Parameter of Orbit given X Coordinate of Parabolic Trajectory Calculator

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The Two Body Problem

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Parabolic Orbits

Circular Orbits

Elliptical Orbits

Fundamental Parameters

Hyperbolic Orbits

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Parabolic Orbit Parameters

Orbital Position as Function of Time

✖X Coordinate Value is the distance of the object in horizontal direction from the origin.ⓘ X Coordinate Value [x]			+10% -10%
✖True Anomaly in Parabolic 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 Parabolic Orbit [θ_p]			+10% -10%

✖Parameter of Parabolic Orbit is defined as the half of chord length through the center of attraction perpendicular to the apse line.ⓘ Parameter of Orbit given X Coordinate of Parabolic Trajectory [p_p]

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Formula

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Parameter of Orbit given X Coordinate of Parabolic Trajectory

Formula

`"p"_{"p"} = "x"*(1+cos("θ"_{"p"}))/cos("θ"_{"p"})`

Example

`"10801.19km"="-7906km"*(1+cos("115°"))/cos("115°")`

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Parameter of Orbit given X Coordinate of Parabolic Trajectory Solution

STEP 0: Pre-Calculation Summary

Formula Used

Parameter of Parabolic Orbit = X Coordinate Value*(1+cos(True Anomaly in Parabolic Orbit))/cos(True Anomaly in Parabolic Orbit)
p_p = x*(1+cos(θ_p))/cos(θ_p)
This formula uses 1 Functions, 3 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)

Variables Used

Parameter of Parabolic Orbit - (Measured in Meter) - Parameter of Parabolic Orbit is defined as the half of chord length through the center of attraction perpendicular to the apse line.
X Coordinate Value - (Measured in Meter) - X Coordinate Value is the distance of the object in horizontal direction from the origin.
True Anomaly in Parabolic Orbit - (Measured in Radian) - True Anomaly in Parabolic 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.

STEP 1: Convert Input(s) to Base Unit

X Coordinate Value: -7906 Kilometer --> -7906000 Meter (Check conversion here)
True Anomaly in Parabolic Orbit: 115 Degree --> 2.0071286397931 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

p_p = x*(1+cos(θ_p))/cos(θ_p) --> (-7906000)*(1+cos(2.0071286397931))/cos(2.0071286397931)

Evaluating ... ...

p_p = 10801189.7164189

STEP 3: Convert Result to Output's Unit

10801189.7164189 Meter -->10801.1897164189 Kilometer (Check conversion here)

FINAL ANSWER

10801.1897164189 ≈ 10801.19 Kilometer <-- Parameter of Parabolic Orbit

(Calculation completed in 00.004 seconds)

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< 10+ Parabolic Orbit Parameters Calculators

X Coordinate of Parabolic Trajectory given Parameter of Orbit

Go X Coordinate Value = Parameter of Parabolic Orbit*(cos(True Anomaly in Parabolic Orbit)/(1+cos(True Anomaly in Parabolic Orbit)))

Y Coordinate of Parabolic Trajectory given Parameter of Orbit

Go Y Coordinate Value = Parameter of Parabolic Orbit*sin(True Anomaly in Parabolic Orbit)/(1+cos(True Anomaly in Parabolic Orbit))

Parameter of Orbit given X Coordinate of Parabolic Trajectory

Go Parameter of Parabolic Orbit = X Coordinate Value*(1+cos(True Anomaly in Parabolic Orbit))/cos(True Anomaly in Parabolic Orbit)

Parameter of Orbit given Y Coordinate of Parabolic Trajectory

Go Parameter of Parabolic Orbit = Y Coordinate Value*(1+cos(True Anomaly in Parabolic Orbit))/sin(True Anomaly in Parabolic Orbit)

Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly

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

True Anomaly in Parabolic Orbit given Radial Position and Angular Momentum

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

Escape Velocity given Radius of Parabolic Trajectory

Go Escape Velocity in Parabolic Orbit = sqrt((2*[GM.Earth])/Radial Position in Parabolic Orbit)

