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Time Period of Elliptical Orbit given Angular Momentum Formula

GoElliptical Orbit Time Period given Angular Momentum and Eccentricity Formula

GoTime Period for One Complete Revolution given Angular Momentum Formula

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The time period of Elliptic Orbit is the amount of time a given astronomical object takes to complete one orbit around another object. Check FAQs

T e = \frac{2 \cdot π}{{[GM.Earth]}^{2}} \cdot {(\frac{h e}{\sqrt{1 - {e e}^{2}}})}^{3}

T_e - Time Period of Elliptic Orbit?h_e - Angular Momentum of Elliptic Orbit?e_e - Eccentricity of Elliptical Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?π - Archimedes' constant?

Time Period of Elliptical Orbit given Angular Momentum Example

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Here is how the Time Period of Elliptical Orbit given Angular Momentum equation looks like with Values.

Here is how the Time Period of Elliptical Orbit given Angular Momentum equation looks like with Units.

Here is how the Time Period of Elliptical Orbit given Angular Momentum equation looks like.

21954.4028 = \frac{2 \cdot 3.1416}{{4E+14}^{2}} \cdot {(\frac{65750}{\sqrt{1 - {0.6}^{2}}})}^{3}

21954.4028s = \frac{2 \cdot 3.1416}{{4E+14m³/s²}^{2}} \cdot {(\frac{65750km²/s}{\sqrt{1 - {0.6}^{2}}})}^{3}

21954.4028 = \frac{2 \cdot 3.1416}{{4E+14}^{2}} \cdot {(\frac{65750}{\sqrt{1 - {0.6}^{2}}})}^{3}

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Time Period of Elliptical Orbit given Angular Momentum Solution

Follow our step by step solution on how to calculate Time Period of Elliptical Orbit given Angular Momentum?

FIRST Step Consider the formula

T e = \frac{2 \cdot π}{{[GM.Earth]}^{2}} \cdot {(\frac{h e}{\sqrt{1 - {e e}^{2}}})}^{3}

Next Step Substitute values of Variables

∴

T e = \frac{2 \cdot π}{{[GM.Earth]}^{2}} \cdot {(\frac{65750km²/s}{\sqrt{1 - {0.6}^{2}}})}^{3}

Next Step Substitute values of Constants

∴

T e = \frac{2 \cdot 3.1416}{{4E+14m³/s²}^{2}} \cdot {(\frac{65750km²/s}{\sqrt{1 - {0.6}^{2}}})}^{3}

Next Step Convert Units

∴

T e = \frac{2 \cdot 3.1416}{{4E+14m³/s²}^{2}} \cdot {(\frac{6.6E+10m²/s}{\sqrt{1 - {0.6}^{2}}})}^{3}

Next Step Prepare to Evaluate

∴

T e = \frac{2 \cdot 3.1416}{{4E+14}^{2}} \cdot {(\frac{6.6E+10}{\sqrt{1 - {0.6}^{2}}})}^{3}

Next Step Evaluate

∴

T e = 21954.4027705855s

LAST Step Rounding Answer

∴

T e = 21954.4028s

Time Period of Elliptical Orbit given Angular Momentum Formula Elements

Variables

Constants

Functions

Time Period of Elliptic Orbit

The time period of Elliptic Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.

Symbol: T_e

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period of Elliptic Orbit

Angular Momentum of Elliptic 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.

Symbol: h_e

Measurement: Specific Angular MomentumUnit: km²/s

Note: Value should be greater than 0.

Formulas to find Angular Momentum of Elliptic Orbit

Eccentricity of Elliptical Orbit

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

Symbol: e_e

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Eccentricity of Elliptical Orbit

Earth’s Geocentric Gravitational Constant

Earth’s Geocentric Gravitational Constant the gravitational parameter for the Earth as the central body.

Symbol: [GM.Earth]

Value: 3.986004418E+14 m³/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Time Period of Elliptic Orbit

Go Elliptical Orbit Time Period given Angular Momentum and Eccentricity

T e = \frac{2 \cdot π}{{[GM.Earth]}^{2}} \cdot {(\frac{h e}{\sqrt{1 - {e e}^{2}}})}^{3}

Go Time Period for One Complete Revolution given Angular Momentum

T e = \frac{2 \cdot π \cdot a e \cdot b e}{h e}

Go Time Period of Elliptical Orbit given Semi-Major Axis

T e = 2 \cdot π \cdot {a e}^{2} \cdot \frac{\sqrt{1 - {e e}^{2}}}{h e}

Other formulas in Elliptical Orbit Parameters category

Go Eccentricity of Elliptical Orbit given Apogee and Perigee

e e = \frac{r e,apogee - r e,perigee}{r e,apogee + r e,perigee}

Go Angular Momentum in Elliptic Orbit Given Apogee Radius and Apogee Velocity

h e = r e,apogee \cdot v apogee

Go Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity

r e,apogee = \frac{{h e}^{2}}{[GM.Earth] \cdot (1 - e e)}

Go Semimajor Axis of Elliptic Orbit given Apogee and Perigee Radii

a e = \frac{r e,apogee + r e,perigee}{2}

How to Evaluate Time Period of Elliptical Orbit given Angular Momentum?

Time Period of Elliptical Orbit given Angular Momentum evaluator 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 evaluate the Time Period of Elliptic Orbit, Time Period of Elliptical Orbit given Angular Momentum formula is defined as a measure of the time taken by an object to complete one orbit around a celestial body, such as a planet, in an elliptical path, which is influenced by the angular momentum of the object and the gravitational force of the celestial body. Time Period of Elliptic Orbit is denoted by T_e symbol.

How to evaluate Time Period of Elliptical Orbit given Angular Momentum using this online evaluator? To use this online evaluator for Time Period of Elliptical Orbit given Angular Momentum, enter Angular Momentum of Elliptic Orbit (h_e) & Eccentricity of Elliptical Orbit (e_e) and hit the calculate button.

FAQs on Time Period of Elliptical Orbit given Angular Momentum

What is the formula to find Time Period of Elliptical Orbit given Angular Momentum?

The formula of Time Period of Elliptical Orbit given Angular Momentum is expressed as Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3. Here is an example- 21954.4 = (2*pi)/[GM.Earth]^2*(65750000000/sqrt(1-0.6^2))^3.

How to calculate Time Period of Elliptical Orbit given Angular Momentum?

With Angular Momentum of Elliptic Orbit (h_e) & Eccentricity of Elliptical Orbit (e_e) we can find Time Period of Elliptical Orbit given Angular Momentum using the formula - Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3. This formula also uses Earth’s Geocentric Gravitational Constant, Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Time Period of Elliptic Orbit?

Here are the different ways to Calculate Time Period 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
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

Can the Time Period of Elliptical Orbit given Angular Momentum be negative?

No, the Time Period of Elliptical Orbit given Angular Momentum, measured in Time cannot be negative.

Which unit is used to measure Time Period of Elliptical Orbit given Angular Momentum?

Time Period of Elliptical Orbit given Angular Momentum is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Time Period of Elliptical Orbit given Angular Momentum can be measured.

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