Gravitational Potential Energy Calculator

Gravitational Potential Energy Equation:

\[ U = -\frac{G \cdot m_1 \cdot m_2}{r} \]

Gravitational Constant (G):

N m²/kg²

Mass 1 (m₁):

Mass 2 (m₂):

Distance (r):

Gravitational Potential Energy (U):

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1. What is Gravitational Potential Energy?

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

2. How Does the Calculator Work?

The calculator uses the gravitational potential energy equation:

\[ U = -\frac{G \cdot m_1 \cdot m_2}{r} \]

Where:

\( G \) — Gravitational constant (6.674×10⁻¹¹ N m²/kg²)
\( m_1 \) — Mass of first object (kg)
\( m_2 \) — Mass of second object (kg)
\( r \) — Distance between centers of masses (m)
\( U \) — Gravitational potential energy (J)

Explanation: The negative sign indicates that the force is attractive. The potential energy increases (becomes less negative) as the distance between masses 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 gravitational interactions between celestial bodies.

4. Using the Calculator

Tips: Enter the gravitational constant (default is 6.674×10⁻¹¹ N m²/kg²), both masses in kilograms, and the separation distance in meters. All values must be positive.

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 masses. Zero potential energy is defined at infinite separation.

Q2: What is the gravitational constant (G)?
A: It's a fundamental physical constant that measures the strength of gravity. Its value is approximately 6.674×10⁻¹¹ N m²/kg².

Q3: Does this equation work for any distance?
A: It works for point masses or spherical objects where r is greater than the sum of their radii. For very small distances, quantum effects become significant.

Q4: How does this relate to orbital mechanics?
A: The total orbital energy is the sum of kinetic energy and gravitational potential energy, which determines the shape of orbits.

Q5: What are typical values for celestial bodies?
A: For Earth-Sun system, U ≈ -5.3×10³³ J. For two 1kg masses 1m apart, U ≈ -6.67×10⁻¹¹ J.