Lunar Eclipse Visibility Calculator

Estimate the visibility of a lunar eclipse based on your latitude, longitude, and the eclipse’s magnitude.

Formulas Used

The visibility index estimates how well a lunar eclipse can be observed, expressed as a percentage score (0–100%).

  1. Latitude Factor:

    \[ \text{LatitudeFactor} = \cos\left(\frac{\text{latitude} \times \pi}{180}\right) \]

    Accounts for visibility based on latitude; equatorial regions (0°) have optimal visibility, decreasing toward the poles.

  2. Longitude Factor:

    \[ \text{LongitudeFactor} = \min\left(1, e^{-\frac{|\text{longitude}|}{90}}\right) \]

    Models visibility based on longitude, favoring locations closer to the prime meridian (0°).

  3. Magnitude Factor:

    \[ \text{MagnitudeFactor} = \text{magnitude} \]

    Directly uses the eclipse magnitude (0 to 1), where higher values indicate a more significant eclipse.

  4. Visibility Index:

    \[ \text{VisibilityIndex} = (\text{LatitudeFactor} \times \text{LongitudeFactor} \times \text{MagnitudeFactor} \times 100)\% \]

    Combines factors to estimate visibility, capped at 100%. Higher scores indicate better visibility.

Example Calculations

Example 1: Total Eclipse at Equator

Inputs: Latitude = 0°, Longitude = 0°, Magnitude = 1.0

Calculations:

  • Latitude Factor: \[ \cos\left(\frac{0 \times \pi}{180}\right) = 1 \]
  • Longitude Factor: \[ \min\left(1, e^{-\frac{|0|}{90}}\right) = 1 \]
  • Magnitude Factor: 1.0
  • Visibility Index: \[ (1 \times 1 \times 1.0 \times 100) = 100\% \]

Result: Visibility Index: 100% (optimal visibility for a total eclipse)

Example 2: Partial Eclipse at Mid-Latitude

Inputs: Latitude = 45°, Longitude = 90°, Magnitude = 0.5

Calculations:

  • Latitude Factor: \[ \cos\left(\frac{45 \times \pi}{180}\right) \approx 0.707 \]
  • Longitude Factor: \[ \min\left(1, e^{-\frac{|90|}{90}}\right) \approx 0.368 \]
  • Magnitude Factor: 0.5
  • Visibility Index: \[ (0.707 \times 0.368 \times 0.5 \times 100) \approx 13.02\% \]

Result: Visibility Index: 13.02% (reduced visibility due to location and partial eclipse)

Example 3: Penumbral Eclipse Near Pole

Inputs: Latitude = 80°, Longitude = 45°, Magnitude = 0.3

Calculations:

  • Latitude Factor: \[ \cos\left(\frac{80 \times \pi}{180}\right) \approx 0.174 \]
  • Longitude Factor: \[ \min\left(1, e^{-\frac{|45|}{90}}\right) \approx 0.607 \]
  • Magnitude Factor: 0.3
  • Visibility Index: \[ (0.174 \times 0.607 \times 0.3 \times 100) \approx 3.17\% \]

Result: Visibility Index: 3.17% (low visibility due to high latitude and penumbral eclipse)

How to Use the Calculator

Follow these steps to estimate lunar eclipse visibility:

  1. Enter Latitude: Input your latitude in degrees (-90 to 90, e.g., 40.7 for New York City).
  2. Enter Longitude: Input your longitude in degrees (-180 to 180, e.g., -74.0 for New York City).
  3. Enter Eclipse Magnitude: Input the eclipse magnitude (0 to 1, e.g., 1.0 for a total eclipse).
  4. Calculate: Click “Calculate Visibility” to see the result.
  5. Interpret Result: The Visibility Index (0–100%) indicates how well the eclipse can be observed. Higher scores mean better visibility. 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 visibility depends on factors like local time, weather, and the eclipse’s phase (penumbral, partial, or total).