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Satellite Orbital Eclipse Umbra & Penumbra Shadow Duration Calculator

Easily calculate and compute satellite orbital eclipse umbra & penumbra shadow duration calculator with accurate equations, live formulas, and expert guidance.

Circular low Earth orbit altitude.

Angle between orbit plane and Sun vector (-90° to +90°).

Calculated Result
35.3 min

Eclipse Duration

Eclipse Duration

35.3 min

Eclipse Duration Minutes

35.3

Sunlight Duration Minutes

59.3

Total Orbital Period Minutes

94.6

Critical Beta No Eclipse Deg

68

35.3 — min

Calculation Breakdown

  1. Applied FormulaCalculates the shadow passage duration (umbra/penumbra) and battery discharge time for satellites in circular Earth orbit as a function of orbital altitude and solar beta angle.\cos\theta = \frac{\cos\rho}{\cos\beta}, \quad T_{\text{ecl}} = \frac{\theta}{\pi} T_{\text{orbit}}

Satellite Eclipse Shadow Duration Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.08.8182635Eclipse Duration

What Is the Satellite Orbital Eclipse Umbra & Penumbra Shadow Duration Calculator?

This tool computes satellite orbital eclipse umbra & penumbra shadow duration calculator with high precision arithmetic.

How Does the Satellite Orbital Eclipse Umbra & Penumbra Shadow Duration Calculator Work?

Calculates the shadow passage duration (umbra/penumbra) and battery discharge time for satellites in circular Earth orbit as a function of orbital altitude and solar beta angle.

Satellite Orbital Eclipse Umbra & Penumbra Shadow Duration Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

cos⁡θ=cos⁡ρcos⁡β,Tecl=θπTorbit\cos\theta = \frac{\cos\rho}{\cos\beta}, \quad T_{\text{ecl}} = \frac{\theta}{\pi} T_{\text{orbit}}

Calculates the shadow passage duration (umbra/penumbra) and battery discharge time for satellites in circular Earth orbit as a function of orbital altitude and solar beta angle.

How to Use the Satellite Orbital Eclipse Umbra & Penumbra Shadow Duration Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Satellite Orbital Eclipse Umbra & Penumbra Shadow Duration Calculator Example

Input Values:

orbitalAltitudeKm:500
betaAngleDeg:15
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required min.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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