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True Anomaly in Parabolic Orbit given Mean Anomaly Formula

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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. Check FAQs

θ p = 2 \cdot a \tan ({(3 \cdot M p + \sqrt{{(3 \cdot M p)}^{2} + 1})}^{\frac{1}{3}} - {(3 \cdot M p + \sqrt{{(3 \cdot M p)}^{2} + 1})}^{- \frac{1}{3}})

θ_p - True Anomaly in Parabolic Orbit?M_p - Mean Anomaly in Parabolic Orbit?

True Anomaly in Parabolic Orbit given Mean Anomaly Example

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Here is how the True Anomaly in Parabolic Orbit given Mean Anomaly equation looks like with Values.

Here is how the True Anomaly in Parabolic Orbit given Mean Anomaly equation looks like with Units.

Here is how the True Anomaly in Parabolic Orbit given Mean Anomaly equation looks like.

115.0331 = 2 \cdot a \tan ({(3 \cdot 82 + \sqrt{{(3 \cdot 82)}^{2} + 1})}^{\frac{1}{3}} - {(3 \cdot 82 + \sqrt{{(3 \cdot 82)}^{2} + 1})}^{- \frac{1}{3}})

115.0331° = 2 \cdot a \tan ({(3 \cdot 82° + \sqrt{{(3 \cdot 82°)}^{2} + 1})}^{\frac{1}{3}} - {(3 \cdot 82° + \sqrt{{(3 \cdot 82°)}^{2} + 1})}^{- \frac{1}{3}})

115.0331 = 2 \cdot a \tan ({(3 \cdot 82 + \sqrt{{(3 \cdot 82)}^{2} + 1})}^{\frac{1}{3}} - {(3 \cdot 82 + \sqrt{{(3 \cdot 82)}^{2} + 1})}^{- \frac{1}{3}})

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True Anomaly in Parabolic Orbit given Mean Anomaly Solution

Follow our step by step solution on how to calculate True Anomaly in Parabolic Orbit given Mean Anomaly?

FIRST Step Consider the formula

θ p = 2 \cdot a \tan ({(3 \cdot M p + \sqrt{{(3 \cdot M p)}^{2} + 1})}^{\frac{1}{3}} - {(3 \cdot M p + \sqrt{{(3 \cdot M p)}^{2} + 1})}^{- \frac{1}{3}})

Next Step Substitute values of Variables

∴

θ p = 2 \cdot a \tan ({(3 \cdot 82° + \sqrt{{(3 \cdot 82°)}^{2} + 1})}^{\frac{1}{3}} - {(3 \cdot 82° + \sqrt{{(3 \cdot 82°)}^{2} + 1})}^{- \frac{1}{3}})

Next Step Convert Units

∴

θ p = 2 \cdot a \tan ({(3 \cdot 1.4312rad + \sqrt{{(3 \cdot 1.4312rad)}^{2} + 1})}^{\frac{1}{3}} - {(3 \cdot 1.4312rad + \sqrt{{(3 \cdot 1.4312rad)}^{2} + 1})}^{- \frac{1}{3}})

Next Step Prepare to Evaluate

∴

θ p = 2 \cdot a \tan ({(3 \cdot 1.4312 + \sqrt{{(3 \cdot 1.4312)}^{2} + 1})}^{\frac{1}{3}} - {(3 \cdot 1.4312 + \sqrt{{(3 \cdot 1.4312)}^{2} + 1})}^{- \frac{1}{3}})

Next Step Evaluate

∴

θ p = 2.00770566777364rad

Next Step Convert to Output's Unit

∴

θ p = 115.033061267946°

LAST Step Rounding Answer

∴

θ p = 115.0331°

True Anomaly in Parabolic Orbit given Mean Anomaly Formula Elements

Variables

Functions

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

Mean Anomaly in Parabolic Orbit

Mean Anomaly in Parabolic Orbit is the fraction of orbit's period that has elapsed since the orbiting body passed periapsis.

Symbol: M_p

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Mean Anomaly in Parabolic Orbit

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Orbital Position as Function of Time category

Go Mean Anomaly in Parabolic Orbit given True Anomaly

M p = \frac{\tan (\frac{θ p}{2})}{2} + \frac{{\tan (\frac{θ p}{2})}^{3}}{6}

Go Time since Periapsis in Parabolic Orbit given Mean Anomaly

t p = \frac{{h p}^{3} \cdot M p}{{[GM.Earth]}^{2}}

Go Mean Anomaly in Parabolic Orbit given Time since Periapsis

M p = \frac{{[GM.Earth]}^{2} \cdot t p}{{h p}^{3}}

How to Evaluate True Anomaly in Parabolic Orbit given Mean Anomaly?

True Anomaly in Parabolic Orbit given Mean Anomaly evaluator uses True Anomaly in Parabolic Orbit = 2*atan((3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(1/3)-(3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(-1/3)) to evaluate the True Anomaly in Parabolic Orbit, The True Anomaly in Parabolic Orbit given Mean Anomaly formula is a parameter used to describe the position of an object in its orbit relative to a reference direction, typically measured from the periapsis ( the point of closest approach to the central body) to the current position of the object along the orbit, given the mean anomaly in a parabolic orbit, the true anomaly can be calculated using specific equations derived from orbital mechanics principles. True Anomaly in Parabolic Orbit is denoted by θ_p symbol.

How to evaluate True Anomaly in Parabolic Orbit given Mean Anomaly using this online evaluator? To use this online evaluator for True Anomaly in Parabolic Orbit given Mean Anomaly, enter Mean Anomaly in Parabolic Orbit (M_p) and hit the calculate button.

FAQs on True Anomaly in Parabolic Orbit given Mean Anomaly

What is the formula to find True Anomaly in Parabolic Orbit given Mean Anomaly?

The formula of True Anomaly in Parabolic Orbit given Mean Anomaly is expressed as True Anomaly in Parabolic Orbit = 2*atan((3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(1/3)-(3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(-1/3)). Here is an example- 6571.667 = 2*atan((3*1.43116998663508+sqrt((3*1.43116998663508)^2+1))^(1/3)-(3*1.43116998663508+sqrt((3*1.43116998663508)^2+1))^(-1/3)).

How to calculate True Anomaly in Parabolic Orbit given Mean Anomaly?

With Mean Anomaly in Parabolic Orbit (M_p) we can find True Anomaly in Parabolic Orbit given Mean Anomaly using the formula - True Anomaly in Parabolic Orbit = 2*atan((3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(1/3)-(3*Mean Anomaly in Parabolic Orbit+sqrt((3*Mean Anomaly in Parabolic Orbit)^2+1))^(-1/3)). This formula also uses Tangent (tan)Inverse Tan (atan), Square Root (sqrt) function(s).

Can the True Anomaly in Parabolic Orbit given Mean Anomaly be negative?

Yes, the True Anomaly in Parabolic Orbit given Mean Anomaly, measured in Angle can be negative.

Which unit is used to measure True Anomaly in Parabolic Orbit given Mean Anomaly?

True Anomaly in Parabolic Orbit given Mean Anomaly is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which True Anomaly in Parabolic Orbit given Mean Anomaly can be measured.

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