Elliptical Orbit Time Period given Angular Momentum and Eccentricity Calculator

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The Two Body Problem

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Elliptical Orbits

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Fundamental Parameters

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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%

✖The time period of Elliptic Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.ⓘ Elliptical Orbit Time Period given Angular Momentum and Eccentricity [T_e]

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Formula

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Elliptical Orbit Time Period given Angular Momentum and Eccentricity

Formula

`"T"_{"e"} = (2*pi)/"[GM.Earth]"^2*("h"_{"e"}/sqrt(1-"e"_{"e"}^2))^3`

Example

`"21954.4s"=(2*pi)/"[GM.Earth]"^2*("65750km²/s"/sqrt(1-("0.6")^2))^3`

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Elliptical Orbit Time Period given Angular Momentum and Eccentricity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3
T_e = (2*pi)/[GM.Earth]^2*(h_e/sqrt(1-e_e^2))^3
This formula uses 2 Constants, 1 Functions, 3 Variables

Constants Used

[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Time Period of Elliptic Orbit - (Measured in Second) - The time period of Elliptic Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.
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

T_e = (2*pi)/[GM.Earth]^2*(h_e/sqrt(1-e_e^2))^3 --> (2*pi)/[GM.Earth]^2*(65750000000/sqrt(1-0.6^2))^3

Evaluating ... ...

T_e = 21954.4027705855

STEP 3: Convert Result to Output's Unit

21954.4027705855 Second --> No Conversion Required

FINAL ANSWER

21954.4027705855 ≈ 21954.4 Second <-- Time Period of Elliptic Orbit

(Calculation completed in 00.020 seconds)

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Created by Harsh Raj

Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

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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)

Elliptical Orbit Time Period given Angular Momentum and Eccentricity Formula

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

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 Elliptical Orbit Time Period given Angular Momentum and Eccentricity?

Elliptical Orbit Time Period given Angular Momentum and Eccentricity calculator uses Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3 to calculate the Time Period of Elliptic Orbit, The Elliptical Orbit Time Period given Angular Momentum and Eccentricity formula is defined as duration it takes for the object to complete one full orbit around the central body. This formula allows for the calculation of the time period based on two essential parameters: angular momentum and eccentricity. Time Period of Elliptic Orbit is denoted by T_e symbol.

How to calculate Elliptical Orbit Time Period given Angular Momentum and Eccentricity using this online calculator? To use this online calculator for Elliptical Orbit Time Period 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 Elliptical Orbit Time Period given Angular Momentum and Eccentricity calculation can be explained with given input values -> 21954.4 = (2*pi)/[GM.Earth]^2*(65750000000/sqrt(1-0.6^2))^3.

FAQ

What is Elliptical Orbit Time Period given Angular Momentum and Eccentricity?

The Elliptical Orbit Time Period given Angular Momentum and Eccentricity formula is defined as duration it takes for the object to complete one full orbit around the central body. This formula allows for the calculation of the time period based on two essential parameters: angular momentum and eccentricity and is represented as T_e = (2*pi)/[GM.Earth]^2*(h_e/sqrt(1-e_e^2))^3 or Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3. 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 Elliptical Orbit Time Period given Angular Momentum and Eccentricity?

The Elliptical Orbit Time Period given Angular Momentum and Eccentricity formula is defined as duration it takes for the object to complete one full orbit around the central body. This formula allows for the calculation of the time period based on two essential parameters: angular momentum and eccentricity is calculated using Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3. To calculate Elliptical Orbit Time Period 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.

How many ways are there to calculate Time Period of Elliptic Orbit?

In this formula, Time Period of Elliptic Orbit uses Angular Momentum of Elliptic Orbit & Eccentricity of Elliptical Orbit. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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