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Specific Energy of Elliptic Orbit given Angular Momentum Formula

GoSpecific Energy of Elliptic Orbit given Semi Major Axis Formula

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Specific Energy of Elliptical 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 e = - \frac{1}{2} \cdot \frac{{[GM.Earth]}^{2}}{{h e}^{2}} \cdot (1 - {e e}^{2})

ε_e - Specific Energy of Elliptical Orbit?h_e - Angular Momentum of Elliptic Orbit?e_e - Eccentricity of Elliptical Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

Specific Energy of Elliptic Orbit given Angular Momentum Example

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Here is how the Specific Energy of Elliptic Orbit given Angular Momentum equation looks like with Values.

Here is how the Specific Energy of Elliptic Orbit given Angular Momentum equation looks like with Units.

Here is how the Specific Energy of Elliptic Orbit given Angular Momentum equation looks like.

-11760.7228 = - \frac{1}{2} \cdot \frac{{4E+14}^{2}}{65750^{2}} \cdot (1 - {0.6}^{2})

-11760.7228kJ/kg = - \frac{1}{2} \cdot \frac{{4E+14m³/s²}^{2}}{{65750km²/s}^{2}} \cdot (1 - {0.6}^{2})

-11760.7228 = - \frac{1}{2} \cdot \frac{{4E+14}^{2}}{65750^{2}} \cdot (1 - {0.6}^{2})

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Specific Energy of Elliptic Orbit given Angular Momentum Solution

Follow our step by step solution on how to calculate Specific Energy of Elliptic Orbit given Angular Momentum?

FIRST Step Consider the formula

ε e = - \frac{1}{2} \cdot \frac{{[GM.Earth]}^{2}}{{h e}^{2}} \cdot (1 - {e e}^{2})

Next Step Substitute values of Variables

∴

ε e = - \frac{1}{2} \cdot \frac{{[GM.Earth]}^{2}}{{65750km²/s}^{2}} \cdot (1 - {0.6}^{2})

Next Step Substitute values of Constants

∴

ε e = - \frac{1}{2} \cdot \frac{{4E+14m³/s²}^{2}}{{65750km²/s}^{2}} \cdot (1 - {0.6}^{2})

Next Step Convert Units

∴

ε e = - \frac{1}{2} \cdot \frac{{4E+14m³/s²}^{2}}{{6.6E+10m²/s}^{2}} \cdot (1 - {0.6}^{2})

Next Step Prepare to Evaluate

∴

ε e = - \frac{1}{2} \cdot \frac{{4E+14}^{2}}{{6.6E+10}^{2}} \cdot (1 - {0.6}^{2})

Next Step Evaluate

∴

ε e = -11760722.8452075J/kg

Next Step Convert to Output's Unit

∴

ε e = -11760.7228452075kJ/kg

LAST Step Rounding Answer

∴

ε e = -11760.7228kJ/kg

Specific Energy of Elliptic Orbit given Angular Momentum Formula Elements

Variables

Constants

Specific Energy of Elliptical Orbit

Specific Energy of Elliptical 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_e

Measurement: Specific EnergyUnit: kJ/kg

Note: Value can be positive or negative.

Formulas to find Specific Energy of Elliptical Orbit

Angular Momentum of Elliptic Orbit

Angular Momentum of Elliptic 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_e

Measurement: Specific Angular MomentumUnit: km²/s

Note: Value should be greater than 0.

Formulas to find Angular Momentum of Elliptic Orbit

Eccentricity of Elliptical Orbit

Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.

Symbol: e_e

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Eccentricity of Elliptical 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 Elliptical Orbit

Go Specific Energy of Elliptic Orbit given Semi Major Axis

ε e = - \frac{[GM.Earth]}{2 \cdot a e}

Other formulas in Elliptical Orbit Parameters category

Go Eccentricity of Elliptical Orbit given Apogee and Perigee

e e = \frac{r e,apogee - r e,perigee}{r e,apogee + r e,perigee}

Go Angular Momentum in Elliptic Orbit Given Apogee Radius and Apogee Velocity

h e = r e,apogee \cdot v apogee

Go Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity

r e,apogee = \frac{{h e}^{2}}{[GM.Earth] \cdot (1 - e e)}

Go Semimajor Axis of Elliptic Orbit given Apogee and Perigee Radii

a e = \frac{r e,apogee + r e,perigee}{2}

How to Evaluate Specific Energy of Elliptic Orbit given Angular Momentum?

Specific Energy of Elliptic Orbit given Angular Momentum evaluator uses Specific Energy of Elliptical Orbit = -1/2*[GM.Earth]^2/Angular Momentum of Elliptic Orbit^2*(1-Eccentricity of Elliptical Orbit^2) to evaluate the Specific Energy of Elliptical Orbit, Specific Energy of Elliptic Orbit given Angular Momentum formula is defined as a measure of the total energy of an object in an elliptical orbit around a central body, such as a planet, taking into account the angular momentum of the object and the gravitational attraction of the central body. Specific Energy of Elliptical Orbit is denoted by ε_e symbol.

How to evaluate Specific Energy of Elliptic Orbit given Angular Momentum using this online evaluator? To use this online evaluator for Specific Energy of Elliptic Orbit given Angular Momentum, enter Angular Momentum of Elliptic Orbit (h_e) & Eccentricity of Elliptical Orbit (e_e) and hit the calculate button.

FAQs on Specific Energy of Elliptic Orbit given Angular Momentum

What is the formula to find Specific Energy of Elliptic Orbit given Angular Momentum?

The formula of Specific Energy of Elliptic Orbit given Angular Momentum is expressed as Specific Energy of Elliptical Orbit = -1/2*[GM.Earth]^2/Angular Momentum of Elliptic Orbit^2*(1-Eccentricity of Elliptical Orbit^2). Here is an example- -11.760723 = -1/2*[GM.Earth]^2/65750000000^2*(1-0.6^2).

How to calculate Specific Energy of Elliptic Orbit given Angular Momentum?

With Angular Momentum of Elliptic Orbit (h_e) & Eccentricity of Elliptical Orbit (e_e) we can find Specific Energy of Elliptic Orbit given Angular Momentum using the formula - Specific Energy of Elliptical Orbit = -1/2*[GM.Earth]^2/Angular Momentum of Elliptic Orbit^2*(1-Eccentricity of Elliptical Orbit^2). This formula also uses Earth’s Geocentric Gravitational Constant .

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

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

Specific Energy of Elliptical Orbit=-[GM.Earth]/(2*Semi Major Axis of Elliptic Orbit)

Can the Specific Energy of Elliptic Orbit given Angular Momentum be negative?

Yes, the Specific Energy of Elliptic Orbit given Angular Momentum, measured in Specific Energy can be negative.

Which unit is used to measure Specific Energy of Elliptic Orbit given Angular Momentum?

Specific Energy of Elliptic Orbit given Angular Momentum 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 Elliptic Orbit given Angular Momentum can be measured.

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