1. What is an Orbital Energy Calculator?

Definition: This calculator computes the total orbital energy of a system consisting of two bodies in a gravitational orbit.

Purpose: It helps astronomers, physicists, and space enthusiasts understand the energy dynamics of orbital systems.

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: Understanding orbital energy helps predict satellite behavior, plan space missions, and study celestial mechanics.

4. Using the Calculator

Tips: Enter the masses of both bodies in kg and the semi-major axis in meters. For Earth, mass ≈ 5.97×10²⁴ kg. For Earth's orbit around Sun, a ≈ 1.496×10¹¹ m.

5. Frequently Asked Questions (FAQ)

Q1: Why is orbital energy negative?
A: Negative energy indicates a bound system. Zero would mean the orbit is just unbound (parabolic), and positive would be hyperbolic.

Q2: What's the gravitational constant value?
A: G = 6.67430×10⁻¹¹ m³ kg⁻¹ s⁻² (2018 CODATA recommended value).

Q3: Can I use this for elliptical orbits?
A: Yes, the formula applies to all bound orbits (circular and elliptical), with 'a' being the semi-major axis.

Q4: How does energy relate to orbital period?
A: Through Kepler's third law: \( T^2 \propto a^3 \), where T is the orbital period.

Q5: What units should I use?
A: Use SI units: kilograms for mass, meters for distance, resulting in Joules for energy.