Y Coordinate of Parabolic Trajectory given Parameter of Orbit Calculator

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The Two Body Problem

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Parabolic Orbits

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Fundamental Parameters

Hyperbolic Orbits

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Parabolic Orbit Parameters

Orbital Position as Function of Time

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

✖Y Coordinate Value is the distance of the object in vertical direction from the origin.ⓘ Y Coordinate of Parabolic Trajectory given Parameter of Orbit [y]

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Formula

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Y Coordinate of Parabolic Trajectory given Parameter of Orbit

Formula

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

Example

`"16952.6km"="10800km"*sin("115°")/(1+cos("115°"))`

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Y Coordinate of Parabolic Trajectory given Parameter of Orbit Solution

STEP 0: Pre-Calculation Summary

Formula Used

Y Coordinate Value = Parameter of Parabolic Orbit*sin(True Anomaly in Parabolic Orbit)/(1+cos(True Anomaly in Parabolic Orbit))
y = p_p*sin(θ_p)/(1+cos(θ_p))
This formula uses 2 Functions, 3 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
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

Y Coordinate Value - (Measured in Meter) - Y Coordinate Value is the distance of the object in vertical direction from the origin.
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.
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

Parameter of Parabolic Orbit: 10800 Kilometer --> 10800000 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

y = p_p*sin(θ_p)/(1+cos(θ_p)) --> 10800000*sin(2.0071286397931)/(1+cos(2.0071286397931))

Evaluating ... ...

y = 16952604.2328618

STEP 3: Convert Result to Output's Unit

16952604.2328618 Meter -->16952.6042328618 Kilometer (Check conversion here)

FINAL ANSWER

16952.6042328618 ≈ 16952.6 Kilometer <-- Y Coordinate Value

(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])

Y Coordinate of Parabolic Trajectory given Parameter of Orbit Formula

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

What causes a parabolic trajectory?

Projectiles travel with a parabolic trajectory due to the fact that the downward force of gravity accelerates them downward from their otherwise straight-line, gravity-free trajectory.

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

Y Coordinate of Parabolic Trajectory given Parameter of Orbit calculator uses Y Coordinate Value = Parameter of Parabolic Orbit*sin(True Anomaly in Parabolic Orbit)/(1+cos(True Anomaly in Parabolic Orbit)) to calculate the Y Coordinate Value, The Y Coordinate of Parabolic Trajectory given Parameter of Orbit formula is defined as the distance of the object in a vertical direction from the origin. Y Coordinate Value is denoted by y symbol.

How to calculate Y Coordinate of Parabolic Trajectory given Parameter of Orbit using this online calculator? To use this online calculator for Y Coordinate of Parabolic Trajectory given Parameter of Orbit, enter Parameter of Parabolic Orbit (p_p) & True Anomaly in Parabolic Orbit (θ_p) and hit the calculate button. Here is how the Y Coordinate of Parabolic Trajectory given Parameter of Orbit calculation can be explained with given input values -> 16.9526 = 10800000*sin(2.0071286397931)/(1+cos(2.0071286397931)).

FAQ

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

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

The Y Coordinate of Parabolic Trajectory given Parameter of Orbit formula is defined as the distance of the object in a vertical direction from the origin is calculated using Y Coordinate Value = Parameter of Parabolic Orbit*sin(True Anomaly in Parabolic Orbit)/(1+cos(True Anomaly in Parabolic Orbit)). To calculate Y Coordinate of Parabolic Trajectory given Parameter of Orbit, you need Parameter of Parabolic Orbit (p_p) & True Anomaly in Parabolic Orbit (θ_p). With our tool, you need to enter the respective value for Parameter of Parabolic Orbit & 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.

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