True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum Calculator

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The Two Body Problem

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Elliptical Orbit Parameters

Orbital Position as Function of Time

✖Angular Momentum of Elliptic 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 Elliptic Orbit [h_e]			+10% -10%
✖Radial Position in Elliptical 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 Elliptical Orbit [r_e]			+10% -10%
✖Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.ⓘ Eccentricity of Elliptical Orbit [e_e]			+10% -10%

✖True Anomaly in Elliptical Orbit 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 in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum [θ_e]

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True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum

Formula

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

Example

`"135.1122°"=acos((("65750km²/s")^2/("[GM.Earth]"*"18865km")-1)/"0.6")`

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True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum Solution

STEP 0: Pre-Calculation Summary

Formula Used

True Anomaly in Elliptical Orbit = acos((Angular Momentum of Elliptic Orbit^2/([GM.Earth]*Radial Position in Elliptical Orbit)-1)/Eccentricity of Elliptical Orbit)
θ_e = acos((h_e^2/([GM.Earth]*r_e)-1)/e_e)
This formula uses 1 Constants, 2 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)
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 in Elliptical Orbit - (Measured in Radian) - True Anomaly in Elliptical Orbit 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.
Angular Momentum of Elliptic Orbit - (Measured in Squaer Meter per Second) - Angular Momentum of Elliptic 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.
Radial Position in Elliptical Orbit - (Measured in Meter) - Radial Position in Elliptical Orbit refers to the distance of the satellite along the radial or straight-line direction connecting the satellite and the center of the body.
Eccentricity of Elliptical Orbit - Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.

STEP 1: Convert Input(s) to Base Unit

Angular Momentum of Elliptic Orbit: 65750 Square Kilometer per Second --> 65750000000 Squaer Meter per Second (Check conversion here)
Radial Position in Elliptical Orbit: 18865 Kilometer --> 18865000 Meter (Check conversion here)
Eccentricity of Elliptical Orbit: 0.6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_e = acos((h_e^2/([GM.Earth]*r_e)-1)/e_e) --> acos((65750000000^2/([GM.Earth]*18865000)-1)/0.6)

Evaluating ... ...

θ_e = 2.35815230055879

STEP 3: Convert Result to Output's Unit

2.35815230055879 Radian -->135.11217427111 Degree (Check conversion here)

FINAL ANSWER

135.11217427111 ≈ 135.1122 Degree <-- True Anomaly in Elliptical Orbit

(Calculation completed in 00.004 seconds)

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Home » Physics » Orbital Mechanics » The Two Body Problem » Elliptical Orbits » Elliptical Orbit Parameters » True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum

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

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< 17 Elliptical Orbit Parameters Calculators

True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum

Go True Anomaly in Elliptical Orbit = acos((Angular Momentum of Elliptic Orbit^2/([GM.Earth]*Radial Position in Elliptical Orbit)-1)/Eccentricity of Elliptical Orbit)

Time Period of Elliptical Orbit given Semi-Major Axis

Go Time Period of Elliptic Orbit = 2*pi*Semi Major Axis of Elliptic Orbit^2*sqrt(1-Eccentricity of Elliptical Orbit^2)/Angular Momentum of Elliptic Orbit

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum

Go Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit

Eccentricity of Elliptical Orbit given Apogee and Perigee

Go Eccentricity of Elliptical Orbit = (Apogee Radius in Elliptic Orbit-Perigee Radius in Elliptic Orbit)/(Apogee Radius in Elliptic Orbit+Perigee Radius in Elliptic Orbit)

Time Period for One Complete Revolution given Angular Momentum

Go Time Period of Elliptic Orbit = (2*pi*Semi Major Axis of Elliptic Orbit*Semi Minor Axis of Elliptic Orbit)/Angular Momentum of Elliptic Orbit

Elliptical Orbit Time Period given Angular Momentum and Eccentricity

Go Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3

Time Period of Elliptical Orbit given Angular Momentum

Go Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3

Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity

Go Apogee Radius in Elliptic Orbit = Angular Momentum of Elliptic Orbit^2/([GM.Earth]*(1-Eccentricity of Elliptical Orbit))

Specific Energy of Elliptic Orbit given Angular Momentum

Go Specific Energy of Elliptical Orbit = -1/2*[GM.Earth]^2/Angular Momentum of Elliptic Orbit^2*(1-Eccentricity of Elliptical Orbit^2)

