Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity Calculator

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The Two Body Problem

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Hyperbolic Orbits

Circular Orbits

Elliptical Orbits

Fundamental Parameters

Parabolic Orbits

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Hperbolic Orbit Parameters

Orbital Position as Function of Time

✖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.ⓘ Angular Momentum of Hyperbolic Orbit [h_h]			+10% -10%
✖Eccentricity of Hyperbolic Orbit describes how much the orbit differs from a perfect circle, and this value typically falls between 1 and infinity.ⓘ Eccentricity of Hyperbolic Orbit [e_h]			+10% -10%

✖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.ⓘ Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity [r_perigee]

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Formula

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Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity

Formula

`"r"_{"perigee"} = "h"_{"h"}^2/("[GM.Earth]"*(1+"e"_{"h"}))`

Example

`"4629.805km"=("65700km²/s")^2/("[GM.Earth]"*(1+"1.339"))`

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Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Perigee Radius = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit))
r_perigee = h_h^2/([GM.Earth]*(1+e_h))
This formula uses 1 Constants, 3 Variables

Constants Used

[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14

Variables Used

Perigee Radius - (Measured in Meter) - 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.
Angular Momentum of Hyperbolic Orbit - (Measured in Squaer Meter per Second) - 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.
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.

STEP 1: Convert Input(s) to Base Unit

Angular Momentum of Hyperbolic Orbit: 65700 Square Kilometer per Second --> 65700000000 Squaer Meter per Second (Check conversion here)
Eccentricity of Hyperbolic Orbit: 1.339 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_perigee = h_h^2/([GM.Earth]*(1+e_h)) --> 65700000000^2/([GM.Earth]*(1+1.339))

Evaluating ... ...

r_perigee = 4629805.44742964

STEP 3: Convert Result to Output's Unit

4629805.44742964 Meter -->4629.80544742964 Kilometer (Check conversion here)

FINAL ANSWER

4629.80544742964 ≈ 4629.805 Kilometer <-- Perigee Radius

(Calculation completed in 00.004 seconds)

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< 6 Hperbolic Orbit Parameters Calculators

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

Go Radial Position in Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit*cos(True Anomaly)))

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

Go Semi Major Axis of Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(Eccentricity of Hyperbolic Orbit^2-1))

Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity

Go Perigee Radius = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit))

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

Go Aiming Radius = Semi Major Axis of Hyperbolic Orbit*sqrt(Eccentricity of Hyperbolic Orbit^2-1)

True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity

Go True Anomaly of Asymptote in Hyperbolic Orbit = acos(-1/Eccentricity of Hyperbolic Orbit)

Turn Angle given Eccentricity

Go Turn Angle = 2*asin(1/Eccentricity of Hyperbolic Orbit)

Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity Formula

Perigee Radius = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit))
r_perigee = h_h^2/([GM.Earth]*(1+e_h))

Kepler's Laws and Gravitational Attraction

Johannes Kepler's laws of planetary motion, developed in the 17th century, provided significant insights into the relationship between celestial bodies and gravity. Kepler's laws describe the elliptical orbits of planets and other objects in the solar system, all of which are governed by the gravitational pull of the central body, such as the Sun. These laws laid the foundation for understanding how gravity affects the motion of objects in space, paving the way for Sir Isaac Newton's formulation of the law of universal gravitation.

How to Calculate Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity?

Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity calculator uses Perigee Radius = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit)) to calculate 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 calculate Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity using this online calculator? To use this online calculator 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. Here is how the Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity calculation can be explained with given input values -> 4.636855 = 65700000000^2/([GM.Earth]*(1+1.339)).

FAQ

What is Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity?

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 and is represented as r_perigee = h_h^2/([GM.Earth]*(1+e_h)) or Perigee Radius = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity 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 & Eccentricity of Hyperbolic Orbit describes how much the orbit differs from a perfect circle, and this value typically falls between 1 and infinity.

How to calculate Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity?

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 is calculated using Perigee Radius = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit)). To calculate Perigee Radius of Hyperbolic Orbit given Angular Momentum and Eccentricity, you need Angular Momentum of Hyperbolic Orbit (h_h) & Eccentricity of Hyperbolic Orbit (e_h). With our tool, you need to enter the respective value for Angular Momentum of Hyperbolic Orbit & Eccentricity of Hyperbolic Orbit and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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