Specific Energy of Elliptic Orbit given Semi Major Axis Calculator

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The Two Body Problem

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Elliptical Orbit Parameters

Orbital Position as Function of Time

✖Semi Major Axis of Elliptic Orbit is half of the major axis, which is the longest diameter of the ellipse describing the orbit.ⓘ Semi Major Axis of Elliptic Orbit [a_e]

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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.ⓘ Specific Energy of Elliptic Orbit given Semi Major Axis [ε_e]

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Formula

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Specific Energy of Elliptic Orbit given Semi Major Axis

Formula

`"ε"_{"e"} = -"[GM.Earth]"/(2*"a"_{"e"})`

Example

`"-11765.066169kJ/kg"=-"[GM.Earth]"/(2*"16940km")`

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Specific Energy of Elliptic Orbit given Semi Major Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Specific Energy of Elliptical Orbit = -[GM.Earth]/(2*Semi Major Axis of Elliptic Orbit)
ε_e = -[GM.Earth]/(2*a_e)
This formula uses 1 Constants, 2 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.
Semi Major Axis of Elliptic Orbit - (Measured in Meter) - Semi Major Axis of Elliptic Orbit is half of the major axis, which is the longest diameter of the ellipse describing the orbit.

STEP 1: Convert Input(s) to Base Unit

Semi Major Axis of Elliptic Orbit: 16940 Kilometer --> 16940000 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_e = -[GM.Earth]/(2*a_e) --> -[GM.Earth]/(2*16940000)

Evaluating ... ...

ε_e = -11765066.1688312

STEP 3: Convert Result to Output's Unit

-11765066.1688312 Joule per Kilogram -->-11765.0661688312 Kilojoule per Kilogram (Check conversion here)

FINAL ANSWER

-11765.0661688312 ≈ -11765.066169 Kilojoule per Kilogram <-- Specific Energy of Elliptical Orbit

(Calculation completed in 00.004 seconds)

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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!

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National Institute Of Technology (NIT), Hamirpur

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< 17 Elliptical Orbit Parameters Calculators

True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum

Go True Anomaly in Elliptical Orbit = acos((Angular Momentum of Elliptic Orbit^2/([GM.Earth]*Radial Position in Elliptical Orbit)-1)/Eccentricity of Elliptical Orbit)

Time Period of Elliptical Orbit given Semi-Major Axis

Go Time Period of Elliptic Orbit = 2*pi*Semi Major Axis of Elliptic Orbit^2*sqrt(1-Eccentricity of Elliptical Orbit^2)/Angular Momentum of Elliptic Orbit

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum

Go Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit

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)

Time Period for One Complete Revolution given Angular Momentum

Go Time Period of Elliptic Orbit = (2*pi*Semi Major Axis of Elliptic Orbit*Semi Minor Axis of Elliptic Orbit)/Angular Momentum of Elliptic Orbit

Elliptical Orbit Time Period given Angular Momentum and Eccentricity

Go Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3

Time Period of Elliptical Orbit given Angular Momentum

Go Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3

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))

Specific Energy of Elliptic Orbit given Angular Momentum

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

Azimuth-Averaged Radius Given Apogee and Perigee Radii

Go Azimuth Averaged Radius = sqrt(Apogee Radius in Elliptic Orbit*Perigee Radius in Elliptic 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 Perigee Radius and Perigee Velocity

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

Radial Velocity in Elliptic Orbit given Radial Position and Angular Momentum

Go Radial Velocity of Satellite = Angular Momentum of Elliptic Orbit/Radial Position in Elliptical Orbit

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

Apogee Velocity in Elliptic Orbit Given Angular Momentum and Apogee Radius

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

Eccentricity of Orbit

Go Eccentricity of Elliptical Orbit = Distance Between Two Foci/(2*Semi Major Axis of Elliptic Orbit)

Specific Energy of Elliptic Orbit given Semi Major Axis

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

Specific Energy of Elliptic Orbit given Semi Major Axis Formula

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

What are the 2 main types of energy?

Many forms of energy exist, but they all fall into two basic categories i.e 1) Kinetic Energy 2) Potential Energy.

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 Semi Major Axis?

Specific Energy of Elliptic Orbit given Semi Major Axis calculator uses Specific Energy of Elliptical Orbit = -[GM.Earth]/(2*Semi Major Axis of Elliptic Orbit) to calculate the Specific Energy of Elliptical Orbit, The Specific Energy of Elliptic Orbit given semi major axis formula is defined as 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 Elliptical Orbit is denoted by ε_e symbol.

How to calculate Specific Energy of Elliptic Orbit given Semi Major Axis using this online calculator? To use this online calculator for Specific Energy of Elliptic Orbit given Semi Major Axis, enter Semi Major Axis of Elliptic Orbit (a_e) and hit the calculate button. Here is how the Specific Energy of Elliptic Orbit given Semi Major Axis calculation can be explained with given input values -> -11765066.168831 = -[GM.Earth]/(2*16940000).

FAQ

What is Specific Energy of Elliptic Orbit given Semi Major Axis?

The Specific Energy of Elliptic Orbit given semi major axis formula is defined as the total orbital energy per unit mass of an orbiting body. It is the sum of the kinetic energy and the gravitational potential energy and is represented as ε_e = -[GM.Earth]/(2*a_e) or Specific Energy of Elliptical Orbit = -[GM.Earth]/(2*Semi Major Axis of Elliptic Orbit). Semi Major Axis of Elliptic Orbit is half of the major axis, which is the longest diameter of the ellipse describing the orbit.

How to calculate Specific Energy of Elliptic Orbit given Semi Major Axis?

The Specific Energy of Elliptic Orbit given semi major axis formula is defined as the total orbital energy per unit mass of an orbiting body. It is the sum of the kinetic energy and the gravitational potential energy is calculated using Specific Energy of Elliptical Orbit = -[GM.Earth]/(2*Semi Major Axis of Elliptic Orbit). To calculate Specific Energy of Elliptic Orbit given Semi Major Axis, you need Semi Major Axis of Elliptic Orbit (a_e). With our tool, you need to enter the respective value for Semi Major Axis of Elliptic 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 Semi Major Axis of Elliptic Orbit. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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