Azimuth-Averaged Radius Given Apogee and Perigee Radii

Go Azimuth Averaged Radius = sqrt(Apogee Radius in Elliptic Orbit*Perigee Radius in Elliptic Orbit)

Semimajor Axis of Elliptic Orbit given Apogee and Perigee Radii

Go Semi Major Axis of Elliptic Orbit = (Apogee Radius in Elliptic Orbit+Perigee Radius in Elliptic Orbit)/2

Angular Momentum in Elliptic Orbit Given Perigee Radius and Perigee Velocity

Go Angular Momentum of Elliptic Orbit = Perigee Radius in Elliptic Orbit*Velocity of Satellite at Perigee

Radial Velocity in Elliptic Orbit given Radial Position and Angular Momentum

Go Radial Velocity of Satellite = Angular Momentum of Elliptic Orbit/Radial Position in Elliptical Orbit

Angular Momentum in Elliptic Orbit Given Apogee Radius and Apogee Velocity

Go Angular Momentum of Elliptic Orbit = Apogee Radius in Elliptic Orbit*Velocity of Satellite at Apogee

Apogee Velocity in Elliptic Orbit Given Angular Momentum and Apogee Radius

Go Velocity of Satellite at Apogee = Angular Momentum of Elliptic Orbit/Apogee Radius in Elliptic Orbit

Eccentricity of Orbit

Go Eccentricity of Elliptical Orbit = Distance Between Two Foci/(2*Semi Major Axis of Elliptic Orbit)

Specific Energy of Elliptic Orbit given Semi Major Axis

Go Specific Energy of Elliptical Orbit = -[GM.Earth]/(2*Semi Major Axis of Elliptic Orbit)

True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum Formula

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 in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum?

True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum calculator uses True Anomaly in Elliptical Orbit = acos((Angular Momentum of Elliptic Orbit^2/([GM.Earth]*Radial Position in Elliptical Orbit)-1)/Eccentricity of Elliptical Orbit) to calculate the True Anomaly in Elliptical Orbit, The True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum formula is defined as current angular position of the object within its elliptic orbit. This formula allows for the calculation of the true anomaly based on three essential parameters: radial position, eccentricity, and angular momentum. True Anomaly in Elliptical Orbit is denoted by θ_e symbol.

How to calculate True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum using this online calculator? To use this online calculator for True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum, enter Angular Momentum of Elliptic Orbit (h_e), Radial Position in Elliptical Orbit (r_e) & Eccentricity of Elliptical Orbit (e_e) and hit the calculate button. Here is how the True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum calculation can be explained with given input values -> 7741.357 = acos((65750000000^2/([GM.Earth]*18865000)-1)/0.6).

FAQ

What is True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum?

The True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum formula is defined as current angular position of the object within its elliptic orbit. This formula allows for the calculation of the true anomaly based on three essential parameters: radial position, eccentricity, and angular momentum and is represented as θ_e = acos((h_e^2/([GM.Earth]*r_e)-1)/e_e) or True Anomaly in Elliptical Orbit = acos((Angular Momentum of Elliptic Orbit^2/([GM.Earth]*Radial Position in Elliptical Orbit)-1)/Eccentricity of Elliptical Orbit). Angular Momentum of Elliptic 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, Radial Position in Elliptical Orbit refers to the distance of the satellite along the radial or straight-line direction connecting the satellite and the center of the body & Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.

How to calculate True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum?

The True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum formula is defined as current angular position of the object within its elliptic orbit. This formula allows for the calculation of the true anomaly based on three essential parameters: radial position, eccentricity, and angular momentum is calculated using True Anomaly in Elliptical Orbit = acos((Angular Momentum of Elliptic Orbit^2/([GM.Earth]*Radial Position in Elliptical Orbit)-1)/Eccentricity of Elliptical Orbit). To calculate True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum, you need Angular Momentum of Elliptic Orbit (h_e), Radial Position in Elliptical Orbit (r_e) & Eccentricity of Elliptical Orbit (e_e). With our tool, you need to enter the respective value for Angular Momentum of Elliptic Orbit, Radial Position in Elliptical Orbit & Eccentricity of Elliptical 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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