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Position Vector Formula

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Position vector is often used to represent the location of a satellite in space. The position vector provides information about the satellite's position relative to a reference point. Check FAQs

r pos = \frac{a major \cdot (1 - e^{2})}{1 + e \cdot \cos (v)}

r_pos - Position Vector?a_major - Major Axis?e - Eccentricity?v - True Anomaly?

Position Vector Example

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Here is how the Position Vector equation looks like with Values.

Here is how the Position Vector equation looks like with Units.

Here is how the Position Vector equation looks like.

9.6936 = \frac{10.75 \cdot (1 - {0.12}^{2})}{1 + 0.12 \cdot \cos (0.684)}

9.6936m = \frac{10.75m \cdot (1 - {0.12}^{2})}{1 + 0.12 \cdot \cos (0.684s)}

9.6936 = \frac{10.75 \cdot (1 - {0.12}^{2})}{1 + 0.12 \cdot \cos (0.684)}

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Position Vector Solution

Follow our step by step solution on how to calculate Position Vector?

FIRST Step Consider the formula

r pos = \frac{a major \cdot (1 - e^{2})}{1 + e \cdot \cos (v)}

Next Step Substitute values of Variables

∴

r pos = \frac{10.75m \cdot (1 - {0.12}^{2})}{1 + 0.12 \cdot \cos (0.684s)}

Next Step Prepare to Evaluate

∴

r pos = \frac{10.75 \cdot (1 - {0.12}^{2})}{1 + 0.12 \cdot \cos (0.684)}

Next Step Evaluate

∴

r pos = 9.69363246830535m

LAST Step Rounding Answer

∴

r pos = 9.6936m

Position Vector Formula Elements

Variables

Functions

Position Vector

Position vector is often used to represent the location of a satellite in space. The position vector provides information about the satellite's position relative to a reference point.

Symbol: r_pos

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Position Vector

Major Axis

The Major Axis refers to the longer dimension or principal axis of an elliptical coverage area or beam pattern.

Symbol: a_major

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Major Axis

Eccentricity

Eccentricity refers to a characteristic of the orbit followed by a satellite around its primary body, typically the Earth.

Symbol: e

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Eccentricity

True Anomaly

True Anomaly is an angular parameter that defines the position of a body moving along a keplerian orbit.

Symbol: v

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find True Anomaly

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 in Satellite Orbital Characteristics category

Go Anomalistic Period

T AP = \frac{2 \cdot π}{n}

Go Local Sidereal Time

LST = GST + E long

Go Mean Anomaly

M = E - e \cdot \sin (E)

Go Mean Motion of Satellite

n = \sqrt{\frac{[GM.Earth]}{{a semi}^{3}}}

How to Evaluate Position Vector?

Position Vector evaluator uses Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly)) to evaluate the Position Vector, The Position Vector formula specify the motion of the satellite in the orbital plane and only the magnitude of position vector is used for measurements. Position Vector is denoted by r_pos symbol.

How to evaluate Position Vector using this online evaluator? To use this online evaluator for Position Vector, enter Major Axis (a_major), Eccentricity (e) & True Anomaly (v) and hit the calculate button.

FAQs on Position Vector

What is the formula to find Position Vector?

The formula of Position Vector is expressed as Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly)). Here is an example- 11.96237 = (10.75*(1-0.12^2))/(1+0.12*cos(0.684)).

How to calculate Position Vector?

With Major Axis (a_major), Eccentricity (e) & True Anomaly (v) we can find Position Vector using the formula - Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly)). This formula also uses Cosine (cos) function(s).

Can the Position Vector be negative?

No, the Position Vector, measured in Length cannot be negative.

Which unit is used to measure Position Vector?

Position Vector is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Position Vector can be measured.

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Position Vector Formula

Position Vector Example

Position Vector Solution

Position Vector Formula Elements

Other formulas in Satellite Orbital Characteristics category

How to Evaluate Position Vector?

FAQs on Position Vector

Variable Name