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Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity Formula

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Radial Position in Hyperbolic Orbit refers to the distance of the satellite along the radial or straight-line direction connecting the satellite and the center of the body. Check FAQs

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

r_h - Radial Position in Hyperbolic Orbit?h_h - Angular Momentum of Hyperbolic Orbit?e_h - Eccentricity of Hyperbolic Orbit?θ - True Anomaly?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity Example

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

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

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

19198.3717 = \frac{65700^{2}}{4E+14 \cdot (1 + 1.339 \cdot \cos (109))}

19198.3717km = \frac{{65700km²/s}^{2}}{4E+14m³/s² \cdot (1 + 1.339 \cdot \cos (109°))}

19198.3717 = \frac{65700^{2}}{4E+14 \cdot (1 + 1.339 \cdot \cos (109))}

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Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r h = \frac{{65700km²/s}^{2}}{[GM.Earth] \cdot (1 + 1.339 \cdot \cos (109°))}

Next Step Substitute values of Constants

∴

r h = \frac{{65700km²/s}^{2}}{4E+14m³/s² \cdot (1 + 1.339 \cdot \cos (109°))}

Next Step Convert Units

∴

r h = \frac{{6.6E+10m²/s}^{2}}{4E+14m³/s² \cdot (1 + 1.339 \cdot \cos (1.9024rad))}

Next Step Prepare to Evaluate

∴

r h = \frac{{6.6E+10}^{2}}{4E+14 \cdot (1 + 1.339 \cdot \cos (1.9024))}

Next Step Evaluate

∴

r h = 19198371.6585885m

Next Step Convert to Output's Unit

∴

r h = 19198.3716585885km

LAST Step Rounding Answer

∴

r h = 19198.3717km

Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity Formula Elements

Variables

Constants

Functions

Radial Position in Hyperbolic Orbit

Radial Position in Hyperbolic 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_h

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Radial Position in Hyperbolic Orbit

Angular Momentum of Hyperbolic Orbit

Angular Momentum of Hyperbolic 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_h

Measurement: Specific Angular MomentumUnit: km²/s

Note: Value should be greater than 0.

Formulas to find Angular Momentum of Hyperbolic Orbit

Eccentricity of Hyperbolic Orbit

Eccentricity of Hyperbolic Orbit describes how much the orbit differs from a perfect circle, and this value typically falls between 1 and infinity.

Symbol: e_h

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Eccentricity of Hyperbolic Orbit

True Anomaly

True Anomaly 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

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find True Anomaly

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)

Other formulas in Hperbolic Orbit Parameters category

Go Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity

r perigee = \frac{{h h}^{2}}{[GM.Earth] \cdot (1 + e h)}

Go Turn Angle given Eccentricity

δ = 2 \cdot a \sin (\frac{1}{e h})

Go Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity

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

Go Aiming Radius in Hyperbolic Orbit given Semi-Major Axis and Eccentricity

Δ = a h \cdot \sqrt{{e h}^{2} - 1}

How to Evaluate Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity?

Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity evaluator uses Radial Position in Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit*cos(True Anomaly))) to evaluate the Radial Position in Hyperbolic Orbit, Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity formula is defined as a method to determine the distance of an object in a hyperbolic trajectory from the central body, considering its angular momentum, true anomaly, and eccentricity. Radial Position in Hyperbolic Orbit is denoted by r_h symbol.

How to evaluate Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity using this online evaluator? To use this online evaluator for Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity, enter Angular Momentum of Hyperbolic Orbit (h_h), Eccentricity of Hyperbolic Orbit (e_h) & True Anomaly (θ) and hit the calculate button.

FAQs on Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity

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

The formula of Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity is expressed as Radial Position in Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit*cos(True Anomaly))). Here is an example- 19.19837 = 65700000000^2/([GM.Earth]*(1+1.339*cos(1.90240888467346))).

How to calculate Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity?

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

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

No, the Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity, measured in Length cannot be negative.

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

Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity is usually measured using the Kilometer[km] for Length. Meter[km], Millimeter[km], Decimeter[km] are the few other units in which Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity can be measured.

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