Grazing Angle (Earth)

The Grazing Angle calculator computes the angle (ψ) above the Earth's horizon to an object.

INSTRUCTIONS: Choose your preferred units and enter the following:  Earth Grazing Angle

• (R)  This is the range from the ground to the object
• (h)  This is the vertical height of the object above the Geoid.

Grazing Angle: The calculator return the grazing angle (ψ) in degrees.  However this can be automatically converted to other angle units via the pull-down menu.

NOTE: The Grazing Angle can be negative.  This means that the object is below the horizon.

The Math / Science

The Grazing Angle equation¹ calculates the angle between a target and a radar antenna.  This equation is named for a very particular situation, but at its heart, it's just trig.  Please see the picture.  This equation is based on simple math, but it's helpful in the context of calculating the Signal-to-Noise of a Synthetic Aperture Radar.

This algorithm use the mean radius of the Earth and h is the height above that.

Earth Model Calculators

• 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 Latitude, Longitude, Altitude
• Earth WGS-84 Equatorial radius in meters: 6378137.0 m
• Earth WGS-84 Polar radius in meters: 6356752.31424518 m 
• Earth Flattening Factor (WGS-84): 0.00335281066474748071984552861852
• Ellipse flattening factor: F = (Er - Pr)/Er  
• Geocentric to Geodetic Latitude
• Geodetic to Geocentric Latitude

1. ^ Performance Limits for Synthetic Aperture Radar - Second Edition.  Sandia National Laboratories, Albuquerque, NM.  Printed February 2006.