Magnitude of Position Vector

The Magnitude of the Position Vector calculator computes the magnitude of a vector base on three Cartesian coordinates

INSTRUCTIONS: Choose units and enter the following:

• (x)  X component of Position vector
• (y)  Y component of Position vector
• (z)  Z component of Position vector

Position Vector Magnitude |V|: The calculator returns the magnitude in kilometers.  However this can be automatically converted to compatible units via the pull-down menu.

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The Math / Science

The magnitude of a position vector is often use to compute the distance of an object (e.g. satellite) from the center of gravity of the system (e.g. the center of the Earth).  Position vectors are based on length units.  The most common units in aerospace are kilometers and nautical miles.

The formula for the magnitude of a position vector is:

    `|V| = sqrt(x^2 + y^2 + z^2)`

where:

• |V| = magnitude of the position vector
• x = x coordinate
• y = y coordinate
• z = z coordinate

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