### Orbital Period Calculator:

Orbital period is the time it takes for one astronomical object to complete one orbit around another object. Generally, it applies to planets, sun, moon, stars and so on. Kepler’s Third Law or Kepler’s Laws of Planetary Motion describes how one planet revolves around another.

Before the availability of orbital period calculators, calculating the orbital period of binary star systems or other planets was difficult.

The meaning of an orbit is clearly defined as the path that a body follows in its motion around another body. For example, Earth’s orbit around the Sun is the path our precious planet takes around the Sun every year.

Orbital period is the time taken to go completely around the central object or in other words, the time taken to go once around the orbit. This is also referred to as the lateral period.

How to calculate such a period for any two objects orbiting each other is to use the gravitational force exerted by one object on the other and solve all the equations.

It uses Kepler’s third law to gradually generate the exact orbital period of a satellite. Find useful information like solved questions and definition, orbital period formula for binary star system.

Below is a step by step procedure for obtaining the orbital period of a satellite or planet or binary star system.

Orbit is nothing but the path of a body around another object. As the earth revolves around the sun.

### Satellite orbital period Formula:

Satellite orbital period formula is T _{(s)} in second is equal to the root three multiply the √ 3π pi value in 3.14 and divided by the gravitational constant G_{(kgf)} in kilogram per force and multiply the density of the central body ρ_{(kgm3)} in kilogram meter3.Hence the satellite orbital period formula can be written as

T _{(s)}=√ 3π / (G_{(kgf)}*ρ_{(kgm3)} )]

Where

T = is the orbital period

G = is the gravitational constant

ρ = is the density of the central body

The binary star system orbital period equation is T binary

=2π * √ a^{2} / (G *(M_{1} + M_{2} )]

Where

M_{1} = is the first body mass

M_{2} = is the second body mass

A = is the semi-major axis

### Example:1

If the density of the earth is 4.28 g /cm^{3} .What is the orbital period?

### Answer:

Given that

Density of the earth p =4.28 g /cm^{3} =4280 kg /m^{3}

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

T = √ 3π / 6.67408 *10^{-11} *4.28

T = 181642.6343 sec

### Example:2

If the density of the earth is 5.48g /cm^{3}.What is the orbital period?

### Answer:

Given that

Density of the earth p =5.48 g /cm^{3} =5480 kg /m^{3}

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

T = √ 3π / 6.67408 *10^{-11} *5.48

T = 160527.4832 sec