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True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum Formula

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True Anomaly in Elliptical 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 e = a \cos (\frac{\frac{{h e}^{2}}{[GM.Earth] \cdot r e} - 1}{e e})

θ_e - True Anomaly in Elliptical Orbit?h_e - Angular Momentum of Elliptic Orbit?r_e - Radial Position in Elliptical Orbit?e_e - Eccentricity of Elliptical Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum Example

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Here is how the True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum equation looks like with Units.

Here is how the True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum equation looks like.

135.1122 = a \cos (\frac{\frac{65750^{2}}{4E+14 \cdot 18865} - 1}{0.6})

135.1122° = a \cos (\frac{\frac{{65750km²/s}^{2}}{4E+14m³/s² \cdot 18865km} - 1}{0.6})

135.1122 = a \cos (\frac{\frac{65750^{2}}{4E+14 \cdot 18865} - 1}{0.6})

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True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum Solution

Follow our step by step solution on how to calculate True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ e = a \cos (\frac{\frac{{65750km²/s}^{2}}{[GM.Earth] \cdot 18865km} - 1}{0.6})

Next Step Substitute values of Constants

∴

θ e = a \cos (\frac{\frac{{65750km²/s}^{2}}{4E+14m³/s² \cdot 18865km} - 1}{0.6})

Next Step Convert Units

∴

θ e = a \cos (\frac{\frac{{6.6E+10m²/s}^{2}}{4E+14m³/s² \cdot 1.9E+7m} - 1}{0.6})

Next Step Prepare to Evaluate

∴

θ e = a \cos (\frac{\frac{{6.6E+10}^{2}}{4E+14 \cdot 1.9E+7} - 1}{0.6})

Next Step Evaluate

∴

θ e = 2.35815230055879rad

Next Step Convert to Output's Unit

∴

θ e = 135.11217427111°

LAST Step Rounding Answer

∴

θ e = 135.1122°

True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum Formula Elements

Variables

Constants

Functions

True Anomaly in Elliptical Orbit

True Anomaly in Elliptical 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_e

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find True Anomaly in Elliptical Orbit

Angular Momentum of Elliptic Orbit

Angular Momentum of Elliptic 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_e

Measurement: Specific Angular MomentumUnit: km²/s

Note: Value should be greater than 0.

Formulas to find Angular Momentum of Elliptic Orbit

Radial Position in Elliptical Orbit

Radial Position in Elliptical 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_e

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Radial Position in Elliptical Orbit

Eccentricity of Elliptical Orbit

Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.

Symbol: e_e

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Eccentricity of Elliptical 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 Elliptical Orbit Parameters category

Go Eccentricity of Elliptical Orbit given Apogee and Perigee

e e = \frac{r e,apogee - r e,perigee}{r e,apogee + r e,perigee}

Go Angular Momentum in Elliptic Orbit Given Apogee Radius and Apogee Velocity

h e = r e,apogee \cdot v apogee

Go Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity

r e,apogee = \frac{{h e}^{2}}{[GM.Earth] \cdot (1 - e e)}

Go Semimajor Axis of Elliptic Orbit given Apogee and Perigee Radii

a e = \frac{r e,apogee + r e,perigee}{2}

How to Evaluate True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum?

True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum evaluator uses True Anomaly in Elliptical Orbit = acos((Angular Momentum of Elliptic Orbit^2/([GM.Earth]*Radial Position in Elliptical Orbit)-1)/Eccentricity of Elliptical Orbit) to evaluate the True Anomaly in Elliptical Orbit, True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum formula is defined as the angle between the position vector of an object in an elliptical orbit and its closest approach to the central body, providing a critical parameter for understanding orbital motion. True Anomaly in Elliptical Orbit is denoted by θ_e symbol.

How to evaluate True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum using this online evaluator? To use this online evaluator for True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum, enter Angular Momentum of Elliptic Orbit (h_e), Radial Position in Elliptical Orbit (r_e) & Eccentricity of Elliptical Orbit (e_e) and hit the calculate button.

FAQs on True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum

What is the formula to find True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum?

The formula of True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum is expressed as True Anomaly in Elliptical Orbit = acos((Angular Momentum of Elliptic Orbit^2/([GM.Earth]*Radial Position in Elliptical Orbit)-1)/Eccentricity of Elliptical Orbit). Here is an example- 7741.357 = acos((65750000000^2/([GM.Earth]*18865000)-1)/0.6).

How to calculate True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum?

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

Can the True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum be negative?

Yes, the True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum, measured in Angle can be negative.

Which unit is used to measure True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum?

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

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