# Orbital Period Calculator

Free Orbital Period Calculator determines the orbital period of a satellite and star binary system. It just takes the central body density along with the semi-major axis, first body mass, second body mass details and gives the orbital period in a less amount of time.

Orbital Period Calculator: Do you know that solving the orbital period problems is simple with our handy calculator tool. It will generate the accurate orbital period of a satellite using Kepler's third law along with the step by step process. Find the solved questions and more useful information like definition, the orbital period formula for binary star system, etc.

## Steps to Calculate Orbital Period

Below given is the step by step proess to get the orbital period of a satellite or planet or binary star system. Follow these techniques and rules to find the result.

Satellite Orbital Period:

• Get the central body density.
• Multiply the central body density with the gravitational constant.
• Divide 3π by the product and apply square root to the result.
• The result is the satellite around central sphere orbital period.

Binary Star System Orbital Period:

• Check the semi-major axis, first body, second body mass.
• Add the masses. Multiply the sum with the gravitational constant.
• Divide the cube of semi-mahor axis by the product.
• Find the square root of the result.
• Multiply it with the 2π to obtain binary system orbital period.

### Satellite Orbital Period Formula

Orbit is nothing but the path of a body that is revolving around a different object. Just like Earth orbits around the sun.

The orbital period is the time taken by an astronomical object to complete one orbit around the other object. In general, it applies to the planets, sun, moon, stars and many more. Kepler's third law or Kepler's laws planetary motion describes how a planet orbits around another.

The formula to calculate the orbital period of a satellite around the central body is T = √[3π / (G * ρ)]

Where,

T is the orbital period

G is the gravitational constant

ρ is the density of the central body

The binary star system has two stars that are close to each other and have similar masses that stars orbit around each other without a material central body. It has elliptical orbits.

The binary star system orbital period equation is Tbinary = 2π * √[a³/(G * (M₁ + M₂))]

Where,

M1 is the first body mass

M2 is the second body mass

a is the semi-major axis.

Example

Question: If the density of the earth is 5.21 g/cm³. What is the orbital period?

Solution:

Given that

Density of the earth ρ = 5.21 g/cm³ = 5210 kg/m³

The formula of orbital period is T = √[3π / (G * ρ)]

T = √[3 x 3.14 / (6.67408 × 10-11 x 5210)]

= √[2.7090 x 107]

= 5204 seconds

= 1.445 hours

Therefore, the orbital period of earth is 1.445 hours

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### Frequently Asked Questions on Orbital Period Calculator

1. How to calculate the orbital period of a binary star system?

To find the binary star system orbital period, you have to know the semi-major axis, first & second bodies mass. Divide the cube of the axis by the product of gravitational constant & sum of masses. Get the square root of the result with 2π to check the binary star orbital period.

2. What is Kepler's third law formula?

Kepler's 3rd law states that the square of the period is proportional to the cube of the semi-major axis of the orbit. Its formula is T = √(a34π²/G(M + m)).

3. What are the types of orbits?

There are different types of orbits, they are low earth orbit, transfer orbits, medium earth orbit, geostationary transfer orbit and sun-synchronous orbit.

4. What are the factors that affect the satellite orbital period?

The factor that affects the orbital period of a satellite is the central body density. By increasing the central body density, the orbital period value decreases. 