## True Anomaly in Parabolic Orbit given Mean Anomaly Solution

STEP 0: Pre-Calculation Summary
Formula Used
True Anomaly in Parabolic Orbit = 2*atan((3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(1/3)-(3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(-1/3))
θp = 2*atan((3*Mp+sqrt((3*Mp)^2+1))^(1/3)-(3*Mp+sqrt((3*Mp)^2+1))^(-1/3))
This formula uses 3 Functions, 2 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)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)
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)
Variables Used
True Anomaly in Parabolic Orbit - (Measured in Radian) - True Anomaly in Parabolic Orbit 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.
Mean Anomaly in Parabolic Orbit - (Measured in Radian) - Mean Anomaly in Parabolic Orbit is the fraction of orbit's period that has elapsed since the orbiting body passed periapsis.
STEP 1: Convert Input(s) to Base Unit
Mean Anomaly in Parabolic Orbit: 82 Degree --> 1.43116998663508 Radian (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
θp = 2*atan((3*Mp+sqrt((3*Mp)^2+1))^(1/3)-(3*Mp+sqrt((3*Mp)^2+1))^(-1/3)) --> 2*atan((3*1.43116998663508+sqrt((3*1.43116998663508)^2+1))^(1/3)-(3*1.43116998663508+sqrt((3*1.43116998663508)^2+1))^(-1/3))
Evaluating ... ...
θp = 2.00770566777364
STEP 3: Convert Result to Output's Unit
2.00770566777364 Radian -->115.033061267946 Degree (Check conversion ​here)
FINAL ANSWER
115.033061267946 115.0331 Degree <-- True Anomaly in Parabolic Orbit
(Calculation completed in 00.004 seconds)
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Created by Harsh Raj
Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal
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## <Orbital Position as Function of Time Calculators

True Anomaly in Parabolic Orbit given Mean Anomaly
​ Go True Anomaly in Parabolic Orbit = 2*atan((3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(1/3)-(3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(-1/3))
Mean Anomaly in Parabolic Orbit given True Anomaly
​ Go Mean Anomaly in Parabolic Orbit = tan(True Anomaly in Parabolic Orbit/2)/2+tan(True Anomaly in Parabolic Orbit/2)^3/6
Time since Periapsis in Parabolic Orbit given Mean Anomaly
​ Go Time since Periapsis in Parabolic Orbit = (Angular Momentum of Parabolic Orbit^3*Mean Anomaly in Parabolic Orbit)/[GM.Earth]^2
Mean Anomaly in Parabolic Orbit given Time since Periapsis
​ Go Mean Anomaly in Parabolic Orbit = ([GM.Earth]^2*Time since Periapsis in Parabolic Orbit)/Angular Momentum of Parabolic Orbit^3

## True Anomaly in Parabolic Orbit given Mean Anomaly Formula

True Anomaly in Parabolic Orbit = 2*atan((3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(1/3)-(3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(-1/3))
θp = 2*atan((3*Mp+sqrt((3*Mp)^2+1))^(1/3)-(3*Mp+sqrt((3*Mp)^2+1))^(-1/3))

## What is parabolic path ?

A parabolic path, also known as a parabolic trajectory, is the path followed by an object under the influence of gravity when it is projected into the air with an initial velocity and then allowed to move freely under the force of gravity.

## How to Calculate True Anomaly in Parabolic Orbit given Mean Anomaly?

True Anomaly in Parabolic Orbit given Mean Anomaly calculator uses True Anomaly in Parabolic Orbit = 2*atan((3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(1/3)-(3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(-1/3)) to calculate the True Anomaly in Parabolic Orbit, The True Anomaly in Parabolic Orbit given Mean Anomaly formula is a parameter used to describe the position of an object in its orbit relative to a reference direction, typically measured from the periapsis ( the point of closest approach to the central body) to the current position of the object along the orbit, given the mean anomaly in a parabolic orbit, the true anomaly can be calculated using specific equations derived from orbital mechanics principles. True Anomaly in Parabolic Orbit is denoted by θp symbol.

How to calculate True Anomaly in Parabolic Orbit given Mean Anomaly using this online calculator? To use this online calculator for True Anomaly in Parabolic Orbit given Mean Anomaly, enter Mean Anomaly in Parabolic Orbit (Mp) and hit the calculate button. Here is how the True Anomaly in Parabolic Orbit given Mean Anomaly calculation can be explained with given input values -> 6571.667 = 2*atan((3*1.43116998663508+sqrt((3*1.43116998663508)^2+1))^(1/3)-(3*1.43116998663508+sqrt((3*1.43116998663508)^2+1))^(-1/3)).

### FAQ

What is True Anomaly in Parabolic Orbit given Mean Anomaly?
The True Anomaly in Parabolic Orbit given Mean Anomaly formula is a parameter used to describe the position of an object in its orbit relative to a reference direction, typically measured from the periapsis ( the point of closest approach to the central body) to the current position of the object along the orbit, given the mean anomaly in a parabolic orbit, the true anomaly can be calculated using specific equations derived from orbital mechanics principles and is represented as θp = 2*atan((3*Mp+sqrt((3*Mp)^2+1))^(1/3)-(3*Mp+sqrt((3*Mp)^2+1))^(-1/3)) or True Anomaly in Parabolic Orbit = 2*atan((3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(1/3)-(3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(-1/3)). Mean Anomaly in Parabolic Orbit is the fraction of orbit's period that has elapsed since the orbiting body passed periapsis.
How to calculate True Anomaly in Parabolic Orbit given Mean Anomaly?
The True Anomaly in Parabolic Orbit given Mean Anomaly formula is a parameter used to describe the position of an object in its orbit relative to a reference direction, typically measured from the periapsis ( the point of closest approach to the central body) to the current position of the object along the orbit, given the mean anomaly in a parabolic orbit, the true anomaly can be calculated using specific equations derived from orbital mechanics principles is calculated using True Anomaly in Parabolic Orbit = 2*atan((3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(1/3)-(3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(-1/3)). To calculate True Anomaly in Parabolic Orbit given Mean Anomaly, you need Mean Anomaly in Parabolic Orbit (Mp). With our tool, you need to enter the respective value for Mean Anomaly in Parabolic 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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