Orbital Period Calculator

Orbital period

“The time that an item or satellite tv for pc takes in final touch of 1 whole rotation around some other large item is called the orbital period”

Orbital period Equation:

The system this is used for the low earth orbit is as follows:

\(T = \sqrt(\dfrac{3\pi}{G*P})\)

To calculate the orbital length of a binary star machine, use the subsequent method::

\(T_b=2\pi \sqrt(\dfrac{a^{3}}{G(M_1 + M_2})\)

The way to Calculate Orbital duration?

Go through the subsequent steps to calculate the orbital length::

For Low Earth Orbit:

• Be aware down the data which you have on paper
• Multiply 3 through the cost of pi
• Now multiply the normal gravitational consistent by the suggest density of the imperative frame
• placed the values within the above-stated orbital duration formulation as we have completed in the following example.

Example:

Suppose the central body density is \(5.51 \, \text{g/cm}^3\), how do we find the orbital period for a low Earth orbit?

Solution:

Given:

• Density (\(P\)) = \(5.51 \, \text{g/cm}^3\)

Convert density into \(\text{kg/m}^3\):

\[ P = 5.51 \times 1000 \times \left(\frac{1}{100}\right)^3 = 5510 \, \text{kg/m}^3 \]

Gravitational constant (\(G\)):

\[ G = 6.67 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2} \]

Orbital period equation:

\[ T = \sqrt{\frac{3 \pi}{G \cdot P}} \]

Substitute the values:

\[ T = \sqrt{\frac{3 \times 3.14159}{(6.67 \times 10^{-11}) \cdot 5510}} \]

Calculate step-by-step:

• \(3 \times 3.14159 = 9.42477\)
• \((6.67 \times 10^{-11}) \cdot 5510 = 3.67617 \times 10^{-7}\)
• \(\frac{9.42477}{3.67617 \times 10^{-7}} = 2.5643 \times 10^{7}\)
• \(\sqrt{2.5643 \times 10^{7}} = 5063.16 \, \text{seconds}\)

Convert seconds to hours:

\[ T = \frac{5063.16}{3600} \approx 1.406 \, \text{hours} \]

Answer: The orbital period is approximately \(1.406 \, \text{hours}\).

For Binary famous person system:

• gather the records approximately the applicable parameters together with the semi-fundamental axis, first frame mass, and second frame mass
• Write down the orbital length formulation
• positioned the values inside the formula for calculating orbital period as we have completed beneath