True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity Calculator

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The Two Body Problem

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Hyperbolic Orbits

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Hperbolic Orbit Parameters

Orbital Position as Function of Time

✖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]

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✖The True Anomaly of Asymptote in Hyperbolic Orbit represents the angular measure of the position of an object within its hyperbolic trajectory relative to the asymptote.ⓘ True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity [θ_inf]

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Formula

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True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity

Formula

`"θ"_{"inf"} = acos(-1/"e"_{"h"})`

Example

`"138.3162°"=acos(-1/"1.339")`

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True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity Solution

STEP 0: Pre-Calculation Summary

Formula Used

True Anomaly of Asymptote in Hyperbolic Orbit = acos(-1/Eccentricity of Hyperbolic Orbit)
θ_inf = acos(-1/e_h)
This formula uses 2 Functions, 2 Variables

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)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

True Anomaly of Asymptote in Hyperbolic Orbit - (Measured in Radian) - The True Anomaly of Asymptote in Hyperbolic Orbit represents the angular measure of the position of an object within its hyperbolic trajectory relative to the asymptote.
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

Eccentricity of Hyperbolic Orbit: 1.339 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_inf = acos(-1/e_h) --> acos(-1/1.339)

Evaluating ... ...

θ_inf = 2.41407271939116

STEP 3: Convert Result to Output's Unit

2.41407271939116 Radian -->138.316178258809 Degree (Check conversion here)

FINAL ANSWER

138.316178258809 ≈ 138.3162 Degree <-- True Anomaly of Asymptote in Hyperbolic Orbit

(Calculation completed in 00.004 seconds)

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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)

True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity Formula

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

Why are parabolic trajectories also called escape trajectories?

If the body of some mass m is launched on a parabolic trajectory, it will coast to infinity, arriving there with zero velocity relative to central body. It will not return. Parabolic paths are therefore called escape trajectories.

How to Calculate True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity?

True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity calculator uses True Anomaly of Asymptote in Hyperbolic Orbit = acos(-1/Eccentricity of Hyperbolic Orbit) to calculate the True Anomaly of Asymptote in Hyperbolic Orbit, The True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity formula is defined as the angular position of satellite when it is on the asymptote of the orbit. True Anomaly of Asymptote in Hyperbolic Orbit is denoted by θ_inf symbol.

How to calculate True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity using this online calculator? To use this online calculator for True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity, enter Eccentricity of Hyperbolic Orbit (e_h) and hit the calculate button. Here is how the True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity calculation can be explained with given input values -> 7924.933 = acos(-1/1.339).

FAQ

What is True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity?

The True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity formula is defined as the angular position of satellite when it is on the asymptote of the orbit and is represented as θ_inf = acos(-1/e_h) or True Anomaly of Asymptote in Hyperbolic Orbit = acos(-1/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.

How to calculate True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity?

The True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity formula is defined as the angular position of satellite when it is on the asymptote of the orbit is calculated using True Anomaly of Asymptote in Hyperbolic Orbit = acos(-1/Eccentricity of Hyperbolic Orbit). To calculate True Anomaly of Asymptote in Hyperbolic Orbit given Eccentricity, you need Eccentricity of Hyperbolic Orbit (e_h). With our tool, you need to enter the respective value for 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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