## Time since Periapsis in Hyperbolic Orbit given Mean 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))*Mean Anomaly in Hyperbolic Orbit
t = hh^3/([GM.Earth]^2*(eh^2-1)^(3/2))*Mh
This formula uses 1 Constants, 4 Variables
Constants Used
[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14
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.
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.
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
Mean Anomaly in Hyperbolic Orbit: 46.29 Degree --> 0.807912910748023 Radian (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
t = hh^3/([GM.Earth]^2*(eh^2-1)^(3/2))*Mh --> 65700000000^3/([GM.Earth]^2*(1.339^2-1)^(3/2))*0.807912910748023
Evaluating ... ...
t = 2042.39729017283
STEP 3: Convert Result to Output's Unit
2042.39729017283 Second --> No Conversion Required
2042.39729017283 2042.397 Second <-- Time since Periapsis
(Calculation completed in 00.004 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 Mean Anomaly Formula

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

## What is Time since Periapsis in Hyperbolic Orbit ?

In hyperbolic orbit, the time since periapsis refers to the elapsed time since the object passed its periapsis, which is the point of closest approach to the central body. It's a measure of how much time has passed since the object was at its closest point to the central body.

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

Time since Periapsis in Hyperbolic Orbit given Mean Anomaly calculator uses 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 to calculate the Time since Periapsis, The Time Since Periapsis in Hyperbolic Orbit given Mean Anomaly formula is an angular parameter that describes the position of an object in its orbit relative to the focus of the hyperbola and a reference line, usually measured from periapsis (the closest point to the central body) to the current position of the object. Time since Periapsis is denoted by t symbol.

How to calculate Time since Periapsis in Hyperbolic Orbit given Mean Anomaly using this online calculator? To use this online calculator for Time since Periapsis in Hyperbolic Orbit given Mean Anomaly, enter Angular Momentum of Hyperbolic Orbit (hh), Eccentricity of Hyperbolic Orbit (eh) & Mean Anomaly in Hyperbolic Orbit (Mh) and hit the calculate button. Here is how the Time since Periapsis in Hyperbolic Orbit given Mean Anomaly calculation can be explained with given input values -> 2042.397 = 65700000000^3/([GM.Earth]^2*(1.339^2-1)^(3/2))*0.807912910748023.

### FAQ

What is Time since Periapsis in Hyperbolic Orbit given Mean Anomaly?
The Time Since Periapsis in Hyperbolic Orbit given Mean Anomaly formula is an angular parameter that describes the position of an object in its orbit relative to the focus of the hyperbola and a reference line, usually measured from periapsis (the closest point to the central body) to the current position of the object and is represented as t = hh^3/([GM.Earth]^2*(eh^2-1)^(3/2))*Mh or 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. 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 & 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.
How to calculate Time since Periapsis in Hyperbolic Orbit given Mean Anomaly?
The Time Since Periapsis in Hyperbolic Orbit given Mean Anomaly formula is an angular parameter that describes the position of an object in its orbit relative to the focus of the hyperbola and a reference line, usually measured from periapsis (the closest point to the central body) to the current position of the object is calculated using 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. To calculate Time since Periapsis in Hyperbolic Orbit given Mean Anomaly, you need Angular Momentum of Hyperbolic Orbit (hh), Eccentricity of Hyperbolic Orbit (eh) & Mean Anomaly in Hyperbolic Orbit (Mh). With our tool, you need to enter the respective value for Angular Momentum of Hyperbolic Orbit, Eccentricity of Hyperbolic Orbit & Mean 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 & Mean 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))*(Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit)
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