Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly 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%

✖The Mean Anomaly in Hyperbolic Orbit is a time-related parameter that represents the angular distance covered by an object in its hyperbolic trajectory since passing through periapsis.ⓘ Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly [M_h]

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Formula

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Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly

Formula

`"M"_{"h"} = "e"_{"h"}*sinh("F")-"F"`

Example

`"46.29253°"="1.339"*sinh("68.22°")-"68.22°"`

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Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean Anomaly in Hyperbolic Orbit = Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit
M_h = e_h*sinh(F)-F
This formula uses 1 Functions, 3 Variables

Functions Used

sinh - The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function., sinh(Number)

Variables Used

Mean Anomaly in Hyperbolic Orbit - (Measured in Radian) - The Mean Anomaly in Hyperbolic Orbit is a time-related parameter that represents the angular distance covered by an object in its hyperbolic trajectory since passing through periapsis.
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

M_h = e_h*sinh(F)-F --> 1.339*sinh(1.19066361571031)-1.19066361571031

Evaluating ... ...

M_h = 0.80795713854162

STEP 3: Convert Result to Output's Unit

0.80795713854162 Radian -->46.2925340659103 Degree (Check conversion here)

FINAL ANSWER

46.2925340659103 ≈ 46.29253 Degree <-- Mean Anomaly in Hyperbolic Orbit

(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 » Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly

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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

Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Formula

Mean Anomaly in Hyperbolic Orbit = Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit
M_h = e_h*sinh(F)-F

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 Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?

Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly calculator uses Mean Anomaly in Hyperbolic Orbit = Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit to calculate the Mean Anomaly in Hyperbolic Orbit, The Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly formula is defined as angular distance covered by an object in its hyperbolic trajectory since passing through periapsis (closest point to the central body). Unlike in elliptical orbits, the Mean Anomaly in a hyperbolic orbit is not directly proportional to time. Mean Anomaly in Hyperbolic Orbit is denoted by M_h symbol.

How to calculate Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly using this online calculator? To use this online calculator for Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly, enter Eccentricity of Hyperbolic Orbit (e_h) & Eccentric Anomaly in Hyperbolic Orbit (F) and hit the calculate button. Here is how the Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly calculation can be explained with given input values -> 2652.367 = 1.339*sinh(1.19066361571031)-1.19066361571031.

FAQ

What is Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?

The Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly formula is defined as angular distance covered by an object in its hyperbolic trajectory since passing through periapsis (closest point to the central body). Unlike in elliptical orbits, the Mean Anomaly in a hyperbolic orbit is not directly proportional to time and is represented as M_h = e_h*sinh(F)-F or Mean Anomaly in Hyperbolic Orbit = Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in 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 is an angular parameter that characterizes the position of an object within its hyperbolic trajectory.

How to calculate Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?

The Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly formula is defined as angular distance covered by an object in its hyperbolic trajectory since passing through periapsis (closest point to the central body). Unlike in elliptical orbits, the Mean Anomaly in a hyperbolic orbit is not directly proportional to time is calculated using Mean Anomaly in Hyperbolic Orbit = Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit. To calculate Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly, 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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