FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly Formula

GoRadial Position in Parabolic Orbit given Escape Velocity Formula

Fx Copy

LaTeX Copy

Radial Position in Parabolic Orbit refers to the distance of the satellite along the radial or straight-line direction connecting the satellite and the center of the body. Check FAQs

r p = \frac{{h p}^{2}}{[GM.Earth] \cdot (1 + \cos (θ p))}

r_p - Radial Position in Parabolic Orbit?h_p - Angular Momentum of Parabolic Orbit?θ_p - True Anomaly in Parabolic Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly Example

With values

With units

Only example

Here is how the Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly equation looks like with Values.

Here is how the Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly equation looks like with Units.

Here is how the Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly equation looks like.

23478.3944 = \frac{73508^{2}}{4E+14 \cdot (1 + \cos (115))}

23478.3944km = \frac{{73508km²/s}^{2}}{4E+14m³/s² \cdot (1 + \cos (115°))}

23478.3944 = \frac{73508^{2}}{4E+14 \cdot (1 + \cos (115))}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Aerospace » Category

Orbital Mechanics » fx Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly

Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly Solution

Follow our step by step solution on how to calculate Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly?

FIRST Step Consider the formula

r p = \frac{{h p}^{2}}{[GM.Earth] \cdot (1 + \cos (θ p))}

Next Step Substitute values of Variables

∴

r p = \frac{{73508km²/s}^{2}}{[GM.Earth] \cdot (1 + \cos (115°))}

Next Step Substitute values of Constants

∴

r p = \frac{{73508km²/s}^{2}}{4E+14m³/s² \cdot (1 + \cos (115°))}

Next Step Convert Units

∴

r p = \frac{{7.4E+10m²/s}^{2}}{4E+14m³/s² \cdot (1 + \cos (2.0071rad))}

Next Step Prepare to Evaluate

∴

r p = \frac{{7.4E+10}^{2}}{4E+14 \cdot (1 + \cos (2.0071))}

Next Step Evaluate

∴

r p = 23478394.4065707m

Next Step Convert to Output's Unit

∴

r p = 23478.3944065706km

LAST Step Rounding Answer

∴

r p = 23478.3944km

Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly Formula Elements

Variables

Constants

Functions

Radial Position in Parabolic Orbit

Radial Position in Parabolic Orbit refers to the distance of the satellite along the radial or straight-line direction connecting the satellite and the center of the body.

Symbol: r_p

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Radial Position in Parabolic Orbit

Angular Momentum of Parabolic Orbit

Angular Momentum of Parabolic 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.

Symbol: h_p

Measurement: Specific Angular MomentumUnit: km²/s

Note: Value should be greater than 0.

Formulas to find Angular Momentum of Parabolic Orbit

True Anomaly in Parabolic Orbit

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.

Symbol: θ_p

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find True Anomaly in Parabolic Orbit

Earth’s Geocentric Gravitational Constant

Earth’s Geocentric Gravitational Constant the gravitational parameter for the Earth as the central body.

Symbol: [GM.Earth]

Value: 3.986004418E+14 m³/s²

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Radial Position in Parabolic Orbit

Go Radial Position in Parabolic Orbit given Escape Velocity

r p = \frac{2 \cdot [GM.Earth]}{{v p,esc}^{2}}

Other formulas in Parabolic Orbit Parameters category

Go Escape Velocity given Radius of Parabolic Trajectory

v p,esc = \sqrt{\frac{2 \cdot [GM.Earth]}{r p}}

Go X Coordinate of Parabolic Trajectory given Parameter of Orbit

x = p p \cdot (\frac{\cos (θ p)}{1 + \cos (θ p)})

Go Y Coordinate of Parabolic Trajectory given Parameter of Orbit

y = p p \cdot \frac{\sin (θ p)}{1 + \cos (θ p)}

Go Parameter of Orbit given X Coordinate of Parabolic Trajectory

p p = x \cdot \frac{1 + \cos (θ p)}{\cos (θ p)}

How to Evaluate Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly?

Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly evaluator uses Radial Position in Parabolic Orbit = Angular Momentum of Parabolic Orbit^2/([GM.Earth]*(1+cos(True Anomaly in Parabolic Orbit))) to evaluate the Radial Position in Parabolic Orbit, The Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly formula is defined as distance from the center of the central body to the current location of the object within the parabolic orbit, this formula allows for the calculation of the radial position based on two essential parameters: angular momentum and true anomaly. Radial Position in Parabolic Orbit is denoted by r_p symbol.

How to evaluate Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly using this online evaluator? To use this online evaluator for Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly, enter Angular Momentum of Parabolic Orbit (h_p) & True Anomaly in Parabolic Orbit (θ_p) and hit the calculate button.

FAQs on Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly

What is the formula to find Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly?

The formula of Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly is expressed as Radial Position in Parabolic Orbit = Angular Momentum of Parabolic Orbit^2/([GM.Earth]*(1+cos(True Anomaly in Parabolic Orbit))). Here is an example- 23.47839 = 73508000000^2/([GM.Earth]*(1+cos(2.0071286397931))).

How to calculate Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly?

With Angular Momentum of Parabolic Orbit (h_p) & True Anomaly in Parabolic Orbit (θ_p) we can find Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly using the formula - Radial Position in Parabolic Orbit = Angular Momentum of Parabolic Orbit^2/([GM.Earth]*(1+cos(True Anomaly in Parabolic Orbit))). This formula also uses Earth’s Geocentric Gravitational Constant and Cosine (cos) function(s).

What are the other ways to Calculate Radial Position in Parabolic Orbit?

Here are the different ways to Calculate Radial Position in Parabolic Orbit-

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

Can the Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly be negative?

No, the Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly, measured in Length cannot be negative.

Which unit is used to measure Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly?

Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly is usually measured using the Kilometer[km] for Length. Meter[km], Millimeter[km], Decimeter[km] are the few other units in which Radial Position in Parabolic Orbit given Angular Momentum and True Anomaly can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!