Orbit Time Calculator

Formula

The formula to calculate the Orbit Time (T) is:

\[ T = 2\pi \sqrt{\frac{a^3}{G \cdot M}} \]

Where:

\( T \) is the orbit time (seconds)
\( a \) is the semi-major axis of the orbit (meters)
\( G \) is the gravitational constant (\(6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}\))
\( M \) is the mass of the Earth (\(5.972 \times 10^{24} \, \text{kg}\))

Orbit Time: The time taken for a satellite or celestial body to make one complete orbit around another body. This time depends on the distance of the object from the body it is orbiting and the mass of the body being orbited.
Semi-Major Axis (a): The longest radius of an elliptical orbit, representing half the longest diameter of the ellipse.
Gravitational Constant (G): A physical constant involved in the calculation of gravitational effects, approximately \(6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}\).
Mass of the Earth (M): The mass of the Earth, approximately \(5.972 \times 10^{24} \, \text{kg}\).

Let's say the semi-major axis is \(7 \times 10^6\) meters. Using the formula:

\[ T = 2\pi \sqrt{\frac{(7 \times 10^6)^3}{6.67430 \times 10^{-11} \cdot 5.972 \times 10^{24}}} \]

We get:

\[ T \approx 5828\text{ seconds} \]

So, the orbit time is approximately 5828 seconds.