Angular Momentum given Perigee Radius of Parabolic Orbit

Go Angular Momentum of Parabolic Orbit = sqrt(2*[GM.Earth]*Perigee Radius in Parabolic Orbit)

Radial Position in Parabolic Orbit given Escape Velocity

Go Radial Position in Parabolic Orbit = (2*[GM.Earth])/Escape Velocity in Parabolic Orbit^2

Perigee Radius of Parabolic Orbit given Angular Momentum

Go Perigee Radius in Parabolic Orbit = Angular Momentum of Parabolic Orbit^2/(2*[GM.Earth])

Parameter of Orbit given X Coordinate of Parabolic Trajectory Formula

Parameter of Parabolic Orbit = X Coordinate Value*(1+cos(True Anomaly in Parabolic Orbit))/cos(True Anomaly in Parabolic Orbit)
p_p = x*(1+cos(θ_p))/cos(θ_p)

Why Parameter of Orbit is also known as Semi-latus rectum?

The latus rectum is the chord through the center of attraction perpendicular to the apse line. By symmetry, the center of attraction divides the latus rectum into two equal parts, each of length p, known historically as the semi-latus rectum. In modern parlance, p is called the parameter of the orbit.

How to Calculate Parameter of Orbit given X Coordinate of Parabolic Trajectory?

Parameter of Orbit given X Coordinate of Parabolic Trajectory calculator uses Parameter of Parabolic Orbit = X Coordinate Value*(1+cos(True Anomaly in Parabolic Orbit))/cos(True Anomaly in Parabolic Orbit) to calculate the Parameter of Parabolic Orbit, The Parameter of Orbit given X Coordinate of Parabolic Trajectory formula is defined as half of chord length through the center of attraction perpendicular to the apse line. Parameter of Parabolic Orbit is denoted by p_p symbol.

How to calculate Parameter of Orbit given X Coordinate of Parabolic Trajectory using this online calculator? To use this online calculator for Parameter of Orbit given X Coordinate of Parabolic Trajectory, enter X Coordinate Value (x) & True Anomaly in Parabolic Orbit (θ_p) and hit the calculate button. Here is how the Parameter of Orbit given X Coordinate of Parabolic Trajectory calculation can be explained with given input values -> 7.163528 = (-7906000)*(1+cos(2.0071286397931))/cos(2.0071286397931).

FAQ

What is Parameter of Orbit given X Coordinate of Parabolic Trajectory?

The Parameter of Orbit given X Coordinate of Parabolic Trajectory formula is defined as half of chord length through the center of attraction perpendicular to the apse line and is represented as p_p = x*(1+cos(θ_p))/cos(θ_p) or Parameter of Parabolic Orbit = X Coordinate Value*(1+cos(True Anomaly in Parabolic Orbit))/cos(True Anomaly in Parabolic Orbit). X Coordinate Value is the distance of the object in horizontal direction from the origin & True Anomaly in Parabolic 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.

How to calculate Parameter of Orbit given X Coordinate of Parabolic Trajectory?

The Parameter of Orbit given X Coordinate of Parabolic Trajectory formula is defined as half of chord length through the center of attraction perpendicular to the apse line is calculated using Parameter of Parabolic Orbit = X Coordinate Value*(1+cos(True Anomaly in Parabolic Orbit))/cos(True Anomaly in Parabolic Orbit). To calculate Parameter of Orbit given X Coordinate of Parabolic Trajectory, you need X Coordinate Value (x) & True Anomaly in Parabolic Orbit (θ_p). With our tool, you need to enter the respective value for X Coordinate Value & True Anomaly in Parabolic Orbit and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Parameter of Parabolic Orbit?

In this formula, Parameter of Parabolic Orbit uses X Coordinate Value & True Anomaly in Parabolic Orbit. We can use 1 other way(s) to calculate the same, which is/are as follows -

Parameter of Parabolic Orbit = Y Coordinate Value*(1+cos(True Anomaly in Parabolic Orbit))/sin(True Anomaly in Parabolic Orbit)

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