Escape Velocity given Radius of Parabolic Trajectory Calculator

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The Two Body Problem

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Parabolic Orbits

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Fundamental Parameters

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Parabolic Orbit Parameters

Orbital Position as Function of Time

✖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]

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✖Escape Velocity in Parabolic Orbit defined as the velocity needed for a body to escape from a gravitational center of attraction without undergoing any further acceleration.ⓘ Escape Velocity given Radius of Parabolic Trajectory [v_p,esc]

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Formula

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Escape Velocity given Radius of Parabolic Trajectory

Formula

`"v"_{"p,esc"} = sqrt((2*"[GM.Earth]")/"r"_{"p"})`

Example

`"5.826988km/s"=sqrt((2*"[GM.Earth]")/"23479km")`

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Escape Velocity given Radius of Parabolic Trajectory Solution

STEP 0: Pre-Calculation Summary

Formula Used

Escape Velocity in Parabolic Orbit = sqrt((2*[GM.Earth])/Radial Position in Parabolic Orbit)
v_p,esc = sqrt((2*[GM.Earth])/r_p)
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

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

Functions Used

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

Escape Velocity in Parabolic Orbit - (Measured in Meter per Second) - Escape Velocity in Parabolic Orbit defined as the velocity needed for a body to escape from a gravitational center of attraction without undergoing any further acceleration.
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

Radial Position in Parabolic Orbit: 23479 Kilometer --> 23479000 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_p,esc = sqrt((2*[GM.Earth])/r_p) --> sqrt((2*[GM.Earth])/23479000)

Evaluating ... ...

v_p,esc = 5826.98751793944

STEP 3: Convert Result to Output's Unit

5826.98751793944 Meter per Second -->5.82698751793944 Kilometer per Second (Check conversion here)

FINAL ANSWER

5.82698751793944 ≈ 5.826988 Kilometer per Second <-- Escape Velocity in Parabolic Orbit

(Calculation completed in 00.004 seconds)

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Created by Karavadiya Divykumar Rasikbhai

Hindustan Institute of Technology and Science (HITS), Chennai, Indian

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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])

Escape Velocity given Radius of Parabolic Trajectory Formula

Escape Velocity in Parabolic Orbit = sqrt((2*[GM.Earth])/Radial Position in Parabolic Orbit)
v_p,esc = sqrt((2*[GM.Earth])/r_p)

What is Escape Velocity of a body at Earth?

On the surface of the Earth, the escape velocity is about 11.2 km/s, which is approximately 33 times the speed of sound (Mach 33) and several times the muzzle velocity of a rifle bullet (up to 1.7 km/s). However, at 9,000 km altitude in "space", it is slightly less than 7.1 km/s.

How to Calculate Escape Velocity given Radius of Parabolic Trajectory?

Escape Velocity given Radius of Parabolic Trajectory calculator uses Escape Velocity in Parabolic Orbit = sqrt((2*[GM.Earth])/Radial Position in Parabolic Orbit) to calculate the Escape Velocity in Parabolic Orbit, The Escape Velocity given Radius of Parabolic Trajectory formula is defined as the velocity needed for a body to escape from a gravitational centre of attraction without undergoing any further acceleration. Escape Velocity in Parabolic Orbit is denoted by v_p,esc symbol.

How to calculate Escape Velocity given Radius of Parabolic Trajectory using this online calculator? To use this online calculator for Escape Velocity given Radius of Parabolic Trajectory, enter Radial Position in Parabolic Orbit (r_p) and hit the calculate button. Here is how the Escape Velocity given Radius of Parabolic Trajectory calculation can be explained with given input values -> 0.005827 = sqrt((2*[GM.Earth])/23479000).

FAQ

What is Escape Velocity given Radius of Parabolic Trajectory?

The Escape Velocity given Radius of Parabolic Trajectory formula is defined as the velocity needed for a body to escape from a gravitational centre of attraction without undergoing any further acceleration and is represented as v_p,esc = sqrt((2*[GM.Earth])/r_p) or Escape Velocity in Parabolic Orbit = sqrt((2*[GM.Earth])/Radial Position in Parabolic Orbit). 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 Escape Velocity given Radius of Parabolic Trajectory?

The Escape Velocity given Radius of Parabolic Trajectory formula is defined as the velocity needed for a body to escape from a gravitational centre of attraction without undergoing any further acceleration is calculated using Escape Velocity in Parabolic Orbit = sqrt((2*[GM.Earth])/Radial Position in Parabolic Orbit). To calculate Escape Velocity given Radius of Parabolic Trajectory, you need Radial Position in Parabolic Orbit (r_p). With our tool, you need to enter the respective value for 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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