Orbital Debris Collision Risk Calculator

Estimate the collision risk for a satellite in low Earth orbit based on altitude, cross-sectional area, and mission duration.

Formulas Used

The collision risk index estimates the likelihood of a satellite colliding with orbital debris, expressed as a percentage score (0–100%).

  1. Altitude Factor:

    \[ \text{AltitudeFactor} = e^{-\frac{|\text{altitude} – 800|}{200}} \]

    Models debris density, peaking at 800 km where LEO debris is most concentrated.

  2. Area Factor:

    \[ \text{AreaFactor} = \min\left(1, \frac{\text{area}}{10}\right) \]

    Scales collision probability based on cross-sectional area, normalized to 10 m².

  3. Duration Factor:

    \[ \text{DurationFactor} = \min\left(1, \frac{\text{duration}}{5}\right) \]

    Scales risk with mission duration, normalized to 5 years.

  4. Collision Risk Index:

    \[ \text{CollisionRiskIndex} = (\text{AltitudeFactor} \times \text{AreaFactor} \times \text{DurationFactor} \times 100)\% \]

    Combines factors to estimate risk, capped at 100%. Higher scores indicate higher collision risk.

Example Calculations

Example 1: Small Satellite in LEO

Inputs: Altitude = 800 km, Area = 10 m², Duration = 5 years

Calculations:

  • Altitude Factor: \[ e^{-\frac{|800 – 800|}{200}} = 1 \]
  • Area Factor: \[ \min\left(1, \frac{10}{10}\right) = 1 \]
  • Duration Factor: \[ \min\left(1, \frac{5}{5}\right) = 1 \]
  • Collision Risk Index: \[ (1 \times 1 \times 1 \times 100) = 100\% \]

Result: Collision Risk Index: 100% (maximum risk at peak debris altitude)

Example 2: CubeSat in Lower LEO

Inputs: Altitude = 400 km, Area = 1 m², Duration = 2 years

Calculations:

  • Altitude Factor: \[ e^{-\frac{|400 – 800|}{200}} \approx 0.135 \]
  • Area Factor: \[ \min\left(1, \frac{1}{10}\right) = 0.1 \]
  • Duration Factor: \[ \min\left(1, \frac{2}{5}\right) = 0.4 \]
  • Collision Risk Index: \[ (0.135 \times 0.1 \times 0.4 \times 100) \approx 0.54\% \]

Result: Collision Risk Index: 0.54% (low risk due to small size and short duration)

Example 3: Large Satellite in Higher LEO

Inputs: Altitude = 1200 km, Area = 20 m², Duration = 10 years

Calculations:

  • Altitude Factor: \[ e^{-\frac{|1200 – 800|}{200}} \approx 0.135 \]
  • Area Factor: \[ \min\left(1, \frac{20}{10}\right) = 1 \]
  • Duration Factor: \[ \min\left(1, \frac{10}{5}\right) = 1 \]
  • Collision Risk Index: \[ (0.135 \times 1 \times 1 \times 100) \approx 13.53\% \]

Result: Collision Risk Index: 13.53% (moderate risk due to large area and long duration)

How to Use the Calculator

Follow these steps to estimate the collision risk for a satellite:

  1. Enter Altitude: Input the satellite’s altitude in kilometers (100–2000 km, typical for LEO).
  2. Enter Cross-Sectional Area: Input the satellite’s cross-sectional area in square meters (e.g., 10 for a typical satellite).
  3. Enter Mission Duration: Input the mission duration in years (e.g., 5 for a standard mission).
  4. Calculate: Click “Calculate Collision Risk” to see the result.
  5. Interpret Result: The Collision Risk Index (0–100%) indicates the likelihood of a debris collision. Higher scores mean higher risk. If you see “Please fill in all fields,” ensure all inputs are provided.
  6. Share or Embed: Use the share buttons to post results on social media, copy the result, or get an embed code for the calculator.

Note: This is a simplified model. Actual collision risk depends on factors like debris size, velocity, and mitigation measures.

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