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## Homework Statement

A radiometer system on a satellite orbiting the earth at an altitude of 1000km has an antenna of gain 46 dBi pointing at the earth’s surface. The antenna is matched to a receiver with an input noise temperature of 50K and a bandwidth of 10MHz. The sky noise temperature is 10K. The earth’s surface temperature is 300K. The surface field reflection coefficient is 0.7. Estimate the approximate area of the earth’s surface that is “seen” by the system. Estimate the total noise power at the receiver input and the fractional change in this noise power caused by a 1K change in the earth’s surface temperature

## Homework Equations

Pd = (Gtx * Pin)/(4*pi*r^2), Pn = KTB , other basic antenna equations

## The Attempt at a Solution

My attempt is probably wrong but here it goes! So I believe the first step is to calculate the Noise Power of the transmitting antenna, this is done by,

P = KTB

P = 1.38*10^-23 * 50 *10*10^6

= 6.9 * 10^-15 W

Now this is the bit im uncertain about but the formulae fits the given variables.

Pd = Gtx Pin/ (4piR^2)

Substituting the numbers gives a power density of 2.18 x 10^-17 W. However I am unsure of what to do next, ive tried a few things but suspect them of being wrong!

Any help given will be appreciated! Thanks!