# Range Difference and Radar Problem

See the attached files.

Part a of the problem - word document - requires determination of the range at point C and P then determining the difference.

I'm unsure if I need to concern myself with the Taylor series expansion of the range equation. In essence I opted to determine theta then solve for R using the range equation (right before the Taylor expansion) found in the latter part of page 2.

In determining the Doppler I tried to use the first term of the doppler equation. See 'word document' for equation that's missing in the PDF.

My approach could be wrong hence, ...

For a description of synthetic aperture radar see:

http://www.sandia.gov/radar/whatis.html.

https://brainmass.com/physics/doppler-shift/range-difference-radar-problem-29259

#### Solution Preview

earth equator velocity Ve = 463 m/s = 0.463 km/s

Because, for stationary earth range,

R = sqrt(xo^2 + (yo-V*t)^2 + h^2)

For rotating earth,

R = sqrt((xo - Ve*t)^2 + (yo-V*t)^2 + h^2)

xo = 300 km

h = 800 km

L = 15 km

V = 7.6 km/s

Assume at t =0: yo = 0 (theta_o = 90 degree)

=> T = L/V = 15/7.6 = 1.97368 s

=> T/2 = 0.98684 s

Therefore,

-0.98684 <= t <= ...

#### Solution Summary

The solution provides step by step calculations for questions with regards to a synthetic aperture radar. The solution involves calculations of range difference at the two edges of a synthetic aperture and the Doppler ship at the center of the synthetic aperture.