Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity Calculator

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The Two Body Problem

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Elliptical Orbits

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Orbital Position as Function of Time

Elliptical Orbit Parameters

✖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%
✖True Anomaly in Elliptical Orbit measures the angle between the object's current position and the perigee (the point of closest approach to the central body) when viewed from the focus of the orbit.ⓘ True Anomaly in Elliptical Orbit [θ_e]			+10% -10%

✖The Eccentric Anomaly is an angular parameter that defines the position of a body that is moving along an Kepler orbit.ⓘ Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity [E]

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Formula

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Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity

Formula

`"E" = 2*atan(sqrt((1-"e"_{"e"})/(1+"e"_{"e"}))*tan("θ"_{"e"}/2))`

Example

`"100.8744°"=2*atan(sqrt((1-"0.6")/(1+"0.6"))*tan("135.11°"/2))`

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Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Eccentric Anomaly = 2*atan(sqrt((1-Eccentricity of Elliptical Orbit)/(1+Eccentricity of Elliptical Orbit))*tan(True Anomaly in Elliptical Orbit/2))
E = 2*atan(sqrt((1-e_e)/(1+e_e))*tan(θ_e/2))
This formula uses 3 Functions, 3 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)
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

Eccentric Anomaly - (Measured in Radian) - The Eccentric Anomaly is an angular parameter that defines the position of a body that is moving along an Kepler orbit.
Eccentricity of Elliptical Orbit - Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.
True Anomaly in Elliptical Orbit - (Measured in Radian) - True Anomaly in Elliptical Orbit measures the angle between the object's current position and the perigee (the point of closest approach to the central body) when viewed from the focus of the orbit.

STEP 1: Convert Input(s) to Base Unit

Eccentricity of Elliptical Orbit: 0.6 --> No Conversion Required
True Anomaly in Elliptical Orbit: 135.11 Degree --> 2.3581143523691 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = 2*atan(sqrt((1-e_e)/(1+e_e))*tan(θ_e/2)) --> 2*atan(sqrt((1-0.6)/(1+0.6))*tan(2.3581143523691/2))

Evaluating ... ...

E = 1.76059061221031

STEP 3: Convert Result to Output's Unit

1.76059061221031 Radian -->100.874411530023 Degree (Check conversion here)

FINAL ANSWER

100.874411530023 ≈ 100.8744 Degree <-- Eccentric Anomaly

(Calculation completed in 00.004 seconds)

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Home » Physics » Orbital Mechanics » The Two Body Problem » Elliptical Orbits » Orbital Position as Function of Time » Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity

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

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< 6 Orbital Position as Function of Time Calculators

Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period

Go Time since Periapsis in Elliptical Orbit = (Eccentric Anomaly-Eccentricity of Elliptical Orbit*sin(Eccentric Anomaly))*Time Period of Elliptic Orbit/(2*Pi(6))

Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity

Go Eccentric Anomaly = 2*atan(sqrt((1-Eccentricity of Elliptical Orbit)/(1+Eccentricity of Elliptical Orbit))*tan(True Anomaly in Elliptical Orbit/2))

True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity

Go True Anomaly in Elliptical Orbit = 2*atan(sqrt((1+Eccentricity of Elliptical Orbit)/(1-Eccentricity of Elliptical Orbit))*tan(Eccentric Anomaly/2))

Mean Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity

Go Mean Anomaly in Elliptical Orbit = Eccentric Anomaly-Eccentricity of Elliptical Orbit*sin(Eccentric Anomaly)

Time since Periapsis in Elliptic Orbit given Mean Anomaly

Go Time since Periapsis in Elliptical Orbit = Mean Anomaly in Elliptical Orbit*Time Period of Elliptic Orbit/(2*pi)

Mean Anomaly in Elliptic Orbit given Time since Periapsis

Go Mean Anomaly in Elliptical Orbit = (2*pi*Time since Periapsis in Elliptical Orbit)/Time Period of Elliptic Orbit

Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity Formula

Eccentric Anomaly = 2*atan(sqrt((1-Eccentricity of Elliptical Orbit)/(1+Eccentricity of Elliptical Orbit))*tan(True Anomaly in Elliptical Orbit/2))
E = 2*atan(sqrt((1-e_e)/(1+e_e))*tan(θ_e/2))

Geometric Visualization of Eccentric Anamoly

The eccentric anomaly, E, is the angle between the direction of periapsis and the current position of an object on its orbit, projected onto the ellipse's Page 10 circumscribing circle perpendicularly to the major axis, measured at the center of the ellipse.

How to Calculate Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity?

Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity calculator uses Eccentric Anomaly = 2*atan(sqrt((1-Eccentricity of Elliptical Orbit)/(1+Eccentricity of Elliptical Orbit))*tan(True Anomaly in Elliptical Orbit/2)) to calculate the Eccentric Anomaly, Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity formula is defined as the angle that defines the object's position within the elliptic orbit, relative to the center of the orbit. Eccentric Anomaly is denoted by E symbol.

How to calculate Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity using this online calculator? To use this online calculator for Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity, enter Eccentricity of Elliptical Orbit (e_e) & True Anomaly in Elliptical Orbit (θ_e) and hit the calculate button. Here is how the Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity calculation can be explained with given input values -> 5779.837 = 2*atan(sqrt((1-0.6)/(1+0.6))*tan(2.3581143523691/2)).

FAQ

What is Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity?

Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity formula is defined as the angle that defines the object's position within the elliptic orbit, relative to the center of the orbit and is represented as E = 2*atan(sqrt((1-e_e)/(1+e_e))*tan(θ_e/2)) or Eccentric Anomaly = 2*atan(sqrt((1-Eccentricity of Elliptical Orbit)/(1+Eccentricity of Elliptical Orbit))*tan(True Anomaly in Elliptical Orbit/2)). Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is & True Anomaly in Elliptical Orbit measures the angle between the object's current position and the perigee (the point of closest approach to the central body) when viewed from the focus of the orbit.

How to calculate Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity?

Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity formula is defined as the angle that defines the object's position within the elliptic orbit, relative to the center of the orbit is calculated using Eccentric Anomaly = 2*atan(sqrt((1-Eccentricity of Elliptical Orbit)/(1+Eccentricity of Elliptical Orbit))*tan(True Anomaly in Elliptical Orbit/2)). To calculate Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity, you need Eccentricity of Elliptical Orbit (e_e) & True Anomaly in Elliptical Orbit (θ_e). With our tool, you need to enter the respective value for Eccentricity of Elliptical Orbit & True Anomaly in 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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