True Anomaly in Parabolic Orbit given Mean Anomaly Calculator

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The Two Body Problem

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Parabolic Orbits

Circular Orbits

Elliptical Orbits

Fundamental Parameters

Hyperbolic Orbits

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Orbital Position as Function of Time

Parabolic Orbit Parameters

✖Mean Anomaly in Parabolic Orbit is the fraction of orbit's period that has elapsed since the orbiting body passed periapsis.ⓘ Mean Anomaly in Parabolic Orbit [M_p]

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✖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.ⓘ True Anomaly in Parabolic Orbit given Mean Anomaly [θ_p]

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Formula

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True Anomaly in Parabolic Orbit given Mean Anomaly

Formula

`"θ"_{"p"} = 2*atan((3*"M"_{"p"}+sqrt((3*"M"_{"p"})^2+1))^(1/3)-(3*"M"_{"p"}+sqrt((3*"M"_{"p"})^2+1))^(-1/3))`

Example

`"115.0331°"=2*atan((3*"82°"+sqrt((3*"82°")^2+1))^(1/3)-(3*"82°"+sqrt((3*"82°")^2+1))^(-1/3))`

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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))
θ_p = 2*atan((3*M_p+sqrt((3*M_p)^2+1))^(1/3)-(3*M_p+sqrt((3*M_p)^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

θ_p = 2*atan((3*M_p+sqrt((3*M_p)^2+1))^(1/3)-(3*M_p+sqrt((3*M_p)^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 ... ...

θ_p = 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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Home » Physics » Orbital Mechanics » The Two Body Problem » Parabolic Orbits » Orbital Position as Function of Time » True Anomaly in Parabolic Orbit given Mean Anomaly

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Created by Harsh Raj

Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

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< 4 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

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 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 defined as the current angular position of the object within the parabolic orbit. True Anomaly in Parabolic Orbit is denoted by θ_p 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 (M_p) 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 defined as the current angular position of the object within the parabolic orbit and is represented as θ_p = 2*atan((3*M_p+sqrt((3*M_p)^2+1))^(1/3)-(3*M_p+sqrt((3*M_p)^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 defined as the current angular position of the object within the parabolic orbit 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 (M_p). 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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