Orbital Radius Given Specific Energy of Circular Orbit Calculator

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The Two Body Problem

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Circular Orbits

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Fundamental Parameters

Hyperbolic Orbits

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Circular Orbit Parameters

Geostationary Earth Satellite

✖The Specific Energy of Orbit is the total orbital energy per unit mass of an orbiting body. It is the sum of the kinetic energy and the gravitational potential energy.ⓘ Specific Energy of Orbit [ε]

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

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Formula

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Orbital Radius Given Specific Energy of Circular Orbit

Formula

`"r" = -("[GM.Earth]")/(2*"ε")`

Example

`"10858.68km"=-("[GM.Earth]")/(2*"-18354kJ/kg")`

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Orbital Radius Given Specific Energy of Circular Orbit Solution

STEP 0: Pre-Calculation Summary

Formula Used

Orbit Radius = -([GM.Earth])/(2*Specific Energy of Orbit)
r = -([GM.Earth])/(2*ε)
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.
Specific Energy of Orbit - (Measured in Joule per Kilogram) - The Specific Energy of Orbit is the total orbital energy per unit mass of an orbiting body. It is the sum of the kinetic energy and the gravitational potential energy.

STEP 1: Convert Input(s) to Base Unit

Specific Energy of Orbit: -18354 Kilojoule per Kilogram --> -18354000 Joule per Kilogram (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = -([GM.Earth])/(2*ε) --> -([GM.Earth])/(2*(-18354000))

Evaluating ... ...

r = 10858680.4456794

STEP 3: Convert Result to Output's Unit

10858680.4456794 Meter -->10858.6804456794 Kilometer (Check conversion here)

FINAL ANSWER

10858.6804456794 ≈ 10858.68 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

Orbital Radius Given Specific Energy of Circular Orbit Formula

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

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 Orbital Radius Given Specific Energy of Circular Orbit?

Orbital Radius Given Specific Energy of Circular Orbit calculator uses Orbit Radius = -([GM.Earth])/(2*Specific Energy of Orbit) to calculate the Orbit Radius, The Orbital Radius Given Specific Energy of Circular Orbit formula is defined as the distance from the center of the orbit to the orbit's path. Orbit Radius is denoted by r symbol.

How to calculate Orbital Radius Given Specific Energy of Circular Orbit using this online calculator? To use this online calculator for Orbital Radius Given Specific Energy of Circular Orbit, enter Specific Energy of Orbit (ε) and hit the calculate button. Here is how the Orbital Radius Given Specific Energy of Circular Orbit calculation can be explained with given input values -> 10.87883 = -([GM.Earth])/(2*(-18354000)).

FAQ

What is Orbital Radius Given Specific Energy of Circular Orbit?

The Orbital Radius Given Specific Energy of Circular Orbit formula is defined as the distance from the center of the orbit to the orbit's path and is represented as r = -([GM.Earth])/(2*ε) or Orbit Radius = -([GM.Earth])/(2*Specific Energy of Orbit). The Specific Energy of Orbit is the total orbital energy per unit mass of an orbiting body. It is the sum of the kinetic energy and the gravitational potential energy.

How to calculate Orbital Radius Given Specific Energy of Circular Orbit?

The Orbital Radius Given Specific Energy of Circular Orbit formula is defined as the distance from the center of the orbit to the orbit's path is calculated using Orbit Radius = -([GM.Earth])/(2*Specific Energy of Orbit). To calculate Orbital Radius Given Specific Energy of Circular Orbit, you need Specific Energy of Orbit (ε). With our tool, you need to enter the respective value for Specific Energy of 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 Specific Energy of Orbit. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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