Orbit Radius Calculator Online

In the realm of celestial mechanics, understanding the orbital radius of celestial bodies like planets and moons is crucial. The Orbit Radius Calculator is a powerful tool that provides a quick and efficient way to determine the orbital radius of an object based on key parameters.

Formula of Orbit Radius Calculator

Celestial Mechanics (Planets, Moons, etc.)

Here, the formula for the orbital radius is:

R = [(G * M * T^2) / (4π^2)]^(1/3)

Where:

• R is the orbital radius (meters)
• G is the gravitational constant (6.6743 × 10^-11 m^3 kg^-1 s^-2)
• M is the mass of the central object (star) in kilograms (kg)
• T is the orbital period of the orbiting object (seconds)
• π (pi) is the mathematical constant (approximately 3.14159)

General Terms Table

Celestial Body	Orbital Period (Earth Days)	Orbital Radius (x 10^9 meters)
Mercury	88	0.39
Venus	225	0.72
Earth	365	1.49
Mars	687	2.28
Jupiter	4,333	7.78
Saturn	10,759	14.3
Uranus	30,689	28.7
Neptune	60,223	44.9

Note: This table provides estimated orbital radii and orbital periods in Earth days for reference. The specific calculator you use might offer values in different units and for additional celestial bodies.

Example of Orbit Radius Calculator

Consider a scenario where the gravitational constant (G) is 6.6743 × 10^-11 m^3 kg^-1 s^-2, the mass of the central object (M) is 5.972 × 10^24 kg (mass of Earth), and the orbital period (T) is 86400 seconds (one day). Using the formula provided:

R = [(6.6743 × 10^-11) * (5.972 × 10^24) * (86400^2) / (4 * 3.14159^2)]^(1/3)

After calculations, we find that the orbital radius R is approximately 3.844 × 10^8 meters, which is the average distance between the Earth and the Moon.

This example demonstrates how the Orbit Radius Calculator can efficiently determine the orbital radius based on essential parameters.

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