True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity Calculator

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

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Formula

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True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity

Formula

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

Example

`"135.2002°"=2*atan(sqrt((1+"0.6")/(1-"0.6"))*tan("101°"/2))`

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True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

STEP 1: Convert Input(s) to Base Unit

Eccentricity of Elliptical Orbit: 0.6 --> No Conversion Required
Eccentric Anomaly: 101 Degree --> 1.76278254451394 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_e = 2*atan(sqrt((1+e_e)/(1-e_e))*tan(E/2)) --> 2*atan(sqrt((1+0.6)/(1-0.6))*tan(1.76278254451394/2))

Evaluating ... ...

θ_e = 2.35968867753432

STEP 3: Convert Result to Output's Unit

2.35968867753432 Radian -->135.200202187549 Degree (Check conversion here)

FINAL ANSWER

135.200202187549 ≈ 135.2002 Degree <-- True Anomaly in Elliptical Orbit

(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 » True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity

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Created by Harsh Raj

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

True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity Formula

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

True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity calculator uses True Anomaly in Elliptical Orbit = 2*atan(sqrt((1+Eccentricity of Elliptical Orbit)/(1-Eccentricity of Elliptical Orbit))*tan(Eccentric Anomaly/2)) to calculate the True Anomaly in Elliptical Orbit, The True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity formula is defined as current angular position of the object within the elliptic orbit, this formula is used to calculate the true anomaly of an object in an elliptic orbit based on two essential parameters: eccentric anomaly and eccentricity. True Anomaly in Elliptical Orbit is denoted by θ_e symbol.

How to calculate True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity using this online calculator? To use this online calculator for True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity, enter Eccentricity of Elliptical Orbit (e_e) & Eccentric Anomaly (E) and hit the calculate button. Here is how the True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity calculation can be explained with given input values -> 7746.401 = 2*atan(sqrt((1+0.6)/(1-0.6))*tan(1.76278254451394/2)).

FAQ

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

The True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity formula is defined as current angular position of the object within the elliptic orbit, this formula is used to calculate the true anomaly of an object in an elliptic orbit based on two essential parameters: eccentric anomaly and eccentricity and is represented as θ_e = 2*atan(sqrt((1+e_e)/(1-e_e))*tan(E/2)) or True Anomaly in Elliptical Orbit = 2*atan(sqrt((1+Eccentricity of Elliptical Orbit)/(1-Eccentricity of Elliptical Orbit))*tan(Eccentric Anomaly/2)). Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is & The Eccentric Anomaly is an angular parameter that defines the position of a body that is moving along an Kepler orbit.

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

The True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity formula is defined as current angular position of the object within the elliptic orbit, this formula is used to calculate the true anomaly of an object in an elliptic orbit based on two essential parameters: eccentric anomaly and eccentricity is calculated using True Anomaly in Elliptical Orbit = 2*atan(sqrt((1+Eccentricity of Elliptical Orbit)/(1-Eccentricity of Elliptical Orbit))*tan(Eccentric Anomaly/2)). To calculate True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity, you need Eccentricity of Elliptical Orbit (e_e) & Eccentric Anomaly (E). With our tool, you need to enter the respective value for Eccentricity of Elliptical Orbit & Eccentric Anomaly 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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