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Escape Velocity given Radius of Parabolic Trajectory Formula

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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. Check FAQs

v p,esc = \sqrt{\frac{2 \cdot [GM.Earth]}{r p}}

v_p,esc - Escape Velocity in Parabolic Orbit?r_p - Radial Position in Parabolic Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

Escape Velocity given Radius of Parabolic Trajectory Example

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Here is how the Escape Velocity given Radius of Parabolic Trajectory equation looks like with Values.

Here is how the Escape Velocity given Radius of Parabolic Trajectory equation looks like with Units.

Here is how the Escape Velocity given Radius of Parabolic Trajectory equation looks like.

5.827 = \sqrt{\frac{2 \cdot 4E+14}{23479}}

5.827km/s = \sqrt{\frac{2 \cdot 4E+14m³/s²}{23479km}}

5.827 = \sqrt{\frac{2 \cdot 4E+14}{23479}}

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Escape Velocity given Radius of Parabolic Trajectory Solution

Follow our step by step solution on how to calculate Escape Velocity given Radius of Parabolic Trajectory?

FIRST Step Consider the formula

v p,esc = \sqrt{\frac{2 \cdot [GM.Earth]}{r p}}

Next Step Substitute values of Variables

∴

v p,esc = \sqrt{\frac{2 \cdot [GM.Earth]}{23479km}}

Next Step Substitute values of Constants

∴

v p,esc = \sqrt{\frac{2 \cdot 4E+14m³/s²}{23479km}}

Next Step Convert Units

∴

v p,esc = \sqrt{\frac{2 \cdot 4E+14m³/s²}{2.3E+7m}}

Next Step Prepare to Evaluate

∴

v p,esc = \sqrt{\frac{2 \cdot 4E+14}{2.3E+7}}

Next Step Evaluate

∴

v p,esc = 5826.98751793944m/s

Next Step Convert to Output's Unit

∴

v p,esc = 5.82698751793944km/s

LAST Step Rounding Answer

∴

v p,esc = 5.827km/s

Escape Velocity given Radius of Parabolic Trajectory Formula Elements

Variables

Constants

Functions

Escape Velocity in Parabolic Orbit

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.

Symbol: v_p,esc

Measurement: SpeedUnit: km/s

Note: Value should be greater than 0.

Formulas to find Escape Velocity in Parabolic Orbit

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.

Symbol: r_p

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Radial Position in Parabolic Orbit

Earth’s Geocentric Gravitational Constant

Earth’s Geocentric Gravitational Constant the gravitational parameter for the Earth as the central body.

Symbol: [GM.Earth]

Value: 3.986004418E+14 m³/s²

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.

Syntax: sqrt(Number)

Other formulas in Parabolic Orbit Parameters category

Go Radial Position in Parabolic Orbit given Escape Velocity

r p = \frac{2 \cdot [GM.Earth]}{{v p,esc}^{2}}

Go X Coordinate of Parabolic Trajectory given Parameter of Orbit

x = p p \cdot (\frac{\cos (θ p)}{1 + \cos (θ p)})

Go Y Coordinate of Parabolic Trajectory given Parameter of Orbit

y = p p \cdot \frac{\sin (θ p)}{1 + \cos (θ p)}

Go Parameter of Orbit given X Coordinate of Parabolic Trajectory

p p = x \cdot \frac{1 + \cos (θ p)}{\cos (θ p)}

How to Evaluate Escape Velocity given Radius of Parabolic Trajectory?

Escape Velocity given Radius of Parabolic Trajectory evaluator uses Escape Velocity in Parabolic Orbit = sqrt((2*[GM.Earth])/Radial Position in Parabolic Orbit) to evaluate 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 evaluate Escape Velocity given Radius of Parabolic Trajectory using this online evaluator? To use this online evaluator for Escape Velocity given Radius of Parabolic Trajectory, enter Radial Position in Parabolic Orbit (r_p) and hit the calculate button.

FAQs on Escape Velocity given Radius of Parabolic Trajectory

What is the formula to find Escape Velocity given Radius of Parabolic Trajectory?

The formula of Escape Velocity given Radius of Parabolic Trajectory is expressed as Escape Velocity in Parabolic Orbit = sqrt((2*[GM.Earth])/Radial Position in Parabolic Orbit). Here is an example- 0.005827 = sqrt((2*[GM.Earth])/23479000).

How to calculate Escape Velocity given Radius of Parabolic Trajectory?

With Radial Position in Parabolic Orbit (r_p) we can find Escape Velocity given Radius of Parabolic Trajectory using the formula - Escape Velocity in Parabolic Orbit = sqrt((2*[GM.Earth])/Radial Position in Parabolic Orbit). This formula also uses Earth’s Geocentric Gravitational Constant and Square Root (sqrt) function(s).

Can the Escape Velocity given Radius of Parabolic Trajectory be negative?

No, the Escape Velocity given Radius of Parabolic Trajectory, measured in Speed cannot be negative.

Which unit is used to measure Escape Velocity given Radius of Parabolic Trajectory?

Escape Velocity given Radius of Parabolic Trajectory is usually measured using the Kilometer per Second[km/s] for Speed. Meter per Second[km/s], Meter per Minute[km/s], Meter per Hour[km/s] are the few other units in which Escape Velocity given Radius of Parabolic Trajectory can be measured.

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