Orbital Period Calculation of a Satellite around the Earth

Orbital Period Calculator

Enter the satellite's average altitude in meters:

function calculateOrbitalPeriod() { const G = 6.67430e-11; const M = 5.9722e24; const R = 6371000; const altitude = Number(document.getElementById("altitude").value); const h = altitude + R; const period = 2 * Math.PI * Math.sqrt(Math.pow(h, 3) / (G * M)); const periodInSeconds = period.toFixed(2); document.getElementById("result").innerHTML = "The orbital period is " + periodInSeconds + " seconds."; }

Orbital period is the time required for a satellite to complete one revolution around its parent body. The time period is related to the distance between the satellite and its parent body.

Briefly I will to discuss how to calculate the orbital period of a satellite orbiting the Earth. We will use the formula:

T = 2π√(a³/μ)

where T is the orbital period, a is the semi-major axis of the orbit, and μ is the standard gravitational parameter of the Earth.

First, we need to define the constants that we will use in the calculation. The gravitational constant (G) is a physical constant that is used to calculate the gravitational force between two objects. The mass of the Earth (M) is also required to calculate the standard gravitational parameter.

G = 6.67e-11 # gravitational constant M = 5.97e24 # mass of Earth

Then, we need to get the input from the user. The semi-major axis of the orbit (a) is the distance from the center of the Earth to the satellite, which is also known as the radius of the orbit. We will ask the user to enter the semi-major axis in meters.

a = float(input("Enter the semi-major axis of the orbit in meters: "))

Next, we use the formula T = 2π√(a³/μ) to calculate the orbital period (T) of the satellite.

T = 2 * math.pi * math.sqrt(a**3 / (G * M))

Lastly, we output the result to the user, with the result rounded to two decimal places.

# Output print(f"The orbital period is {T:.2f} seconds.")