The Kepler’s Third Law Calculator calculates the orbital period of a planet around a star based on fundamental astronomical parameters. It determines the time taken by a planet to complete one full orbit around its host star, using Kepler’s Third Law of planetary motion.
Formula of Kepler’s Third Law Calculator
The formula used by the Kepler’s Third Law Calculator is:
T^2 = (4 * π^2 * a^3) / (G * (M1 + M2))
Where:
- T is the orbital period of the planet (time it takes to complete one orbit).
- G is the gravitational constant (6.67430e-11 m^3/kg/s^2)
- M1 and M2 are the masses of the two objects in the system (usually a planet and a star).
- a is the semi-major axis of the planet’s orbit.
π (pi) is a mathematical constant approximately equal to 3.14159265359.
Table for General Terms and Common Searches
| Term | Description |
|---|---|
| Orbital Period | Signifies time taken by a planet to complete an orbit |
| Semi-Major Axis | Represents the longest radius of an ellipse |
| Gravitational Constant | Determines the strength of gravitational force |
| Mass | Indicates the amount of matter in an object |
| Pi | Represents the mathematical constant (approx. 3.14) |
This table provides an overview of commonly used terms related to the Kepler’s Third Law Calculator, aiding users in understanding essential concepts without the need for repeated calculations.
Example of Kepler’s Third Law Calculator
Consider a scenario where a planet has a semi-major axis of 10,000 meters, while the combined mass of its star and the planet is 5×10245×1024 kilograms. By utilizing the Kepler’s Third Law Calculator, we can determine the orbital period of the planet around its star using the following formula:
T^2 = (4 * π^2 * 10,000^3) / (6.67430 \times 10^{-11} * 5 \times 10^{24})
After computing this formula, the orbital period of the planet will be determined.
Most Common FAQs
Kepler’s Third Law elucidates the relationship between a planet’s orbital period and its average distance from the sun. It is pivotal in understanding the dynamics of celestial bodies.
To utilize the calculator efficiently, ensure accurate inputs of the orbital period, semi-major axis, and masses of the celestial objects. Double-check the units to guarantee precise calculations.
Absolutely. Kepler’s Third Law is a fundamental principle governing the orbital dynamics of planets around stars and holds true universally.
