Specific Energy of Elliptic Orbit given Angular Momentum Calculator

✖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.ⓘ Angular Momentum of Elliptic Orbit [h_e]			+10% -10%
✖Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.ⓘ Eccentricity of Elliptical Orbit [e_e]			+10% -10%

✖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.ⓘ Specific Energy of Elliptic Orbit given Angular Momentum [ε_e]

⎘ Copy

👎

Formula

✖

Specific Energy of Elliptic Orbit given Angular Momentum

Formula

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

Example

-11760.722845 kJ/kg = - \frac{1}{2} \cdot \frac{{[GM.Earth]}^{2}}{{65750 km²/s}^{2}} \cdot (1 - {0.6}^{2})

Calculator

LaTeX

Reset

👍

Download Elliptical Orbits Formulas PDF PDF Image

Specific Energy of Elliptic Orbit given Angular Momentum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Specific Energy of Elliptical Orbit = -1/2*[GM.Earth]^2/Angular Momentum of Elliptic Orbit^2*(1-Eccentricity of Elliptical Orbit^2)
ε_e = -1/2*[GM.Earth]^2/h_e^2*(1-e_e^2)
This formula uses 1 Constants, 3 Variables

Constants Used

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

Variables Used

Specific Energy of Elliptical Orbit - (Measured in Joule per Kilogram) - 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.
Angular Momentum of Elliptic Orbit - (Measured in Squaer Meter per Second) - 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.
Eccentricity of Elliptical Orbit - Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.

STEP 1: Convert Input(s) to Base Unit

Angular Momentum of Elliptic Orbit: 65750 Square Kilometer per Second --> 65750000000 Squaer Meter per Second (Check conversion here)
Eccentricity of Elliptical Orbit: 0.6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_e = -1/2*[GM.Earth]^2/h_e^2*(1-e_e^2) --> -1/2*[GM.Earth]^2/65750000000^2*(1-0.6^2)

Evaluating ... ...

ε_e = -11760722.8452075

STEP 3: Convert Result to Output's Unit

-11760722.8452075 Joule per Kilogram -->-11760.7228452075 Kilojoule per Kilogram (Check conversion here)

FINAL ANSWER

-11760.7228452075 ≈ -11760.722845 Kilojoule per Kilogram <-- Specific Energy of Elliptical Orbit

(Calculation completed in 00.017 seconds)

You are here -

Home » Physics » Orbital Mechanics » The Two Body Problem » Elliptical Orbits » Aerospace » Elliptical Orbit Parameters » Specific Energy of Elliptic Orbit given Angular Momentum

Credits

Created by Karavadiya Divykumar Rasikbhai

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

Karavadiya Divykumar Rasikbhai has created this Calculator and 10+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< Elliptical Orbit Parameters Calculators

Eccentricity of Elliptical Orbit given Apogee and Perigee

Go Eccentricity of Elliptical Orbit = (Apogee Radius in Elliptic Orbit-Perigee Radius in Elliptic Orbit)/(Apogee Radius in Elliptic Orbit+Perigee Radius in Elliptic Orbit)

Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity

Go Apogee Radius in Elliptic Orbit = Angular Momentum of Elliptic Orbit^2/([GM.Earth]*(1-Eccentricity of Elliptical Orbit))

Semimajor Axis of Elliptic Orbit given Apogee and Perigee Radii

Go Semi Major Axis of Elliptic Orbit = (Apogee Radius in Elliptic Orbit+Perigee Radius in Elliptic Orbit)/2

Angular Momentum in Elliptic Orbit Given Apogee Radius and Apogee Velocity

Go Angular Momentum of Elliptic Orbit = Apogee Radius in Elliptic Orbit*Velocity of Satellite at Apogee

Specific Energy of Elliptic Orbit given Angular Momentum Formula

Specific Energy of Elliptical Orbit = -1/2*[GM.Earth]^2/Angular Momentum of Elliptic Orbit^2*(1-Eccentricity of Elliptical Orbit^2)
ε_e = -1/2*[GM.Earth]^2/h_e^2*(1-e_e^2)

What is Angular momentum ?

Angular momentum is a fundamental concept in physics that describes the rotational motion of an object around a fixed point or axis. It is a vector quantity, meaning it has both magnitude and direction.

What is the specific energy of an elliptical orbit?

For an elliptic orbit the specific orbital energy is the negative of the additional energy required to accelerate a mass of one kilogram to escape velocity.

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

Specific Energy of Elliptic Orbit given Angular Momentum calculator uses Specific Energy of Elliptical Orbit = -1/2*[GM.Earth]^2/Angular Momentum of Elliptic Orbit^2*(1-Eccentricity of Elliptical Orbit^2) to calculate 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 calculate Specific Energy of Elliptic Orbit given Angular Momentum using this online calculator? To use this online calculator 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. Here is how the Specific Energy of Elliptic Orbit given Angular Momentum calculation can be explained with given input values -> -11.760723 = -1/2*[GM.Earth]^2/65750000000^2*(1-0.6^2).

FAQ

What is Specific Energy of Elliptic Orbit given Angular Momentum?

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 and is represented as ε_e = -1/2*[GM.Earth]^2/h_e^2*(1-e_e^2) or Specific Energy of Elliptical Orbit = -1/2*[GM.Earth]^2/Angular Momentum of Elliptic Orbit^2*(1-Eccentricity of Elliptical Orbit^2). 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 & Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.

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

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 is calculated using Specific Energy of Elliptical Orbit = -1/2*[GM.Earth]^2/Angular Momentum of Elliptic Orbit^2*(1-Eccentricity of Elliptical Orbit^2). To calculate Specific Energy of Elliptic Orbit given Angular Momentum, you need Angular Momentum of Elliptic Orbit (h_e) & Eccentricity of Elliptical Orbit (e_e). With our tool, you need to enter the respective value for Angular Momentum of Elliptic Orbit & Eccentricity of Elliptical 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 Specific Energy of Elliptical Orbit?

In this formula, Specific Energy of Elliptical Orbit uses Angular Momentum of Elliptic Orbit & Eccentricity of Elliptical Orbit. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search