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`R = f(oA,sA,alpha)`
Enter a value for all fields
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). 
INSTRUCTIONS: Choose units and enter the following:
- (sA) Station Altitude above Mean Earth Radius
- (α) Elevation Angle from the Station above the horizon to object.
- (oA) Object Altitude above Mean Earth Radius
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 the law of cosines. In the obtuse triangle below:
- 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°
` a/(sin("AA")) = b / (sin("BA")) = c / (sin("CA"))`
`c = sqrt( a^2 + b^2 - 2a*b*cos(CA) )`
3D Vector Calculator Functions:
- Slant Range using Position Vectors
- Slant Range from Elevation Angle (α)
- Slant Range using Subtended Angle (β)
- Distance to Horizon
- Angle of Satellite Visibility
- Grazing Angle
- XYZ to Lat/Lon/Altitude
- k V - scalar multiplication
- V / |V| - Computes the Unit Vector
- |V| - Computes the magnitude of a vector
- U + V - Vector addition
- U - V - Vector subtraction
- |U - V| - Distance between vector endpoints.
- |U + V| - Magnitude of vector sum.
- V • U - Computes the dot product of two vectors
- V x U - Computes the cross product of two vectors
- Vector Angle - Computes the angle between two vectors
- Vector Projection - Compute the vector projection of V onto U.
- Vector Rotation - Compute the result vector after rotating around an axis.
- (ρ, θ, φ) to (x,y,z) - Spherical to Cartesian coordinates
- (x,y,z) to (ρ, θ, φ) - Cartesian to Spherical coordinates
- (r, θ, z) to (x,y,z) - Cylindrical to Cartesian coordinates
- (x,y,z) to (r, θ, z) - Cartesian to Cylindrical coordinates