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Circular Orbital Radius Formula

GoCircular Orbital Radius Given Velocity of Circular Orbit Formula

GoCircular Orbital Radius Given Time Period of Circular Orbit Formula

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

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

r - Orbit Radius?h_c - Angular Momentum of Circular Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

Circular Orbital Radius Example

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Here is how the Circular Orbital Radius equation looks like with Values.

Here is how the Circular Orbital Radius equation looks like with Units.

Here is how the Circular Orbital Radius equation looks like.

10858.474 = \frac{65789^{2}}{4E+14}

10858.474km = \frac{{65789km²/s}^{2}}{4E+14m³/s²}

10858.474 = \frac{65789^{2}}{4E+14}

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Circular Orbital Radius Solution

Follow our step by step solution on how to calculate Circular Orbital Radius?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r = \frac{{65789km²/s}^{2}}{[GM.Earth]}

Next Step Substitute values of Constants

∴

r = \frac{{65789km²/s}^{2}}{4E+14m³/s²}

Next Step Convert Units

∴

r = \frac{{6.6E+10m²/s}^{2}}{4E+14m³/s²}

Next Step Prepare to Evaluate

∴

r = \frac{{6.6E+10}^{2}}{4E+14}

Next Step Evaluate

∴

r = 10858473.9682042m

Next Step Convert to Output's Unit

∴

r = 10858.4739682042km

LAST Step Rounding Answer

∴

r = 10858.474km

Circular Orbital Radius Formula Elements

Variables

Constants

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

Angular Momentum of Circular Orbit

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.

Symbol: h_c

Measurement: Specific Angular MomentumUnit: km²/s

Note: Value should be greater than 0.

Formulas to find Angular Momentum of Circular Orbit

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

Other Formulas to find Orbit Radius

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}}

Go Orbital Radius Given Specific Energy of Circular Orbit

r = - \frac{[GM.Earth]}{2 \cdot ε}

Other formulas in Circular Orbit Parameters category

Go Orbital Period

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

Go Velocity of Circular Orbit

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

Go Time Period of Circular Orbit

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

Go Specific Energy of Circular Orbit

ε = - \frac{{[GM.Earth]}^{2}}{2 \cdot {h c}^{2}}

How to Evaluate Circular Orbital Radius?

Circular Orbital Radius evaluator uses Orbit Radius = Angular Momentum of Circular Orbit^2/[GM.Earth] to evaluate the Orbit Radius, Circular Orbital Radius formula is defined as the distance from the center of the Earth to the satellite in a circular orbit, which is critical in understanding the motion of satellites and space debris in Earth's gravitational field, and is essential in aerospace engineering and space mission design. Orbit Radius is denoted by r symbol.

How to evaluate Circular Orbital Radius using this online evaluator? To use this online evaluator for Circular Orbital Radius, enter Angular Momentum of Circular Orbit (h_c) and hit the calculate button.

FAQs on Circular Orbital Radius

What is the formula to find Circular Orbital Radius?

The formula of Circular Orbital Radius is expressed as Orbit Radius = Angular Momentum of Circular Orbit^2/[GM.Earth]. Here is an example- 10.85847 = 65789000000^2/[GM.Earth].

How to calculate Circular Orbital Radius?

With Angular Momentum of Circular Orbit (h_c) we can find Circular Orbital Radius using the formula - Orbit Radius = Angular Momentum of Circular Orbit^2/[GM.Earth]. This formula also uses Earth’s Geocentric Gravitational Constant .

What are the other ways to Calculate Orbit Radius?

Here are the different ways to Calculate Orbit Radius-

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)

Can the Circular Orbital Radius be negative?

No, the Circular Orbital Radius, measured in Length cannot be negative.

Which unit is used to measure Circular Orbital Radius?

Circular Orbital Radius is usually measured using the Kilometer[km] for Length. Meter[km], Millimeter[km], Decimeter[km] are the few other units in which Circular Orbital Radius can be measured.

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