Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity Calculator

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The Two Body Problem

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Elliptical Orbit Parameters

Orbital Position as Function of Time

✖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%

✖Apogee Radius in Elliptic Orbit represents the maximum distance between an orbiting body and the object it orbits.ⓘ Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity [r_e,apogee]

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Formula

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Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity

Formula

`"r"_{"e,apogee"} = "h"_{"e"}^2/("[GM.Earth]"*(1-"e"_{"e"}))`

Example

`"27114.01km"=("65750km²/s")^2/("[GM.Earth]"*(1-"0.6"))`

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Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Apogee Radius in Elliptic Orbit = Angular Momentum of Elliptic Orbit^2/([GM.Earth]*(1-Eccentricity of Elliptical Orbit))
r_e,apogee = h_e^2/([GM.Earth]*(1-e_e))
This formula uses 1 Constants, 3 Variables

Constants Used

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

Variables Used

Apogee Radius in Elliptic Orbit - (Measured in Meter) - Apogee Radius in Elliptic Orbit represents the maximum distance between an orbiting body and the object it orbits.
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

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

Evaluating ... ...

r_e,apogee = 27114009.7115668

STEP 3: Convert Result to Output's Unit

27114009.7115668 Meter -->27114.0097115668 Kilometer (Check conversion here)

FINAL ANSWER

27114.0097115668 ≈ 27114.01 Kilometer <-- Apogee Radius in Elliptic Orbit

(Calculation completed in 00.004 seconds)

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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)

Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity Formula

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

Kepler's Laws and Gravitational Attraction

Johannes Kepler's laws of planetary motion, developed in the 17th century, provided significant insights into the relationship between celestial bodies and gravity. Kepler's laws describe the elliptical orbits of planets and other objects in the solar system, all of which are governed by the gravitational pull of the central body, such as the Sun. These laws laid the foundation for understanding how gravity affects the motion of objects in space, paving the way for Sir Isaac Newton's formulation of the law of universal gravitation.

How to Calculate Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity?

Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity calculator uses Apogee Radius in Elliptic Orbit = Angular Momentum of Elliptic Orbit^2/([GM.Earth]*(1-Eccentricity of Elliptical Orbit)) to calculate the Apogee Radius in Elliptic Orbit, Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity formula is defined as distance from the center of the central body to the farthest point of the elliptical orbit. This formula allows for the calculation of the apogee radius based on two essential parameters: angular momentum and eccentricity. Apogee Radius in Elliptic Orbit is denoted by r_e,apogee symbol.

How to calculate Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity using this online calculator? To use this online calculator for Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity, enter Angular Momentum of Elliptic Orbit (h_e) & Eccentricity of Elliptical Orbit (e_e) and hit the calculate button. Here is how the Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity calculation can be explained with given input values -> 27.11401 = 65750000000^2/([GM.Earth]*(1-0.6)).

FAQ

What is Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity?

Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity formula is defined as distance from the center of the central body to the farthest point of the elliptical orbit. This formula allows for the calculation of the apogee radius based on two essential parameters: angular momentum and eccentricity and is represented as r_e,apogee = h_e^2/([GM.Earth]*(1-e_e)) or Apogee Radius in Elliptic Orbit = Angular Momentum of Elliptic Orbit^2/([GM.Earth]*(1-Eccentricity of Elliptical 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 & Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.

How to calculate Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity?

Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity formula is defined as distance from the center of the central body to the farthest point of the elliptical orbit. This formula allows for the calculation of the apogee radius based on two essential parameters: angular momentum and eccentricity is calculated using Apogee Radius in Elliptic Orbit = Angular Momentum of Elliptic Orbit^2/([GM.Earth]*(1-Eccentricity of Elliptical Orbit)). To calculate Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity, 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.

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