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

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Semi Major Axis of Hyperbolic Orbit is a fundamental parameter that characterizes the size and shape of the hyperbolic trajectory. It represents half the length of the major axis of the orbit. Check FAQs

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

a_h - Semi Major Axis of Hyperbolic Orbit?h_h - Angular Momentum of Hyperbolic Orbit?e_h - Eccentricity of Hyperbolic Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

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

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Here is how the Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity equation looks like with Values.

Here is how the Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity equation looks like with Units.

Here is how the Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity equation looks like.

13657.2432 = \frac{65700^{2}}{4E+14 \cdot ({1.339}^{2} - 1)}

13657.2432km = \frac{{65700km²/s}^{2}}{4E+14m³/s² \cdot ({1.339}^{2} - 1)}

13657.2432 = \frac{65700^{2}}{4E+14 \cdot ({1.339}^{2} - 1)}

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

Follow our step by step solution on how to calculate Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

a h = \frac{{65700km²/s}^{2}}{[GM.Earth] \cdot ({1.339}^{2} - 1)}

Next Step Substitute values of Constants

∴

a h = \frac{{65700km²/s}^{2}}{4E+14m³/s² \cdot ({1.339}^{2} - 1)}

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

a h = \frac{{6.6E+10}^{2}}{4E+14 \cdot ({1.339}^{2} - 1)}

Next Step Evaluate

∴

a h = 13657243.2077571m

Next Step Convert to Output's Unit

∴

a h = 13657.2432077571km

LAST Step Rounding Answer

∴

a h = 13657.2432km

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

Variables

Constants

Semi Major Axis of Hyperbolic Orbit

Semi Major Axis of Hyperbolic Orbit is a fundamental parameter that characterizes the size and shape of the hyperbolic trajectory. It represents half the length of the major axis of the orbit.

Symbol: a_h

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Semi Major Axis of 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

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

Other formulas in Hperbolic Orbit Parameters category

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

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

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

Δ = a h \cdot \sqrt{{e h}^{2} - 1}

How to Evaluate Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity?

Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity evaluator uses Semi Major Axis of Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(Eccentricity of Hyperbolic Orbit^2-1)) to evaluate the Semi Major Axis of Hyperbolic Orbit, The Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity formula is defined as a mathematical expression used to calculate the semi-major axis of an object in a hyperbolic orbit, the semi-major axis is a fundamental parameter that characterizes the size and shape of the hyperbolic orbit, this formula allows for the calculation of the semi-major axis based on two crucial parameters: angular momentum and eccentricity. Semi Major Axis of Hyperbolic Orbit is denoted by a_h symbol.

How to evaluate Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity using this online evaluator? To use this online evaluator for Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity, enter Angular Momentum of Hyperbolic Orbit (h_h) & Eccentricity of Hyperbolic Orbit (e_h) and hit the calculate button.

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

What is the formula to find Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity?

The formula of Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity is expressed as Semi Major Axis of Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(Eccentricity of Hyperbolic Orbit^2-1)). Here is an example- 13.65724 = 65700000000^2/([GM.Earth]*(1.339^2-1)).

How to calculate Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity?

With Angular Momentum of Hyperbolic Orbit (h_h) & Eccentricity of Hyperbolic Orbit (e_h) we can find Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity using the formula - Semi Major Axis of Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(Eccentricity of Hyperbolic Orbit^2-1)). This formula also uses Earth’s Geocentric Gravitational Constant .

Can the Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity be negative?

No, the Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity, measured in Length cannot be negative.

Which unit is used to measure Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity?

Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity is usually measured using the Kilometer[km] for Length. Meter[km], Millimeter[km], Decimeter[km] are the few other units in which Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity can be measured.

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