Time Period of Elliptical Orbit given Semi-Major Axis Calculator

⤿

The Two Body Problem

⤿

Elliptical Orbits

Circular Orbits

Fundamental Parameters

Hyperbolic Orbits

Parabolic Orbits

⤿

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]			+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]

⎘ Copy

👎

Formula

✖

Time Period of Elliptical Orbit given Semi-Major Axis

Formula

`"T"_{"e"} = 2*pi*"a"_{"e"}^2*sqrt(1-"e"_{"e"}^2)/"h"_{"e"}`

Example

`"21938.2s"=2*pi*("16940km")^2*sqrt(1-("0.6")^2)/"65750km²/s"`

Calculator

LaTeX

Reset

👍

Download Elliptical Orbits Formulas PDF PDF Image

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 00.004 seconds)

You are here -

Home » Physics » Orbital Mechanics » The Two Body Problem » Elliptical Orbits » Elliptical Orbit Parameters » Time Period of Elliptical Orbit given Semi-Major Axis

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 Akshat Nama

Indian Institute of Information Technology, Design And Manufacturing (IIITDM ), Jabalpur

Akshat Nama has verified this Calculator and 10+ more calculators!

< 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)

Time Period of Elliptical Orbit given Semi-Major Axis Formula

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 planet with the shortest orbital period (year) is Mercury. The innermost planet in our Solar System completes its elliptical orbit around the Sun once every 87 (Earth) days 21 hours.

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, The Time Period of Elliptical Orbit given Semi-Major Axis formula is defined as the amount of time a given astronomical object takes to complete a revolution in an elliptical orbit. 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?

The Time Period of Elliptical Orbit given Semi-Major Axis formula is defined as the amount of time a given astronomical object takes to complete a revolution in an elliptical orbit 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?

The Time Period of Elliptical Orbit given Semi-Major Axis formula is defined as the amount of time a given astronomical object takes to complete a revolution in an elliptical orbit 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

Home

FREE PDFs

🔍 Search