physics
• Applications: Mission planning, parametric studies, teaching

For LEO Without Space Weather Data:

• Recommended: HarrisPriester
• Rationale: Diurnal density variation without requiring space indices
• Applications: Quick trade studies, historical analysis without index data

For Smooth Derivatives (Optimization / AD):

• Recommended: HarrisPriesterModified
• Rationale: C³ continuity avoids discontinuities in gradient-based methods
• Applications: Orbit optimization, sensitivity analysis, AD-based orbit determination

For High-Altitude or Interplanetary Missions:

• Recommended: NoAtmosphere
• Rationale: Negligible atmospheric effects
• Applications: GEO satellites, lunar missions, deep space

Computational Performance Comparison

*Perfect for vacuum conditions

Usage Examples

Basic Drag Model Setup

using AstroForceModels
using SatelliteToolboxAtmosphericModels
using SatelliteToolboxBase

# Define spacecraft properties
satellite_model = CannonballFixedDrag(
    area = 1.2,      # m²
    drag_coeff = 2.2, # dimensionless
    mass = 100.0     # kg
)

# Load Earth orientation parameters
eop_data = fetch_iers_eop()

# Create drag model with different atmospheric models
drag_model_jb2008 = DragAstroModel(
    satellite_drag_model = satellite_model,
    atmosphere_model = JB2008(),
    eop_data = eop_data
)

# Compute acceleration (typically called within integrator)
acceleration(state, parameters, time, drag_model_jb2008)

Comparing Different Atmospheric Models

using AstroForceModels
using ComponentArrays

# Test state (ISS-like orbit)
state = [6378.137 + 408.0, 0.0, 0.0, 0.0, 7.6600, 0.0]  # [km, km/s]
JD = date_to_jd(2024, 1, 5, 12, 0, 0.0)
p = ComponentVector(; JD=JD)
time = 0.0

# Create models with different atmospheres
models = [
    DragAstroModel(satellite_model, JB2008(), eop_data),
    DragAstroModel(satellite_model, JR1971(), eop_data), 
    DragAstroModel(satellite_model, MSIS2000(), eop_data),
    DragAstroModel(satellite_model, HarrisPriester(), eop_data),
    DragAstroModel(satellite_model, HarrisPriesterModified(), eop_data),
    DragAstroModel(satellite_model, ExpAtmo(), eop_data),
    DragAstroModel(satellite_model, NoAtmosphere(), eop_data)
]

model_names = ["JB2008", "JR1971", "MSIS2000", "HarrisPriester", "HarrisPriesterModified", "ExpAtmo", "NoAtmosphere"]

# Compare accelerations
for (i, model) in enumerate(models)
    accel = acceleration(state, p, time, model)
    println("$(model_names[i]): $(norm(accel)) m/s²")
end

Implementation Details

The drag acceleration computation involves:

1. Density Calculation: Using the specified atmospheric model and current spacecraft position
2. Relative Velocity: Computing spacecraft motion relative to the rotating atmosphere
3. Cross-sectional Area: Determining effective area based on velocity direction
4. Force Calculation: Computing the drag force and converting to acceleration

References

[1] Vallado, David A. "Fundamentals of Astrodynamics and Applications." 4th ed., 2013. [2] Montenbruck, Oliver, and Eberhard Gill. "Satellite Orbits: Models, Methods and Applications." Springer, 2000.