Position Vector Calculator

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Satellite Orbital Characteristics

Geostationary Orbit

Radio Wave Propagation

✖The Major Axis refers to the longer dimension or principal axis of an elliptical coverage area or beam pattern.ⓘ Major Axis [a_major]			+10% -10%
✖Eccentricity refers to a characteristic of the orbit followed by a satellite around its primary body, typically the Earth.ⓘ Eccentricity [e]			+10% -10%
✖True Anomaly is an angular parameter that defines the position of a body moving along a keplerian orbit.ⓘ True Anomaly [v]			+10% -10%

✖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.ⓘ Position Vector [r_pos]

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Formula

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Position Vector

Formula

`"r"_{"pos"} = ("a"_{"major"}*(1-"e"^2))/(1+"e"*cos("v"))`

Example

`"9.693632m"=("10.75m"*(1-("0.12")^2))/(1+"0.12"*cos("0.684s"))`

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Download Satellite Orbital Characteristics Formulas PDF

Position Vector Solution

STEP 0: Pre-Calculation Summary

Formula Used

Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly))
r_pos = (a_major*(1-e^2))/(1+e*cos(v))
This formula uses 1 Functions, 4 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

Position Vector - (Measured in Meter) - 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.
Major Axis - (Measured in Meter) - The Major Axis refers to the longer dimension or principal axis of an elliptical coverage area or beam pattern.
Eccentricity - Eccentricity refers to a characteristic of the orbit followed by a satellite around its primary body, typically the Earth.
True Anomaly - (Measured in Second) - True Anomaly is an angular parameter that defines the position of a body moving along a keplerian orbit.

STEP 1: Convert Input(s) to Base Unit

Major Axis: 10.75 Meter --> 10.75 Meter No Conversion Required
Eccentricity: 0.12 --> No Conversion Required
True Anomaly: 0.684 Second --> 0.684 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_pos = (a_major*(1-e^2))/(1+e*cos(v)) --> (10.75*(1-0.12^2))/(1+0.12*cos(0.684))

Evaluating ... ...

r_pos = 9.69363246830535

STEP 3: Convert Result to Output's Unit

9.69363246830535 Meter --> No Conversion Required

FINAL ANSWER

9.69363246830535 ≈ 9.693632 Meter <-- Position Vector

(Calculation completed in 00.004 seconds)

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Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

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< 16 Satellite Orbital Characteristics Calculators

Position Vector

Go Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly))

Kepler's First Law

Go Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis

Mean Anomaly

Go Mean Anomaly = Eccentric Anomaly-Eccentricity*sin(Eccentric Anomaly)

True Anomaly

Go True Anomaly = Mean Anomaly+(2*Eccentricity*sin(Mean Anomaly))

Universal Time

Go Universal Time = (1/24)*(Time in Hour+(Time in Minutes/60)+(Time in Seconds/3600))

Reference Time in Julian Centuries

Go Reference Time = (Julian Day-Julian Day Reference)/Julian Century

Julian Day

Go Julian Day = (Reference Time*Julian Century)+Julian Day Reference

Julian Century

Go Julian Century = (Julian Day-Julian Day Reference)/Reference Time

Nominal Mean Motion

Go Nominal Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3)

Mean Motion of Satellite

Go Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3)

Local Sidereal Time

Go Local Sidereal Time = Greenwich Sidereal Time+East Longitude

Kepler's Third Law

Go Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3)

Range Vector

Go Range Vector = Satellite Radius Vector-[Earth-R]

Orbital Period of Satellite in Minutes

Go Orbital Period in Minutes = 2*pi/Mean Motion

Anomalistic Period

Go Anomalistic Period = (2*pi)/Mean Motion

Universal Time Degree

Go Universal Time Degree = (Universal Time*360)

Position Vector Formula

Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly))
r_pos = (a_major*(1-e^2))/(1+e*cos(v))

What is position and direction vector?

Position vectors describe where an object is located in space, while direction vectors indicate the object's orientation or the direction in which it's moving. These vectors are foundational for understanding the motion and behavior of objects in satellite orbits and orbital mechanics.

How to Calculate Position Vector?

Position Vector calculator uses Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly)) to calculate 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 calculate Position Vector using this online calculator? To use this online calculator for Position Vector, enter Major Axis (a_major), Eccentricity (e) & True Anomaly (v) and hit the calculate button. Here is how the Position Vector calculation can be explained with given input values -> 11.96237 = (10.75*(1-0.12^2))/(1+0.12*cos(0.684)).

FAQ

What is 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 and is represented as r_pos = (a_major*(1-e^2))/(1+e*cos(v)) or Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly)). The Major Axis refers to the longer dimension or principal axis of an elliptical coverage area or beam pattern, Eccentricity refers to a characteristic of the orbit followed by a satellite around its primary body, typically the Earth & True Anomaly is an angular parameter that defines the position of a body moving along a keplerian orbit.

How to calculate 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 is calculated using Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly)). To calculate Position Vector, you need Major Axis (a_major), Eccentricity (e) & True Anomaly (v). With our tool, you need to enter the respective value for Major Axis, Eccentricity & True Anomaly 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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