1. What is Gravitational Binding Energy?

Gravitational binding energy (GBE) is the minimum energy that must be added to a system for it to cease being in a gravitationally bound state. For a water body, it represents the energy needed to disperse all its mass to infinity against gravitational attraction.

2. How Does the Calculator Work?

The calculator uses the gravitational binding energy formula:

Where:

• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg s²)
• \( M \) — Mass of the water body (kg)
• \( R \) — Radius of the water body (m)
• \( GBE \) — Gravitational binding energy (J)

Explanation: The formula calculates the energy required to overcome gravitational attraction and disperse the water mass to infinity.

3. Importance of GBE Calculation

Details: Calculating gravitational binding energy is important in astrophysics, planetary science, and understanding the stability and formation of celestial bodies composed primarily of water.

4. Using the Calculator

Tips: Enter the mass in kilograms and radius in meters. Both values must be positive numbers. The result will be in joules (J).

5. Frequently Asked Questions (FAQ)

Q1: Why is the binding energy negative?
A: The negative sign indicates that energy must be added to the system to unbind it. A more negative value means a more strongly bound system.

Q2: Does this formula work for all shapes?
A: This formula assumes a uniform spherical distribution. For irregular shapes, the calculation would be more complex.

Q3: What's the significance of the 3/5 factor?
A: The 3/5 factor comes from integrating the gravitational potential energy over a sphere of uniform density.

Q4: How does water's density affect the calculation?
A: For a given mass, the radius is determined by density. Water's density (≈1000 kg/m³) is factored into the radius input.

Q5: Can this be used for real celestial bodies?
A: While simplified, this calculation provides a good approximation for homogeneous water bodies like icy moons or theoretical water planets.