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Orbital Period Formula

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

T_or - Time Period of Orbit?r - Orbit Radius?M - Central Body Mass?[G.] - Gravitational constant?π - Archimedes' constant?

Orbital Period Example

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Here is how the Orbital Period equation looks like with Values.

Here is how the Orbital Period equation looks like with Units.

Here is how the Orbital Period equation looks like.

11235.5229 = 2 \cdot 3.1416 \cdot \sqrt{\frac{10859^{3}}{6.7E-11 \cdot 6E+24}}

11235.5229s = 2 \cdot 3.1416 \cdot \sqrt{\frac{{10859km}^{3}}{6.7E-11 \cdot 6E+24kg}}

11235.5229 = 2 \cdot 3.1416 \cdot \sqrt{\frac{10859^{3}}{6.7E-11 \cdot 6E+24}}

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Orbital Period Solution

Follow our step by step solution on how to calculate Orbital Period?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

T or = 2 \cdot π \cdot \sqrt{\frac{{10859km}^{3}}{[G.] \cdot 6E+24kg}}

Next Step Substitute values of Constants

∴

T or = 2 \cdot 3.1416 \cdot \sqrt{\frac{{10859km}^{3}}{6.7E-11 \cdot 6E+24kg}}

Next Step Convert Units

∴

T or = 2 \cdot 3.1416 \cdot \sqrt{\frac{{1.1E+7m}^{3}}{6.7E-11 \cdot 6E+24kg}}

Next Step Prepare to Evaluate

∴

T or = 2 \cdot 3.1416 \cdot \sqrt{\frac{{1.1E+7}^{3}}{6.7E-11 \cdot 6E+24}}

Next Step Evaluate

∴

T or = 11235.5228888116s

LAST Step Rounding Answer

∴

T or = 11235.5229s

Orbital Period 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

Central Body Mass

Central Body Mass is the mass of the body being orbited (e.g. planet or sun).

Symbol: M

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Central Body Mass

Gravitational constant

Gravitational constant is a fundamental constant in physics that appears in Newton's law of universal gravitation and Einstein's theory of general relativity.

Symbol: [G.]

Value: 6.67408E-11

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 Time Period of Circular Orbit

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

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 Orbital Period?

Orbital Period evaluator uses Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass)) to evaluate the Time Period of Orbit, Orbital Period formula is defined as the time taken by an object to complete one full orbit around a celestial body, which is a fundamental concept in understanding the motion of planets, moons, and other celestial objects in our solar system and beyond. Time Period of Orbit is denoted by T_or symbol.

How to evaluate Orbital Period using this online evaluator? To use this online evaluator for Orbital Period, enter Orbit Radius (r) & Central Body Mass (M) and hit the calculate button.

FAQs on Orbital Period

What is the formula to find Orbital Period?

The formula of Orbital Period is expressed as Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass)). Here is an example- 8.7E+6 = 2*pi*sqrt((10859000^3)/([G.]*6E+24)).

How to calculate Orbital Period?

With Orbit Radius (r) & Central Body Mass (M) we can find Orbital Period using the formula - Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass)). This formula also uses 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*Orbit Radius^(3/2))/(sqrt([GM.Earth]))

Can the Orbital Period be negative?

No, the Orbital Period, measured in Time cannot be negative.

Which unit is used to measure Orbital Period?

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

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Orbital Period Formula

​GoTime Period of Circular Orbit Formula

Orbital Period Example

Orbital Period Solution

Orbital Period Formula Elements

Other Formulas to find Time Period of Orbit

Other formulas in Circular Orbit Parameters category

How to Evaluate Orbital Period?

FAQs on Orbital Period

Variable Name

GoTime Period of Circular Orbit Formula