The Eclipse Percentage Calculator helps determine how much of the Sun is cover during a solar eclipse. It calculates the obscuration percentage based on the apparent sizes of the Sun and Moon and their distance apart during the event. This percentage is crucial for astronomers, photographers, and enthusiasts who want to understand the extent of an eclipse visible from their location. The higher the percentage, the more of the Sun is obscured, with 100% representing a total solar eclipse.
formula of Eclipse Percentage Calculator
Obscuration Percentage = [(Area of Moon's Disk Overlapping Sun's Disk) / (Total Area of Sun's Disk)] * 100
Où :
Area of Moon's Disk Overlapping Sun's Disk = π × (Radius of Moon)^2 × √[1 − (Distance / (Radius of Sun + Radius of Moon))^2] + π × (Radius of Sun)^2 × √[1 − (Distance / (Radius of Sun + Radius of Moon))^2] − 2 × (Radius of Sun) × (Radius of Moon) × arccos(((Distance)^2 + (Radius of Sun)^2 − (Radius of Moon)^2) / (2 × Distance × Radius of Sun))
Total Area of Sun's Disk = π × (Radius of Sun)^2
Radius of Sun and Radius of Moon are the apparent angular radii (in radians or consistent units)
Distance between centers of Sun and Moon is the angular separation between the centers of the Sun and Moon (in the same units as the radii)
Tableau de référence général
| Eclipse Type | Approx. Obscuration (%) | Description |
|---|---|---|
| Éclipse partielle | 1% - 90% | Sun is partially covered |
| Eclipse annulaire | ~90% - 99.5% | Sun appears as a ring |
| Total Eclipse | 100% | Sun is completely covered |
| Penumbral Coverage | Very minor dimming, barely noticeable |
This table offers a quick reference based on commonly observed eclipse types.
Example of Eclipse Percentage Calculator
Supposer:
- Radius of Sun = 0.26 (radians)
- Radius of Moon = 0.25 (radians)
- Distance between centers = 0.05 (radians)
First, calculate the total area of the Sun: Total Area = π * (0.26)^2 = 0.2123
Next, plug into the overlapping area formula (simplified here for example): Overlapping Area ≈ 0.1703
Then calculate: Obscuration Percentage = (0.1703 / 0.2123) * 100 ≈ 80.21%
So, approximately 80.21% of the Sun is cover.
FAQ les plus courantes
It is the amount of the Sun's surface covered by the Moon during a solar eclipse, express as a percentage.
No, this calculator is design for solar eclipses and the Sun-Moon overlap. Lunar eclipses follow a different visibility and shadow model.
It helps determine how much light is blocked, which affects visibility, safety precautions, and astronomical observations.