Time Period of Elliptical Orbit given Semi-Major Axis Calculator

✖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]			+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%
✖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%

✖The time period of Elliptic Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.ⓘ Time Period of Elliptical Orbit given Semi-Major Axis [T_e]

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Time Period of Elliptical Orbit given Semi-Major Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
T_e = 2*pi*a_e^2*sqrt(1-e_e^2)/h_e
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

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

STEP 1: Convert Input(s) to Base Unit

Semi Major Axis of Elliptic Orbit: 16940 Kilometer --> 16940000 Meter (Check conversion here)
Eccentricity of Elliptical Orbit: 0.6 --> No Conversion Required
Angular Momentum of Elliptic Orbit: 65750 Square Kilometer per Second --> 65750000000 Squaer Meter per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_e = 2*pi*a_e^2*sqrt(1-e_e^2)/h_e --> 2*pi*16940000^2*sqrt(1-0.6^2)/65750000000

Evaluating ... ...

T_e = 21938.1958961565

STEP 3: Convert Result to Output's Unit

21938.1958961565 Second --> No Conversion Required

FINAL ANSWER

21938.1958961565 ≈ 21938.2 Second <-- Time Period of Elliptic Orbit

(Calculation completed in 00.020 seconds)

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Created by Karavadiya Divykumar Rasikbhai

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

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< Elliptical Orbit Parameters Calculators

Eccentricity of Elliptical Orbit given Apogee and Perigee

LaTeX 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

LaTeX 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

LaTeX 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

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

Time Period of Elliptical Orbit given Semi-Major Axis Formula

LaTeX 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
T_e = 2*pi*a_e^2*sqrt(1-e_e^2)/h_e

What is the shortest orbit time?

The shortest orbit time, or orbital period, depends on various factors such as the mass of the central body, the distance of the orbiting object from the central body, and its orbital velocity, in terms of celestial objects orbiting the Sun, the shortest orbit time belongs to Mercury, the innermost planet in our solar system. Mercury has the shortest orbital period among the planets, completing one orbit around the Sun in approximately 88 Earth days.

How to Calculate Time Period of Elliptical Orbit given Semi-Major Axis?

Time Period of Elliptical Orbit given Semi-Major Axis calculator uses 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 to calculate the Time Period of Elliptic Orbit, Time Period of Elliptical Orbit given Semi-Major Axis formula is defined as a measure of the time taken by an object to complete one full orbit around a celestial body in an elliptical path, providing valuable insights into the orbital characteristics of celestial bodies in our solar system. Time Period of Elliptic Orbit is denoted by T_e symbol.

How to calculate Time Period of Elliptical Orbit given Semi-Major Axis using this online calculator? To use this online calculator for Time Period of Elliptical Orbit given Semi-Major Axis, enter Semi Major Axis of Elliptic Orbit (a_e), Eccentricity of Elliptical Orbit (e_e) & Angular Momentum of Elliptic Orbit (h_e) and hit the calculate button. Here is how the Time Period of Elliptical Orbit given Semi-Major Axis calculation can be explained with given input values -> 21938.2 = 2*pi*16940000^2*sqrt(1-0.6^2)/65750000000.

FAQ

What is Time Period of Elliptical Orbit given Semi-Major Axis?

Time Period of Elliptical Orbit given Semi-Major Axis formula is defined as a measure of the time taken by an object to complete one full orbit around a celestial body in an elliptical path, providing valuable insights into the orbital characteristics of celestial bodies in our solar system and is represented as T_e = 2*pi*a_e^2*sqrt(1-e_e^2)/h_e or 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. Semi Major Axis of Elliptic Orbit is half of the major axis, which is the longest diameter of the ellipse describing the orbit, Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is & 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.

How to calculate Time Period of Elliptical Orbit given Semi-Major Axis?

Time Period of Elliptical Orbit given Semi-Major Axis formula is defined as a measure of the time taken by an object to complete one full orbit around a celestial body in an elliptical path, providing valuable insights into the orbital characteristics of celestial bodies in our solar system is calculated using 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. To calculate Time Period of Elliptical Orbit given Semi-Major Axis, you need Semi Major Axis of Elliptic Orbit (a_e), Eccentricity of Elliptical Orbit (e_e) & Angular Momentum of Elliptic Orbit (h_e). With our tool, you need to enter the respective value for Semi Major Axis of Elliptic Orbit, Eccentricity of Elliptical Orbit & Angular Momentum 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 Time Period of Elliptic Orbit?

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

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

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