Perigee Radius of Parabolic Orbit given Angular Momentum Calculator

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The Two Body Problem

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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]

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✖Perigee Radius in Parabolic Orbit refers to the distance between the center of the Earth and the point in a satellite's orbit that is closest to the Earth's surface.ⓘ Perigee Radius of Parabolic Orbit given Angular Momentum [r_p,perigee]

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Formula

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Perigee Radius of Parabolic Orbit given Angular Momentum

Formula

`"r"_{"p,perigee"} = "h"_{"p"}^2/(2*"[GM.Earth]")`

Example

`"6777.998km"=("73508km²/s")^2/(2*"[GM.Earth]")`

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Perigee Radius of Parabolic Orbit given Angular Momentum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Perigee Radius in Parabolic Orbit = Angular Momentum of Parabolic Orbit^2/(2*[GM.Earth])
r_p,perigee = h_p^2/(2*[GM.Earth])
This formula uses 1 Constants, 2 Variables

Constants Used

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

Variables Used

Perigee Radius in Parabolic Orbit - (Measured in Meter) - Perigee Radius in Parabolic Orbit refers to the distance between the center of the Earth and the point in a satellite's orbit that is closest to the Earth's surface.
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.

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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_p,perigee = h_p^2/(2*[GM.Earth]) --> 73508000000^2/(2*[GM.Earth])

Evaluating ... ...

r_p,perigee = 6777998.08700563

STEP 3: Convert Result to Output's Unit

6777998.08700563 Meter -->6777.99808700563 Kilometer (Check conversion here)

FINAL ANSWER

6777.99808700563 ≈ 6777.998 Kilometer <-- Perigee Radius 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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< 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])

Perigee Radius of Parabolic Orbit given Angular Momentum Formula

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

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 Perigee Radius of Parabolic Orbit given Angular Momentum?

Perigee Radius of Parabolic Orbit given Angular Momentum calculator uses Perigee Radius in Parabolic Orbit = Angular Momentum of Parabolic Orbit^2/(2*[GM.Earth]) to calculate the Perigee Radius in Parabolic Orbit, The Perigee Radius of Parabolic Orbit given Angular Momentum formula is defined as the distance from the center of the central body to the closest point of the parabolic orbit. This formula allows for the calculation of the perigee radius based on one critical parameter: angular momentum. Perigee Radius in Parabolic Orbit is denoted by r_p,perigee symbol.

How to calculate Perigee Radius of Parabolic Orbit given Angular Momentum using this online calculator? To use this online calculator for Perigee Radius of Parabolic Orbit given Angular Momentum, enter Angular Momentum of Parabolic Orbit (h_p) and hit the calculate button. Here is how the Perigee Radius of Parabolic Orbit given Angular Momentum calculation can be explained with given input values -> 1.12895 = 73508000000^2/(2*[GM.Earth]).

FAQ

What is Perigee Radius of Parabolic Orbit given Angular Momentum?

The Perigee Radius of Parabolic Orbit given Angular Momentum formula is defined as the distance from the center of the central body to the closest point of the parabolic orbit. This formula allows for the calculation of the perigee radius based on one critical parameter: angular momentum and is represented as r_p,perigee = h_p^2/(2*[GM.Earth]) or Perigee Radius in Parabolic Orbit = Angular Momentum of Parabolic Orbit^2/(2*[GM.Earth]). 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.

How to calculate Perigee Radius of Parabolic Orbit given Angular Momentum?

The Perigee Radius of Parabolic Orbit given Angular Momentum formula is defined as the distance from the center of the central body to the closest point of the parabolic orbit. This formula allows for the calculation of the perigee radius based on one critical parameter: angular momentum is calculated using Perigee Radius in Parabolic Orbit = Angular Momentum of Parabolic Orbit^2/(2*[GM.Earth]). To calculate Perigee Radius of Parabolic Orbit given Angular Momentum, you need Angular Momentum of Parabolic Orbit (h_p). With our tool, you need to enter the respective value for Angular Momentum of 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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