Orbital Period Calculator

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The Two Body Problem

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Circular Orbits

Elliptical Orbits

Fundamental Parameters

Hyperbolic Orbits

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Circular Orbit Parameters

Geostationary Earth Satellite

✖The Orbit Radius is defined as the distance from the center of the orbit to the orbit's path.ⓘ Orbit Radius [r]			+10% -10%
✖Central Body Mass is the mass of the body being orbited (e.g. planet or sun).ⓘ Central Body Mass [M]			+10% -10%

✖The time period of Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.ⓘ Orbital Period [T_or]

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Formula

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Orbital Period

Formula

`"T"_{"or"} = 2*pi*sqrt(("r"^3)/("[G.]"*"M"))`

Example

`"11235.52s"=2*pi*sqrt((("10859km")^3)/("[G.]"*"6E^24kg"))`

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Orbital Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass))
T_or = 2*pi*sqrt((r^3)/([G.]*M))
This formula uses 2 Constants, 1 Functions, 3 Variables

Constants Used

[G.] - Gravitational constant Value Taken As 6.67408E-11
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Time Period of Orbit - (Measured in Second) - The time period of Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.
Orbit Radius - (Measured in Meter) - The Orbit Radius is defined as the distance from the center of the orbit to the orbit's path.
Central Body Mass - (Measured in Kilogram) - Central Body Mass is the mass of the body being orbited (e.g. planet or sun).

STEP 1: Convert Input(s) to Base Unit

Orbit Radius: 10859 Kilometer --> 10859000 Meter (Check conversion here)
Central Body Mass: 6E+24 Kilogram --> 6E+24 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_or = 2*pi*sqrt((r^3)/([G.]*M)) --> 2*pi*sqrt((10859000^3)/([G.]*6E+24))

Evaluating ... ...

T_or = 11235.5228888116

STEP 3: Convert Result to Output's Unit

11235.5228888116 Second --> No Conversion Required

FINAL ANSWER

11235.5228888116 ≈ 11235.52 Second <-- Time Period of Orbit

(Calculation completed in 00.021 seconds)

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Created by Kaki Varun Krishna

Mahatma Gandhi Institute of Technology (MGIT), Hyderabad

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National Institute Of Technology (NIT), Hamirpur

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< 11 Circular Orbit Parameters Calculators

Orbital Period

Go Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass))

Circular Orbital Radius Given Time Period of Circular Orbit

Go Orbit Radius = ((Time Period of Orbit*sqrt([GM.Earth]))/(2*pi))^(2/3)

Speed of Satellite in Circular LEO as Function of Altitude

Go Speed of Satellite = sqrt([GM.Earth]/([Earth-R]+Height of Satellite))

Time Period of Circular Orbit

Go Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth]))

Velocity of Circular Orbit

Go Velocity of Circular Orbit = sqrt([GM.Earth]/Orbit Radius)

Circular Orbital Radius

Go Orbit Radius = Angular Momentum of Circular Orbit^2/[GM.Earth]

Specific Energy of Circular Orbit Given Orbital Radius

Go Specific Energy of Orbit = -([GM.Earth])/(2*Orbit Radius)

Orbital Radius Given Specific Energy of Circular Orbit

Go Orbit Radius = -([GM.Earth])/(2*Specific Energy of Orbit)

Circular Orbital Radius Given Velocity of Circular Orbit

Go Orbit Radius = [GM.Earth]/Velocity of Circular Orbit^2

Specific Energy of Circular Orbit

Go Specific Energy of Orbit = -([GM.Earth]^2)/(2*Angular Momentum of Circular Orbit^2)

Escape Velocity given Speed of Satellite in Circular Orbit

Go Escape Velocity = sqrt(2)*Velocity of Circular Orbit

Orbital Period Formula

Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass))
T_or = 2*pi*sqrt((r^3)/([G.]*M))

What is Earth's Orbital period?

Earth orbits the Sun at an average distance of 149.60 million km (92.96 million mi) in a counterclockwise pattern viewed above the northern hemisphere. One complete orbit takes 365.256 days (1 sidereal year)

How to Calculate Orbital Period?

Orbital Period calculator uses Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass)) to calculate the Time Period of Orbit, Orbital Period (also revolution period) is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars. Time Period of Orbit is denoted by T_or symbol.

How to calculate Orbital Period using this online calculator? To use this online calculator for Orbital Period, enter Orbit Radius (r) & Central Body Mass (M) and hit the calculate button. Here is how the Orbital Period calculation can be explained with given input values -> 8.7E+6 = 2*pi*sqrt((10859000^3)/([G.]*6E+24)).

FAQ

What is Orbital Period?

Orbital Period (also revolution period) is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars and is represented as T_or = 2*pi*sqrt((r^3)/([G.]*M)) or Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass)). The Orbit Radius is defined as the distance from the center of the orbit to the orbit's path & Central Body Mass is the mass of the body being orbited (e.g. planet or sun).

How to calculate Orbital Period?

Orbital Period (also revolution period) is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars is calculated using Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass)). To calculate Orbital Period, you need Orbit Radius (r) & Central Body Mass (M). With our tool, you need to enter the respective value for Orbit Radius & Central Body Mass and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Time Period of Orbit?

In this formula, Time Period of Orbit uses Orbit Radius & Central Body Mass. We can use 1 other way(s) to calculate the same, which is/are as follows -

Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth]))

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