Radial Position in Parabolic Orbit given Angular Momentum and True 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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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%
✖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 [θ_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 given Angular Momentum and True Anomaly [r_p]

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Formula

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Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly

Formula

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

Example

`"23478.39km"=("73508km²/s")^2/("[GM.Earth]"*(1+cos("115°")))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.

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)
True Anomaly in Parabolic Orbit: 115 Degree --> 2.0071286397931 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_p = h_p^2/([GM.Earth]*(1+cos(θ_p))) --> 73508000000^2/([GM.Earth]*(1+cos(2.0071286397931)))

Evaluating ... ...

r_p = 23478394.4065707

STEP 3: Convert Result to Output's Unit

23478394.4065707 Meter -->23478.3944065706 Kilometer (Check conversion here)

FINAL ANSWER

23478.3944065706 ≈ 23478.39 Kilometer <-- Radial Position 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 » Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly

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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!

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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])

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

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

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

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

How to calculate Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly using this online calculator? To use this online calculator for Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly, enter Angular Momentum of Parabolic Orbit (h_p) & True Anomaly in Parabolic Orbit (θ_p) and hit the calculate button. Here is how the Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly calculation can be explained with given input values -> 23.47839 = 73508000000^2/([GM.Earth]*(1+cos(2.0071286397931))).

FAQ

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

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

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

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

How many ways are there to calculate Radial Position in Parabolic Orbit?

In this formula, Radial Position in Parabolic Orbit uses Angular Momentum of Parabolic Orbit & True Anomaly in Parabolic Orbit. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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