1. What is Gravitational Potential Energy?

Gravitational potential energy (U) is the energy an object possesses due to its position in a gravitational field. It represents the work done against gravity to bring masses from infinity to their current positions.

2. How Does the Calculator Work?

The calculator uses the gravitational potential energy equation:

Where:

• \( U \) — Gravitational potential energy (J)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ N·m²/kg²)
• \( m_1 \) — Mass of first object (kg)
• \( m_2 \) — Mass of second object (kg)
• \( r \) — Distance between centers of mass (m)

Explanation: The negative sign indicates that the force is attractive. The potential energy increases (becomes less negative) as the distance between objects increases.

3. Importance of Gravitational Potential Energy

Details: This concept is fundamental in astrophysics, orbital mechanics, and understanding celestial motion. It helps calculate escape velocities, orbital energies, and is essential for space mission planning.

4. Using the Calculator

Tips: Enter masses in kilograms and distance in meters. All values must be positive, with distance greater than zero. For astronomical calculations, use scientific notation (e.g., 5.972e24 for Earth's mass).

5. Frequently Asked Questions (FAQ)

Q1: Why is gravitational potential energy negative?
A: The negative sign indicates that work must be done against gravity to separate the objects. Zero potential energy is defined at infinite separation.

Q2: How does this relate to gravitational force?
A: The gravitational force is the negative derivative of potential energy with respect to distance (\( F = -\frac{dU}{dr} \)).

Q3: Can this be used for objects near Earth's surface?
A: For small height changes near Earth, we typically use the simplified \( U = mgh \), where g is gravitational acceleration (9.81 m/s²).

Q4: What are typical values for celestial bodies?
A: For Earth-Sun system: ~-5.3 × 10³³ J. For a 1kg object at Earth's surface: ~-6.25 × 10⁷ J.

Q5: How is this different from gravitational potential?
A: Gravitational potential is potential energy per unit mass (\( \Phi = \frac{U}{m} \)), measured in J/kg.