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

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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. Check FAQs

θ p = a \cos (\frac{{h p}^{2}}{[GM.Earth] \cdot r p} - 1)

θ_p - True Anomaly in Parabolic Orbit?h_p - Angular Momentum of Parabolic Orbit?r_p - Radial Position in Parabolic Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

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

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Here is how the True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum equation looks like with Values.

Here is how the True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum equation looks like with Units.

Here is how the True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum equation looks like.

115.0009 = a \cos (\frac{73508^{2}}{4E+14 \cdot 23479} - 1)

115.0009° = a \cos (\frac{{73508km²/s}^{2}}{4E+14m³/s² \cdot 23479km} - 1)

115.0009 = a \cos (\frac{73508^{2}}{4E+14 \cdot 23479} - 1)

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

Follow our step by step solution on how to calculate True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum?

FIRST Step Consider the formula

θ p = a \cos (\frac{{h p}^{2}}{[GM.Earth] \cdot r p} - 1)

Next Step Substitute values of Variables

∴

θ p = a \cos (\frac{{73508km²/s}^{2}}{[GM.Earth] \cdot 23479km} - 1)

Next Step Substitute values of Constants

∴

θ p = a \cos (\frac{{73508km²/s}^{2}}{4E+14m³/s² \cdot 23479km} - 1)

Next Step Convert Units

∴

θ p = a \cos (\frac{{7.4E+10m²/s}^{2}}{4E+14m³/s² \cdot 2.3E+7m} - 1)

Next Step Prepare to Evaluate

∴

θ p = a \cos (\frac{{7.4E+10}^{2}}{4E+14 \cdot 2.3E+7} - 1)

Next Step Evaluate

∴

θ p = 2.00714507179796rad

Next Step Convert to Output's Unit

∴

θ p = 115.000941484527°

LAST Step Rounding Answer

∴

θ p = 115.0009°

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

Variables

Constants

Functions

True Anomaly in Parabolic Orbit

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.

Symbol: θ_p

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find True Anomaly in Parabolic Orbit

Angular Momentum of 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.

Symbol: h_p

Measurement: Specific Angular MomentumUnit: km²/s

Note: Value should be greater than 0.

Formulas to find Angular Momentum of 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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: acos(Number)

Other formulas in Parabolic Orbit Parameters category

Go Escape Velocity given Radius of Parabolic Trajectory

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

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)}

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

True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum evaluator uses True Anomaly in Parabolic Orbit = acos(Angular Momentum of Parabolic Orbit^2/([GM.Earth]*Radial Position in Parabolic Orbit)-1) to evaluate 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 evaluate True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum using this online evaluator? To use this online evaluator 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.

FAQs on True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum

What is the formula to find True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum?

The formula of True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum is expressed as True Anomaly in Parabolic Orbit = acos(Angular Momentum of Parabolic Orbit^2/([GM.Earth]*Radial Position in Parabolic Orbit)-1). Here is an example- 4333.819 = acos(73508000000^2/([GM.Earth]*23479000)-1).

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

With Angular Momentum of Parabolic Orbit (h_p) & Radial Position in Parabolic Orbit (r_p) we can find True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum using the formula - True Anomaly in Parabolic Orbit = acos(Angular Momentum of Parabolic Orbit^2/([GM.Earth]*Radial Position in Parabolic Orbit)-1). This formula also uses Earth’s Geocentric Gravitational Constant and , Cosine (cos), Inverse Cosine (acos) function(s).

Can the True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum be negative?

Yes, the True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum, measured in Angle can be negative.

Which unit is used to measure True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum?

True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum can be measured.

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