Semi-Major Axis 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%

✖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.ⓘ Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity [a_h]

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Formula

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

Formula

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

Example

`"13657.24km"=("65700km²/s")^2/("[GM.Earth]"*(("1.339")^2-1))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Semi Major Axis of Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(Eccentricity of Hyperbolic Orbit^2-1))
a_h = h_h^2/([GM.Earth]*(e_h^2-1))
This formula uses 1 Constants, 3 Variables

Constants Used

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

Variables Used

Semi Major Axis of Hyperbolic Orbit - (Measured in Meter) - 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.
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

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

Evaluating ... ...

a_h = 13657243.2077571

STEP 3: Convert Result to Output's Unit

13657243.2077571 Meter -->13657.2432077571 Kilometer (Check conversion here)

FINAL ANSWER

13657.2432077571 ≈ 13657.24 Kilometer <-- Semi Major Axis of Hyperbolic Orbit

(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)

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

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

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

Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity calculator uses Semi Major Axis of Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(Eccentricity of Hyperbolic Orbit^2-1)) to calculate 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 calculate Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity using this online calculator? To use this online calculator 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. Here is how the Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity calculation can be explained with given input values -> 13.65724 = 65700000000^2/([GM.Earth]*(1.339^2-1)).

FAQ

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

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 and is represented as a_h = h_h^2/([GM.Earth]*(e_h^2-1)) or Semi Major Axis of Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(Eccentricity of Hyperbolic Orbit^2-1)). 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 Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity?

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 is calculated using Semi Major Axis of Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(Eccentricity of Hyperbolic Orbit^2-1)). To calculate Semi-Major Axis 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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