True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum 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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Parabolic Orbit Parameters

Orbital Position as Function of Time

✖Angular Momentum of Parabolic 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.ⓘ Angular Momentum of Parabolic Orbit [h_p]			+10% -10%
✖Radial Position in Parabolic Orbit refers to the distance of the satellite along the radial or straight-line direction connecting the satellite and the center of the body.ⓘ Radial Position in Parabolic Orbit [r_p]			+10% -10%

✖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 Radial Position and Angular Momentum [θ_p]

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Formula

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True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum

Formula

`"θ"_{"p"} = acos("h"_{"p"}^2/("[GM.Earth]"*"r"_{"p"})-1)`

Example

`"115.0009°"=acos(("73508km²/s")^2/("[GM.Earth]"*"23479km")-1)`

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True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum Solution

STEP 0: Pre-Calculation Summary

Formula Used

True Anomaly in Parabolic Orbit = acos(Angular Momentum of Parabolic Orbit^2/([GM.Earth]*Radial Position in Parabolic Orbit)-1)
θ_p = acos(h_p^2/([GM.Earth]*r_p)-1)
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(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.
Angular Momentum of Parabolic Orbit - (Measured in Squaer Meter per Second) - Angular Momentum of Parabolic 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.
Radial Position in Parabolic Orbit - (Measured in Meter) - Radial Position in Parabolic Orbit refers to the distance of the satellite along the radial or straight-line direction connecting the satellite and the center of the body.

STEP 1: Convert Input(s) to Base Unit

Angular Momentum of Parabolic Orbit: 73508 Square Kilometer per Second --> 73508000000 Squaer Meter per Second (Check conversion here)
Radial Position in Parabolic Orbit: 23479 Kilometer --> 23479000 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_p = acos(h_p^2/([GM.Earth]*r_p)-1) --> acos(73508000000^2/([GM.Earth]*23479000)-1)

Evaluating ... ...

θ_p = 2.00714507179796

STEP 3: Convert Result to Output's Unit

2.00714507179796 Radian -->115.000941484527 Degree (Check conversion here)

FINAL ANSWER

115.000941484527 ≈ 115.0009 Degree <-- True Anomaly in Parabolic Orbit

(Calculation completed in 00.020 seconds)

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Home » Physics » Orbital Mechanics » The Two Body Problem » Parabolic Orbits » Parabolic Orbit Parameters » True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum

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Created by Harsh Raj

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

Harsh Raj has created this Calculator and 50+ more calculators!

Verified by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

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< 10+ Parabolic Orbit Parameters Calculators

X Coordinate of Parabolic Trajectory given Parameter of Orbit

Go X Coordinate Value = Parameter of Parabolic Orbit*(cos(True Anomaly in Parabolic Orbit)/(1+cos(True Anomaly in Parabolic Orbit)))

Y Coordinate of Parabolic Trajectory given Parameter of Orbit

Go Y Coordinate Value = Parameter of Parabolic Orbit*sin(True Anomaly in Parabolic Orbit)/(1+cos(True Anomaly in Parabolic Orbit))

Parameter of Orbit given X Coordinate of Parabolic Trajectory

Go Parameter of Parabolic Orbit = X Coordinate Value*(1+cos(True Anomaly in Parabolic Orbit))/cos(True Anomaly in Parabolic Orbit)

Parameter of Orbit given Y Coordinate of Parabolic Trajectory

Go Parameter of Parabolic Orbit = Y Coordinate Value*(1+cos(True Anomaly in Parabolic Orbit))/sin(True Anomaly in Parabolic Orbit)

Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly

Go Radial Position in Parabolic Orbit = Angular Momentum of Parabolic Orbit^2/([GM.Earth]*(1+cos(True Anomaly in Parabolic Orbit)))

True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum

Go True Anomaly in Parabolic Orbit = acos(Angular Momentum of Parabolic Orbit^2/([GM.Earth]*Radial Position in Parabolic Orbit)-1)

Escape Velocity given Radius of Parabolic Trajectory

Go Escape Velocity in Parabolic Orbit = sqrt((2*[GM.Earth])/Radial Position in Parabolic Orbit)

Angular Momentum given Perigee Radius of Parabolic Orbit

Go Angular Momentum of Parabolic Orbit = sqrt(2*[GM.Earth]*Perigee Radius in Parabolic Orbit)

Radial Position in Parabolic Orbit given Escape Velocity

Go Radial Position in Parabolic Orbit = (2*[GM.Earth])/Escape Velocity in Parabolic Orbit^2

Perigee Radius of Parabolic Orbit given Angular Momentum

Go Perigee Radius in Parabolic Orbit = Angular Momentum of Parabolic Orbit^2/(2*[GM.Earth])

True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum Formula

True Anomaly in Parabolic Orbit = acos(Angular Momentum of Parabolic Orbit^2/([GM.Earth]*Radial Position in Parabolic Orbit)-1)
θ_p = acos(h_p^2/([GM.Earth]*r_p)-1)

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 Radial Position and Angular Momentum?

True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum calculator uses True Anomaly in Parabolic Orbit = acos(Angular Momentum of Parabolic Orbit^2/([GM.Earth]*Radial Position in Parabolic Orbit)-1) to calculate the True Anomaly in Parabolic Orbit, The True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum formula is defined as current angular position of the object within its parabolic orbit. This formula allows for the calculation of the true anomaly based on two essential parameters: radial position and angular momentum. True Anomaly in Parabolic Orbit is denoted by θ_p symbol.

How to calculate True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum using this online calculator? To use this online calculator for True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum, enter Angular Momentum of Parabolic Orbit (h_p) & Radial Position in Parabolic Orbit (r_p) and hit the calculate button. Here is how the True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum calculation can be explained with given input values -> 4333.819 = acos(73508000000^2/([GM.Earth]*23479000)-1).

FAQ

What is True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum?

The True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum formula is defined as current angular position of the object within its parabolic orbit. This formula allows for the calculation of the true anomaly based on two essential parameters: radial position and angular momentum and is represented as θ_p = acos(h_p^2/([GM.Earth]*r_p)-1) or True Anomaly in Parabolic Orbit = acos(Angular Momentum of Parabolic Orbit^2/([GM.Earth]*Radial Position in Parabolic Orbit)-1). Angular Momentum of Parabolic 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 & Radial Position in Parabolic Orbit refers to the distance of the satellite along the radial or straight-line direction connecting the satellite and the center of the body.

How to calculate True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum?

The True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum formula is defined as current angular position of the object within its parabolic orbit. This formula allows for the calculation of the true anomaly based on two essential parameters: radial position and angular momentum is calculated using True Anomaly in Parabolic Orbit = acos(Angular Momentum of Parabolic Orbit^2/([GM.Earth]*Radial Position in Parabolic Orbit)-1). To calculate True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum, you need Angular Momentum of Parabolic Orbit (h_p) & Radial Position in Parabolic Orbit (r_p). With our tool, you need to enter the respective value for Angular Momentum of Parabolic Orbit & Radial Position 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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