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Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity Formula

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Perigee Radius refers to the distance between the center of the Earth and the point in a satellite's orbit that is closest to the Earth's surface. Check FAQs

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

r_perigee - Perigee Radius?h_h - Angular Momentum of Hyperbolic Orbit?e_h - Eccentricity of Hyperbolic Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity Example

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Here is how the Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity equation looks like with Values.

Here is how the Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity equation looks like with Units.

Here is how the Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity equation looks like.

4629.8054 = \frac{65700^{2}}{4E+14 \cdot (1 + 1.339)}

4629.8054km = \frac{{65700km²/s}^{2}}{4E+14m³/s² \cdot (1 + 1.339)}

4629.8054 = \frac{65700^{2}}{4E+14 \cdot (1 + 1.339)}

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Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity Solution

Follow our step by step solution on how to calculate Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r perigee = 4629805.44742964m

Next Step Convert to Output's Unit

∴

r perigee = 4629.80544742964km

LAST Step Rounding Answer

∴

r perigee = 4629.8054km

Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity Formula Elements

Variables

Constants

Perigee Radius

Perigee Radius refers to the distance between the center of the Earth and the point in a satellite's orbit that is closest to the Earth's surface.

Symbol: r_perigee

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Perigee Radius

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 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 Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity?

Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity evaluator uses Perigee Radius = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit)) to evaluate the Perigee Radius, The Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity formula is defined as the distance from the center of the central body to the closest point of the hyperbolic orbit, this formula allows for the calculation of the perigee radius based on two critical parameters: angular momentum and eccentricity. Perigee Radius is denoted by r_perigee symbol.

How to evaluate Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity using this online evaluator? To use this online evaluator for Perigee Radius 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 Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity

What is the formula to find Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity?

The formula of Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity is expressed as Perigee Radius = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit)). Here is an example- 4.629805 = 65700000000^2/([GM.Earth]*(1+1.339)).

How to calculate Perigee Radius 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 Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity using the formula - Perigee Radius = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit)). This formula also uses Earth’s Geocentric Gravitational Constant .

Can the Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity be negative?

No, the Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity, measured in Length cannot be negative.

Which unit is used to measure Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity?

Perigee Radius 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 Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity can be measured.

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