Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly Calculator

⤿

The Two Body Problem

⤿

Hyperbolic Orbits

Circular Orbits

Elliptical Orbits

Fundamental Parameters

Parabolic Orbits

⤿

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%
✖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 [θ]			+10% -10%

✖Eccentric Anomaly in Hyperbolic Orbit is an angular parameter that characterizes the position of an object within its hyperbolic trajectory.ⓘ Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly [F]

⎘ Copy

👎

Formula

✖

Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly

Formula

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

Example

`"68.22073°"=2*atanh(sqrt(("1.339"-1)/("1.339"+1))*tan("109°"/2))`

Calculator

LaTeX

Reset

👍

Download Hyperbolic Orbits Formulas PDF PDF Image

Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly Solution

STEP 0: Pre-Calculation Summary

Formula Used

Eccentric Anomaly in Hyperbolic Orbit = 2*atanh(sqrt((Eccentricity of Hyperbolic Orbit-1)/(Eccentricity of Hyperbolic Orbit+1))*tan(True Anomaly/2))
F = 2*atanh(sqrt((e_h-1)/(e_h+1))*tan(θ/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)
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)
atanh - The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number., atanh(Number)

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Eccentricity of Hyperbolic Orbit: 1.339 --> No Conversion Required
True Anomaly: 109 Degree --> 1.90240888467346 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F = 2*atanh(sqrt((e_h-1)/(e_h+1))*tan(θ/2)) --> 2*atanh(sqrt((1.339-1)/(1.339+1))*tan(1.90240888467346/2))

Evaluating ... ...

F = 1.19067631954554

STEP 3: Convert Result to Output's Unit

1.19067631954554 Radian -->68.2207278761425 Degree (Check conversion here)

FINAL ANSWER

68.2207278761425 ≈ 68.22073 Degree <-- Eccentric Anomaly in Hyperbolic Orbit

(Calculation completed in 00.004 seconds)

You are here -

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

Credits

Created by Harsh Raj

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

Harsh Raj has created this Calculator and 50+ more calculators!

Verified by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

Kartikay Pandit has verified this Calculator and 400+ more calculators!

< 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

Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly Formula

Eccentric Anomaly in Hyperbolic Orbit = 2*atanh(sqrt((Eccentricity of Hyperbolic Orbit-1)/(Eccentricity of Hyperbolic Orbit+1))*tan(True Anomaly/2))
F = 2*atanh(sqrt((e_h-1)/(e_h+1))*tan(θ/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 Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly?

Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly calculator uses Eccentric Anomaly in Hyperbolic Orbit = 2*atanh(sqrt((Eccentricity of Hyperbolic Orbit-1)/(Eccentricity of Hyperbolic Orbit+1))*tan(True Anomaly/2)) to calculate the Eccentric Anomaly in Hyperbolic Orbit, The Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly formula is defined as angle that defines the object's position within the hyperbolic orbit, given the true anomaly. Eccentric Anomaly in Hyperbolic Orbit is denoted by F symbol.

How to calculate Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly using this online calculator? To use this online calculator for Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly, enter Eccentricity of Hyperbolic Orbit (e_h) & True Anomaly (θ) and hit the calculate button. Here is how the Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly calculation can be explained with given input values -> 3908.76 = 2*atanh(sqrt((1.339-1)/(1.339+1))*tan(1.90240888467346/2)).

FAQ

What is Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly?

The Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly formula is defined as angle that defines the object's position within the hyperbolic orbit, given the true anomaly and is represented as F = 2*atanh(sqrt((e_h-1)/(e_h+1))*tan(θ/2)) or Eccentric Anomaly in Hyperbolic Orbit = 2*atanh(sqrt((Eccentricity of Hyperbolic Orbit-1)/(Eccentricity of Hyperbolic Orbit+1))*tan(True Anomaly/2)). Eccentricity of Hyperbolic Orbit describes how much the orbit differs from a perfect circle, and this value typically falls between 1 and infinity & 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.

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

The Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly formula is defined as angle that defines the object's position within the hyperbolic orbit, given the true anomaly is calculated using Eccentric Anomaly in Hyperbolic Orbit = 2*atanh(sqrt((Eccentricity of Hyperbolic Orbit-1)/(Eccentricity of Hyperbolic Orbit+1))*tan(True Anomaly/2)). To calculate Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly, you need Eccentricity of Hyperbolic Orbit (e_h) & True Anomaly (θ). With our tool, you need to enter the respective value for Eccentricity of Hyperbolic Orbit & True Anomaly and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search