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Time Period of Circular Orbit Formula

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The Time Period of Orbit is the amount of time a given astronomical object takes to complete one orbit around another object. Check FAQs

T or = \frac{2 \cdot π \cdot r^{\frac{3}{2}}}{\sqrt{[GM.Earth]}}

T_or - Time Period of Orbit?r - Orbit Radius?[GM.Earth] - Earth’s Geocentric Gravitational Constant?π - Archimedes' constant?

Time Period of Circular Orbit Example

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Here is how the Time Period of Circular Orbit equation looks like with Values.

Here is how the Time Period of Circular Orbit equation looks like with Units.

Here is how the Time Period of Circular Orbit equation looks like.

11261.4867 = \frac{2 \cdot 3.1416 \cdot 10859^{\frac{3}{2}}}{\sqrt{4E+14}}

11261.4867s = \frac{2 \cdot 3.1416 \cdot {10859km}^{\frac{3}{2}}}{\sqrt{4E+14m³/s²}}

11261.4867 = \frac{2 \cdot 3.1416 \cdot 10859^{\frac{3}{2}}}{\sqrt{4E+14}}

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Time Period of Circular Orbit Solution

Follow our step by step solution on how to calculate Time Period of Circular Orbit?

FIRST Step Consider the formula

T or = \frac{2 \cdot π \cdot r^{\frac{3}{2}}}{\sqrt{[GM.Earth]}}

Next Step Substitute values of Variables

∴

T or = \frac{2 \cdot π \cdot {10859km}^{\frac{3}{2}}}{\sqrt{[GM.Earth]}}

Next Step Substitute values of Constants

∴

T or = \frac{2 \cdot 3.1416 \cdot {10859km}^{\frac{3}{2}}}{\sqrt{4E+14m³/s²}}

Next Step Convert Units

∴

T or = \frac{2 \cdot 3.1416 \cdot {1.1E+7m}^{\frac{3}{2}}}{\sqrt{4E+14m³/s²}}

Next Step Prepare to Evaluate

∴

T or = \frac{2 \cdot 3.1416 \cdot {1.1E+7}^{\frac{3}{2}}}{\sqrt{4E+14}}

Next Step Evaluate

∴

T or = 11261.4867499914s

LAST Step Rounding Answer

∴

T or = 11261.4867s

Time Period of Circular Orbit Formula Elements

Variables

Constants

Functions

Time Period of Orbit

The Time Period of Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.

Symbol: T_or

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period of Orbit

Orbit Radius

The Orbit Radius is defined as the distance from the center of the orbit to the orbit's path.

Symbol: r

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Orbit Radius

Earth’s Geocentric Gravitational Constant

Earth’s Geocentric Gravitational Constant the gravitational parameter for the Earth as the central body.

Symbol: [GM.Earth]

Value: 3.986004418E+14 m³/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Time Period of Orbit

Go Orbital Period

T or = 2 \cdot π \cdot \sqrt{\frac{r^{3}}{[G.] \cdot M}}

Other formulas in Circular Orbit Parameters category

Go Circular Orbital Radius

r = \frac{{h c}^{2}}{[GM.Earth]}

Go Velocity of Circular Orbit

v cir = \sqrt{\frac{[GM.Earth]}{r}}

Go Circular Orbital Radius Given Velocity of Circular Orbit

r = \frac{[GM.Earth]}{{v cir}^{2}}

Go Circular Orbital Radius Given Time Period of Circular Orbit

r = {(\frac{T or \cdot \sqrt{[GM.Earth]}}{2 \cdot π})}^{\frac{2}{3}}

How to Evaluate Time Period of Circular Orbit?

Time Period of Circular Orbit evaluator uses Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth])) to evaluate the Time Period of Orbit, Time Period of Circular Orbit formula is defined as a measure of the time taken by an object to complete one full orbit around a celestial body, such as a planet, in a circular path, which is influenced by the gravitational force of the central body and the radius of the orbit. Time Period of Orbit is denoted by T_or symbol.

How to evaluate Time Period of Circular Orbit using this online evaluator? To use this online evaluator for Time Period of Circular Orbit, enter Orbit Radius (r) and hit the calculate button.

FAQs on Time Period of Circular Orbit

What is the formula to find Time Period of Circular Orbit?

The formula of Time Period of Circular Orbit is expressed as Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth])). Here is an example- 11261.49 = (2*pi*10859000^(3/2))/(sqrt([GM.Earth])).

How to calculate Time Period of Circular Orbit?

With Orbit Radius (r) we can find Time Period of Circular Orbit using the formula - Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth])). This formula also uses Earth’s Geocentric Gravitational Constant, Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Time Period of Orbit?

Here are the different ways to Calculate Time Period of Orbit-

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

Can the Time Period of Circular Orbit be negative?

No, the Time Period of Circular Orbit, measured in Time cannot be negative.

Which unit is used to measure Time Period of Circular Orbit?

Time Period of Circular Orbit is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Time Period of Circular Orbit can be measured.

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