## Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
t = hh^3/([GM.Earth]^2*(eh^2-1)^(3/2))*(eh*sinh(F)-F)
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14
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
Time since Periapsis - (Measured in Second) - The Time since Periapsis is a measure of the duration that has passed since an object in orbit, such as a satellite, passed through its closest point to the central body, known as periapsis.
Angular Momentum of Hyperbolic Orbit - (Measured in Squaer Meter per Second) - Angular Momentum of Hyperbolic Orbit is a fundamental physical quantity that characterizes the rotational motion of an object in orbit around a celestial body, such as a planet or a star.
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
Angular Momentum of Hyperbolic Orbit: 65700 Square Kilometer per Second --> 65700000000 Squaer Meter per Second (Check conversion ​here)
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
t = hh^3/([GM.Earth]^2*(eh^2-1)^(3/2))*(eh*sinh(F)-F) --> 65700000000^3/([GM.Earth]^2*(1.339^2-1)^(3/2))*(1.339*sinh(1.19066361571031)-1.19066361571031)
Evaluating ... ...
t = 2042.50909767657
STEP 3: Convert Result to Output's Unit
2042.50909767657 Second --> No Conversion Required
2042.50909767657 2042.509 Second <-- Time since Periapsis
(Calculation completed in 00.020 seconds)
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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
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
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 Hyperbolic Orbit^3/([GM.Earth]^2*(Eccentricity of Hyperbolic Orbit^2-1)^(3/2))*Mean Anomaly in Hyperbolic Orbit

## Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Formula

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)
t = hh^3/([GM.Earth]^2*(eh^2-1)^(3/2))*(eh*sinh(F)-F)

## What is Hyperbolic Eccentric Anomaly ?

In the context of orbital mechanics, the concept of eccentric anomaly is typically associated with elliptical orbits and is used to describe the position of an object in its orbit relative to the central body. However, in hyperbolic orbits, where the trajectory of the object is open-ended, there isn't a direct analogue to the eccentric anomaly.

## How to Calculate Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?

Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly calculator uses 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) to calculate the Time since Periapsis, The Time Since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly formula is defined as time that has elapsed since an object in a hyperbolic orbit passed through periapsis (the point of closest approach to the central body) based on the eccentric anomaly. Time since Periapsis is denoted by t symbol.

How to calculate Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly using this online calculator? To use this online calculator for Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly, enter Angular Momentum of Hyperbolic Orbit (hh), Eccentricity of Hyperbolic Orbit (eh) & Eccentric Anomaly in Hyperbolic Orbit (F) and hit the calculate button. Here is how the Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly calculation can be explained with given input values -> 2042.509 = 65700000000^3/([GM.Earth]^2*(1.339^2-1)^(3/2))*(1.339*sinh(1.19066361571031)-1.19066361571031).

### FAQ

What is Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?
The Time Since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly formula is defined as time that has elapsed since an object in a hyperbolic orbit passed through periapsis (the point of closest approach to the central body) based on the eccentric anomaly and is represented as t = hh^3/([GM.Earth]^2*(eh^2-1)^(3/2))*(eh*sinh(F)-F) or 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). Angular Momentum of Hyperbolic Orbit is a fundamental physical quantity that characterizes the rotational motion of an object in orbit around a celestial body, such as a planet or a star, 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 Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?
The Time Since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly formula is defined as time that has elapsed since an object in a hyperbolic orbit passed through periapsis (the point of closest approach to the central body) based on the eccentric anomaly is calculated using 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). To calculate Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly, you need Angular Momentum of Hyperbolic Orbit (hh), Eccentricity of Hyperbolic Orbit (eh) & Eccentric Anomaly in Hyperbolic Orbit (F). With our tool, you need to enter the respective value for Angular Momentum of Hyperbolic Orbit, 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.
How many ways are there to calculate Time since Periapsis?
In this formula, Time since Periapsis uses Angular Momentum of Hyperbolic Orbit, Eccentricity of Hyperbolic Orbit & Eccentric Anomaly in Hyperbolic Orbit. We can use 1 other way(s) to calculate the same, which is/are as follows -
• 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
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