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Specific Energy of Circular Orbit Formula

GoSpecific Energy of Circular Orbit Given Orbital Radius Formula

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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. Check FAQs

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

ε - Specific Energy of Orbit?h_c - Angular Momentum of Circular Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

Specific Energy of Circular Orbit Example

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Here is how the Specific Energy of Circular Orbit equation looks like with Values.

Here is how the Specific Energy of Circular Orbit equation looks like with Units.

Here is how the Specific Energy of Circular Orbit equation looks like.

-18354.349 = - \frac{{4E+14}^{2}}{2 \cdot 65789^{2}}

-18354.349kJ/kg = - \frac{{4E+14m³/s²}^{2}}{2 \cdot {65789km²/s}^{2}}

-18354.349 = - \frac{{4E+14}^{2}}{2 \cdot 65789^{2}}

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Specific Energy of Circular Orbit Solution

Follow our step by step solution on how to calculate Specific Energy of Circular Orbit?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

ε = - \frac{{4E+14}^{2}}{2 \cdot {6.6E+10}^{2}}

Next Step Evaluate

∴

ε = -18354349.0073827J/kg

Next Step Convert to Output's Unit

∴

ε = -18354.3490073827kJ/kg

LAST Step Rounding Answer

∴

ε = -18354.349kJ/kg

Specific Energy of Circular Orbit Formula Elements

Variables

Constants

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.

Symbol: ε

Measurement: Specific EnergyUnit: kJ/kg

Note: Value can be positive or negative.

Formulas to find Specific Energy of Orbit

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 Specific Energy of Orbit

Go Specific Energy of Circular Orbit Given Orbital Radius

ε = - \frac{[GM.Earth]}{2 \cdot r}

Other formulas in Circular Orbit Parameters category

Go Orbital Period

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

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}}

How to Evaluate Specific Energy of Circular Orbit?

Specific Energy of Circular Orbit evaluator uses Specific Energy of Orbit = -([GM.Earth]^2)/(2*Angular Momentum of Circular Orbit^2) to evaluate the Specific Energy of Orbit, Specific Energy of Circular Orbit formula is defined as the total energy per unit mass required to maintain a satellite in a circular orbit around the Earth, which is a critical parameter in space mission design and orbit determination. Specific Energy of Orbit is denoted by ε symbol.

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

FAQs on Specific Energy of Circular Orbit

What is the formula to find Specific Energy of Circular Orbit?

The formula of Specific Energy of Circular Orbit is expressed as Specific Energy of Orbit = -([GM.Earth]^2)/(2*Angular Momentum of Circular Orbit^2). Here is an example- -18.354349 = -([GM.Earth]^2)/(2*65789000000^2).

How to calculate Specific Energy of Circular Orbit?

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

What are the other ways to Calculate Specific Energy of Orbit?

Here are the different ways to Calculate Specific Energy of Orbit-

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

Can the Specific Energy of Circular Orbit be negative?

Yes, the Specific Energy of Circular Orbit, measured in Specific Energy can be negative.

Which unit is used to measure Specific Energy of Circular Orbit?

Specific Energy of Circular Orbit is usually measured using the Kilojoule per Kilogram[kJ/kg] for Specific Energy. Joule per Kilogram[kJ/kg], Joule per Gram[kJ/kg], Joule per Centigram[kJ/kg] are the few other units in which Specific Energy of Circular Orbit can be measured.

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