Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, 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%
✖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.ⓘ True Anomaly [θ]			+10% -10%

✖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.ⓘ Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity [r_h]

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Formula

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

Formula

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

Example

`"19198.37km"=("65700km²/s")^2/("[GM.Earth]"*(1+"1.339"*cos("109°")))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Radial Position in Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit*cos(True Anomaly)))
r_h = h_h^2/([GM.Earth]*(1+e_h*cos(θ)))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

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

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Radial Position in Hyperbolic Orbit - (Measured in Meter) - 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.
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.
True Anomaly - (Measured in Radian) - 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.

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
True Anomaly: 109 Degree --> 1.90240888467346 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_h = h_h^2/([GM.Earth]*(1+e_h*cos(θ))) --> 65700000000^2/([GM.Earth]*(1+1.339*cos(1.90240888467346)))

Evaluating ... ...

r_h = 19198371.6585885

STEP 3: Convert Result to Output's Unit

19198371.6585885 Meter -->19198.3716585885 Kilometer (Check conversion here)

FINAL ANSWER

19198.3716585885 ≈ 19198.37 Kilometer <-- Radial Position in Hyperbolic Orbit

(Calculation completed in 00.004 seconds)

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Home » Physics » Orbital Mechanics » The Two Body Problem » Hyperbolic Orbits » Hperbolic Orbit Parameters » Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity

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Created by Harsh Raj

Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

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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)

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

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

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

Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity calculator uses Radial Position in Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit*cos(True Anomaly))) to calculate the Radial Position in Hyperbolic Orbit, The Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity formula is defined as distance from the center of the central body to the current location of the object within the hyperbolic orbit. This formula allows for the calculation of the radial position based on three essential parameters: angular momentum, true anomaly, and eccentricity. Radial Position in Hyperbolic Orbit is denoted by r_h symbol.

How to calculate Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity using this online calculator? To use this online calculator 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. Here is how the Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity calculation can be explained with given input values -> 19.19837 = 65700000000^2/([GM.Earth]*(1+1.339*cos(1.90240888467346))).

FAQ

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

The Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity formula is defined as distance from the center of the central body to the current location of the object within the hyperbolic orbit. This formula allows for the calculation of the radial position based on three essential parameters: angular momentum, true anomaly, and eccentricity and is represented as r_h = h_h^2/([GM.Earth]*(1+e_h*cos(θ))) or Radial Position in Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit*cos(True Anomaly))). 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 & 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.

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

The Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity formula is defined as distance from the center of the central body to the current location of the object within the hyperbolic orbit. This formula allows for the calculation of the radial position based on three essential parameters: angular momentum, true anomaly, and eccentricity is calculated using Radial Position in Hyperbolic Orbit = Angular Momentum of Hyperbolic Orbit^2/([GM.Earth]*(1+Eccentricity of Hyperbolic Orbit*cos(True Anomaly))). To calculate Radial Position in Hyperbolic Orbit given Angular Momentum, True Anomaly, and Eccentricity, you need Angular Momentum of Hyperbolic Orbit (h_h), Eccentricity of Hyperbolic Orbit (e_h) & True Anomaly (θ). With our tool, you need to enter the respective value for Angular Momentum of Hyperbolic Orbit, Eccentricity of Hyperbolic Orbit & True Anomaly 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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