## 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
Mh = eh*sinh(F)-F
This formula uses 1 Functions, 3 Variables
Functions Used
sinh - Hyperbolic 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: 2.3 Radian --> 2.3 Radian No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Mh = eh*sinh(F)-F --> 1.339*sinh(2.3)-2.3
Evaluating ... ...
Mh = 4.31059185762604
STEP 3: Convert Result to Output's Unit
4.31059185762604 Radian --> No Conversion Required
4.31059185762604 4.310592 Radian <-- Mean Anomaly in Hyperbolic Orbit
(Calculation completed in 00.004 seconds)
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## Credits

Created by Harsh Raj
Indian Institute of Technology, Kharagpur (IIT KGP), Kharagpur, West Bengal
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## < 5 Orbital Position as Function of Time Calculators

Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly
Time since Periapsis = Angular Momentum of 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
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
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
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
Time since Periapsis = Angular Momentum of 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
Mh = eh*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 Mh 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 (eh) & 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 -> 4.310592 = 1.339*sinh(2.3)-2.3.

### 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 Mh = eh*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 (eh) & 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. Let Others Know