1. What is an Orbital Energy Calculator?

Definition: This calculator computes the total orbital energy of a two-body system using their masses and the semi-major axis of the orbit.

Purpose: It helps astronomers, physicists, and space enthusiasts understand the energy dynamics of celestial bodies in orbit.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( E \) — Orbital energy (Joules)
• \( G \) — Gravitational constant (6.674×10⁻¹¹ m³/kg·s²)
• \( M \) — Mass of central body (kg)
• \( m \) — Mass of orbiting body (kg)
• \( a \) — Semi-major axis (m)

Explanation: The negative sign indicates a bound system. The energy represents the sum of kinetic and potential energy in the orbit.

3. Importance of Orbital Energy Calculation

Details: Orbital energy helps determine if a system is bound (negative energy) or unbound (positive energy), and is fundamental in celestial mechanics.

4. Using the Calculator

Tips: Enter the masses of both bodies in kilograms and the semi-major axis in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is orbital energy negative?
A: Negative energy indicates a bound system where the orbiting body cannot escape the gravitational pull of the central body.

Q2: What's the gravitational constant value?
A: G = 6.674×10⁻¹¹ m³/kg·s², a fundamental constant of nature measured experimentally.

Q3: How do I find the semi-major axis?
A: For circular orbits, it's equal to the orbital radius. For elliptical orbits, it's half the longest diameter.

Q4: Can I use this for planets orbiting the Sun?
A: Yes, this works for any two-body system, from atomic to galactic scales.

Q5: What if I get positive energy?
A: Positive energy means the system is unbound (hyperbolic orbit), and the objects will escape each other's gravity.