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

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The Two Body Problem

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Hyperbolic Orbits

Circular Orbits

Elliptical Orbits

Fundamental Parameters

Parabolic Orbits

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Orbital Position as Function of Time

Hperbolic Orbit Parameters

✖Eccentricity of Hyperbolic Orbit describes how much the orbit differs from a perfect circle, and this value typically falls between 1 and infinity.ⓘ Eccentricity of Hyperbolic Orbit [e_h]			+10% -10%
✖Eccentric Anomaly in Hyperbolic Orbit is an angular parameter that characterizes the position of an object within its hyperbolic trajectory.ⓘ Eccentric Anomaly in Hyperbolic Orbit [F]			+10% -10%

✖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.ⓘ True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity [θ]

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Formula

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True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity

Formula

`"θ" = 2*atan(sqrt(("e"_{"h"}+1)/("e"_{"h"}-1))*tanh("F"/2))`

Example

`"108.9995°"=2*atan(sqrt(("1.339"+1)/("1.339"-1))*tanh("68.22°"/2))`

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

STEP 0: Pre-Calculation Summary

Formula Used

True Anomaly = 2*atan(sqrt((Eccentricity of Hyperbolic Orbit+1)/(Eccentricity of Hyperbolic Orbit-1))*tanh(Eccentric Anomaly in Hyperbolic Orbit/2))
θ = 2*atan(sqrt((e_h+1)/(e_h-1))*tanh(F/2))
This formula uses 4 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)
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)., tanh(Number)

Variables Used

True Anomaly - (Measured in Radian) - 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.
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.
Eccentric Anomaly in Hyperbolic Orbit - (Measured in Radian) - Eccentric Anomaly in Hyperbolic Orbit is an angular parameter that characterizes the position of an object within its hyperbolic trajectory.

STEP 1: Convert Input(s) to Base Unit

Eccentricity of Hyperbolic Orbit: 1.339 --> No Conversion Required
Eccentric Anomaly in Hyperbolic Orbit: 68.22 Degree --> 1.19066361571031 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = 2*atan(sqrt((e_h+1)/(e_h-1))*tanh(F/2)) --> 2*atan(sqrt((1.339+1)/(1.339-1))*tanh(1.19066361571031/2))

Evaluating ... ...

θ = 1.90240083733286

STEP 3: Convert Result to Output's Unit

1.90240083733286 Radian -->108.999538921347 Degree (Check conversion here)

FINAL ANSWER

108.999538921347 ≈ 108.9995 Degree <-- True Anomaly

(Calculation completed in 00.004 seconds)

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Home » Physics » Orbital Mechanics » The Two Body Problem » Hyperbolic Orbits » Orbital Position as Function of Time » True Anomaly in Hyperbolic Orbit given Hyperbolic 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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< 5 Orbital Position as Function of Time Calculators

Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly

Go Time since Periapsis = Angular Momentum of Hyperbolic Orbit^3/([GM.Earth]^2*(Eccentricity of Hyperbolic Orbit^2-1)^(3/2))*(Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit)

True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity

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

Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly

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

Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly

Go Mean Anomaly in Hyperbolic Orbit = Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit

Time since Periapsis in Hyperbolic Orbit given Mean Anomaly

Go Time since Periapsis = Angular Momentum of Hyperbolic Orbit^3/([GM.Earth]^2*(Eccentricity of Hyperbolic Orbit^2-1)^(3/2))*Mean Anomaly in Hyperbolic Orbit

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

True Anomaly = 2*atan(sqrt((Eccentricity of Hyperbolic Orbit+1)/(Eccentricity of Hyperbolic Orbit-1))*tanh(Eccentric Anomaly in Hyperbolic Orbit/2))
θ = 2*atan(sqrt((e_h+1)/(e_h-1))*tanh(F/2))

Why are parabolic trajectories also called escape trajectories?

If the body of some mass m is launched on a parabolic trajectory, it will coast to infinity, arriving there with zero velocity relative to central body. It will not return. Parabolic paths are therefore called escape trajectories.

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

True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity calculator uses True Anomaly = 2*atan(sqrt((Eccentricity of Hyperbolic Orbit+1)/(Eccentricity of Hyperbolic Orbit-1))*tanh(Eccentric Anomaly in Hyperbolic Orbit/2)) to calculate the True Anomaly, The True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity formula is defined as the current angular position of the object within the hyperbolic orbit based on eccentric anomaly and eccentricity. True Anomaly is denoted by θ symbol.

How to calculate True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity using this online calculator? To use this online calculator 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. Here is how the True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity calculation can be explained with given input values -> 7519.887 = 2*atan(sqrt((1.339+1)/(1.339-1))*tanh(1.19066361571031/2)).

FAQ

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

The True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity formula is defined as the current angular position of the object within the hyperbolic orbit based on eccentric anomaly and eccentricity and is represented as θ = 2*atan(sqrt((e_h+1)/(e_h-1))*tanh(F/2)) or True Anomaly = 2*atan(sqrt((Eccentricity of Hyperbolic Orbit+1)/(Eccentricity of Hyperbolic Orbit-1))*tanh(Eccentric Anomaly in Hyperbolic Orbit/2)). Eccentricity of Hyperbolic Orbit describes how much the orbit differs from a perfect circle, and this value typically falls between 1 and infinity & Eccentric Anomaly in Hyperbolic Orbit is an angular parameter that characterizes the position of an object within its hyperbolic trajectory.

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

The True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity formula is defined as the current angular position of the object within the hyperbolic orbit based on eccentric anomaly and eccentricity is calculated using True Anomaly = 2*atan(sqrt((Eccentricity of Hyperbolic Orbit+1)/(Eccentricity of Hyperbolic Orbit-1))*tanh(Eccentric Anomaly in Hyperbolic Orbit/2)). To calculate True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity, you need Eccentricity of Hyperbolic Orbit (e_h) & Eccentric Anomaly in Hyperbolic Orbit (F). With our tool, you need to enter the respective value for Eccentricity of Hyperbolic Orbit & Eccentric Anomaly in Hyperbolic 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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