What is the maximum distance a radar can detect objects on the Earth's surface?

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The discussion centers on calculating the maximum detection distance of a radar system with a power of 1kW operating at 10GHz from a height of 500m. The key formula mentioned is D = sqrt(2 * height * radius), which helps determine the distance to the horizon based on the radar's height and the Earth's radius. Participants express uncertainty about the problem and seek clarification on the equation's derivation and references. The equation effectively provides the correct answer for the radar's detection range. Overall, the conversation highlights the importance of understanding the relationship between radar height and detection distance.
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Homework Statement


A radar has power 1kW and is operating at a frequency of 10GHz. It is located on a mountain top of height 500m. The maximum distance upto which it can detect object located on the surface of the earth(Radius of Earth = 6.4*10^6 m) is


Homework Equations



The Attempt at a Solution


I'm not sure what to do here because I'm facing this kind of problem for the first time. Can anyone suggest me some equations to start with?
 
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D = sqrt(2*height*radius) I think
 
Rellek said:
D = sqrt(2*height*radius) I think

This gives me the correct answer but how did you think of this? Can you give some references regarding this equation?
 
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