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True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity Formula

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True Anomaly 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. Check FAQs

θ = 2 \cdot a \tan (\sqrt{\frac{e h + 1}{e h - 1}} \cdot \tanh (\frac{F}{2}))

θ - True Anomaly?e_h - Eccentricity of Hyperbolic Orbit?F - Eccentric Anomaly in Hyperbolic Orbit?

True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity Example

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Here is how the True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity equation looks like.

108.9995 = 2 \cdot a \tan (\sqrt{\frac{1.339 + 1}{1.339 - 1}} \cdot \tanh (\frac{68.22}{2}))

108.9995° = 2 \cdot a \tan (\sqrt{\frac{1.339 + 1}{1.339 - 1}} \cdot \tanh (\frac{68.22°}{2}))

108.9995 = 2 \cdot a \tan (\sqrt{\frac{1.339 + 1}{1.339 - 1}} \cdot \tanh (\frac{68.22}{2}))

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True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity Solution

Follow our step by step solution on how to calculate True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity?

FIRST Step Consider the formula

θ = 2 \cdot a \tan (\sqrt{\frac{e h + 1}{e h - 1}} \cdot \tanh (\frac{F}{2}))

Next Step Substitute values of Variables

∴

θ = 2 \cdot a \tan (\sqrt{\frac{1.339 + 1}{1.339 - 1}} \cdot \tanh (\frac{68.22°}{2}))

Next Step Convert Units

∴

θ = 2 \cdot a \tan (\sqrt{\frac{1.339 + 1}{1.339 - 1}} \cdot \tanh (\frac{1.1907rad}{2}))

Next Step Prepare to Evaluate

∴

θ = 2 \cdot a \tan (\sqrt{\frac{1.339 + 1}{1.339 - 1}} \cdot \tanh (\frac{1.1907}{2}))

Next Step Evaluate

∴

θ = 1.90240083733286rad

Next Step Convert to Output's Unit

∴

θ = 108.999538921347°

LAST Step Rounding Answer

∴

θ = 108.9995°

True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity Formula Elements

Variables

Functions

True Anomaly

True Anomaly 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.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find True Anomaly

Eccentricity of Hyperbolic Orbit

Eccentricity of Hyperbolic Orbit describes how much the orbit differs from a perfect circle, and this value typically falls between 1 and infinity.

Symbol: e_h

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Eccentricity of Hyperbolic Orbit

Eccentric Anomaly in Hyperbolic Orbit

Eccentric Anomaly in Hyperbolic Orbit is an angular parameter that characterizes the position of an object within its hyperbolic trajectory.

Symbol: F

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Eccentric Anomaly in Hyperbolic Orbit

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.

Syntax: 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.

Syntax: 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.

Syntax: sqrt(Number)

tanh

The hyperbolic tangent function (tanh) is a function that is defined as the ratio of the hyperbolic sine function (sinh) to the hyperbolic cosine function (cosh).

Syntax: tanh(Number)

Other formulas in Orbital Position as Function of Time category

Go Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly

M h = e h \cdot \sinh (F) - F

Go Time since Periapsis in Hyperbolic Orbit given Mean Anomaly

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

Go Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly

t = \frac{{h h}^{3}}{{[GM.Earth]}^{2} \cdot {({e h}^{2} - 1)}^{\frac{3}{2}}} \cdot (e h \cdot \sinh (F) - F)

Go Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly

F = 2 \cdot a \tanh (\sqrt{\frac{e h - 1}{e h + 1}} \cdot \tan (\frac{θ}{2}))

How to Evaluate True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity?

True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity evaluator uses True Anomaly = 2*atan(sqrt((Eccentricity of Hyperbolic Orbit+1)/(Eccentricity of Hyperbolic Orbit-1))*tanh(Eccentric Anomaly in Hyperbolic Orbit/2)) to evaluate the True Anomaly, True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity formula is defined as a method to determine the position of an object in a hyperbolic trajectory relative to its focus, based on its eccentricity and hyperbolic eccentric anomaly. True Anomaly is denoted by θ symbol.

How to evaluate True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity using this online evaluator? To use this online evaluator for True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity, enter Eccentricity of Hyperbolic Orbit (e_h) & Eccentric Anomaly in Hyperbolic Orbit (F) and hit the calculate button.

FAQs on True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity

What is the formula to find True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity?

The formula of True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity is expressed as True Anomaly = 2*atan(sqrt((Eccentricity of Hyperbolic Orbit+1)/(Eccentricity of Hyperbolic Orbit-1))*tanh(Eccentric Anomaly in Hyperbolic Orbit/2)). Here is an example- 7519.887 = 2*atan(sqrt((1.339+1)/(1.339-1))*tanh(1.19066361571031/2)).

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

With Eccentricity of Hyperbolic Orbit (e_h) & Eccentric Anomaly in Hyperbolic Orbit (F) we can find True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity using the formula - True Anomaly = 2*atan(sqrt((Eccentricity of Hyperbolic Orbit+1)/(Eccentricity of Hyperbolic Orbit-1))*tanh(Eccentric Anomaly in Hyperbolic Orbit/2)). This formula also uses Tangent (tan)Inverse Tan (atan)Square Root (sqrt), Hyperbolic Tangent (tanh) function(s).

Can the True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity be negative?

Yes, the True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity, measured in Angle can be negative.

Which unit is used to measure True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity?

True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity can be measured.

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