Orbital Energy Calculator
Total Mechanical Energy: Joules
What is Orbital Energy?
Orbital energy refers to the total mechanical energy of an object in orbit around a larger central body. In celestial mechanics, this energy is the sum of two distinct components: kinetic energy (the energy of motion) and gravitational potential energy (the energy stored due to its position in a gravitational field). For a stable, closed orbit, the total energy is negative, which signifies that the object is "bound" to the central body and does not have enough energy to escape its gravitational pull.
The Physics Formula
The calculation for total specific orbital energy (ε) for a circular orbit is derived from the formula:
ε = -GM / 2r
Where:
- G: The universal gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²).
- M: The mass of the central body (e.g., Earth).
- r: The orbital radius (distance from the center of the central body to the object).
To find the total mechanical energy (E), we multiply the specific energy by the mass (m) of the orbiting object: E = ε × m.
How to Use the Calculator
Using this tool is straightforward. First, select the central body from the dropdown menu (Earth, Moon, or Sun) or enter a custom mass. Next, input the mass of your satellite or celestial object in kilograms. Finally, enter the orbital radius in meters. Keep in mind that the radius is measured from the center of the planet, not from the surface. If you have the altitude, add the planet's radius to it (Earth's average radius is approximately 6,371,000 meters).
Frequently Asked Questions
Why is the orbital energy negative?
In physics, a negative total energy indicates a bound state. Since potential energy is defined as zero at an infinite distance, any object trapped within a gravitational field has negative potential energy that outweighs its positive kinetic energy.
What happens if the energy becomes zero or positive?
If an object's total energy reaches zero, it is on a parabolic trajectory and has just enough speed to reach escape velocity. If the energy is positive, the object is on a hyperbolic trajectory and will leave the system entirely.