Circular Orbital Radius Calculator

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The Two Body Problem

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Fundamental Parameters

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Circular Orbit Parameters

Geostationary Earth Satellite

✖Angular Momentum of Circular Orbit is a fundamental physical quantity that characterizes the rotational motion of an object in orbit around a celestial body, such as a planet or a star.ⓘ Angular Momentum of Circular Orbit [h_c]

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✖The Orbit Radius is defined as the distance from the center of the orbit to the orbit's path.ⓘ Circular Orbital Radius [r]

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Formula

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Circular Orbital Radius

Formula

`"r" = "h"_{"c"}^2/"[GM.Earth]"`

Example

`"10858.47km"=("65789km²/s")^2/"[GM.Earth]"`

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Circular Orbital Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Orbit Radius = Angular Momentum of Circular Orbit^2/[GM.Earth]
r = h_c^2/[GM.Earth]
This formula uses 1 Constants, 2 Variables

Constants Used

[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14

Variables Used

Orbit Radius - (Measured in Meter) - The Orbit Radius is defined as the distance from the center of the orbit to the orbit's path.
Angular Momentum of Circular Orbit - (Measured in Squaer Meter per Second) - Angular Momentum of Circular Orbit is a fundamental physical quantity that characterizes the rotational motion of an object in orbit around a celestial body, such as a planet or a star.

STEP 1: Convert Input(s) to Base Unit

Angular Momentum of Circular Orbit: 65789 Square Kilometer per Second --> 65789000000 Squaer Meter per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = h_c^2/[GM.Earth] --> 65789000000^2/[GM.Earth]

Evaluating ... ...

r = 10858473.9682042

STEP 3: Convert Result to Output's Unit

10858473.9682042 Meter -->10858.4739682042 Kilometer (Check conversion here)

FINAL ANSWER

10858.4739682042 ≈ 10858.47 Kilometer <-- Orbit Radius

(Calculation completed in 00.004 seconds)

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Created by Karavadiya Divykumar Rasikbhai

Hindustan Institute of Technology and Science (HITS), Chennai, Indian

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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

Circular Orbital Radius Formula

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

What is circular orbital radius in simple?

For approximately circular orbits the orbital radius is the distance from an object in space to the body which it is orbiting.

How to Calculate Circular Orbital Radius?

Circular Orbital Radius calculator uses Orbit Radius = Angular Momentum of Circular Orbit^2/[GM.Earth] to calculate the Orbit Radius, The Circular Orbital Radius formula is defined as the distance from the center of mass of the larger object to the orbital path. Orbit Radius is denoted by r symbol.

How to calculate Circular Orbital Radius using this online calculator? To use this online calculator for Circular Orbital Radius, enter Angular Momentum of Circular Orbit (h_c) and hit the calculate button. Here is how the Circular Orbital Radius calculation can be explained with given input values -> 10.85847 = 65789000000^2/[GM.Earth].

FAQ

What is Circular Orbital Radius?

The Circular Orbital Radius formula is defined as the distance from the center of mass of the larger object to the orbital path and is represented as r = h_c^2/[GM.Earth] or Orbit Radius = Angular Momentum of Circular Orbit^2/[GM.Earth]. Angular Momentum of Circular Orbit is a fundamental physical quantity that characterizes the rotational motion of an object in orbit around a celestial body, such as a planet or a star.

How to calculate Circular Orbital Radius?

The Circular Orbital Radius formula is defined as the distance from the center of mass of the larger object to the orbital path is calculated using Orbit Radius = Angular Momentum of Circular Orbit^2/[GM.Earth]. To calculate Circular Orbital Radius, you need Angular Momentum of Circular Orbit (h_c). With our tool, you need to enter the respective value for Angular Momentum of Circular Orbit 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 Orbit Radius?

In this formula, Orbit Radius uses Angular Momentum of Circular Orbit. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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