Slant Range

Not Reviewed
Equation / Last modified by KurtHeckman on 2019/07/29 23:56
Rating
ID
KurtHeckman.Slant Range
UUID
9963c8d9-7a3b-11e8-abb7-bc764e2038f2

The Slant Range calculator computes the slant range (R) from a ground station to an object (satellite or aircraft) based on the station and object altitudes and the elevation angle (α). SlantRangeBeta.png

INSTRUCTIONS: Choose units and enter the following:

Slant Range (R):  The range is returned in kilometers.  However this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The formula for the slant range uses both the law of sines and cosines.   In the obtuse triangle below:Law of Sines and Cosines.png

  • b = Re + sA
  • a = Re + oA
  • c is the slant range
  • CA is the Earth Central Angle
  • BA is the subtended angle (β)
  • AA is elevation angle (α) + 90°

where:

      ` a/(sin("AA")) = b / (sin("BA")) = c / (sin("CA"))`

therefore:

       `c = sqrt( a^2 + b^2 - 2a*b*cos(CA) )`

3D Vector Calculator Functions: SlantRangeVector.png