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Me and a couple of class mates are working on our bachelor's project of which the mission is to measure the temperature of the sun using a parabolic antenna. We are having great troubles trying to come up with an equation relating the antenna temperature (which we are able to calculate with a system of components including an LNB, detector and arduino) to the temperature of the sun. We are fairly certain that we have managed to correctly calculate the antenna temperature T_{A}, so how do we proceed?

We have looked at the following article to gain some insight:

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?2002ASPC..278..293O&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf [Broken]

and specifically on equation 8 which seemingly gives the answer to our question. But in the integral on the RHS of the equation we need to have access to the power pattern of our parabolic antenna, which we do NOT have. The power pattern is also needed for calculation of the antenna solid angle Ω_{A}which figures in the equation as well. Ideally we would like to have the power pattern function and divide the T_{source}up into 3 parts: T_{sun}, T_{sky}and T_{ground}which would simply give us an equation with one unknown (T_{sun}) which we solve for.

Our supervisor gave us the advice early on that we should just regard our power pattern as a gaussian function which looks like e^{-2θ2}. This function is just one main lobe which very quickly tapers of to 0 as θ increases. If we use this as our power pattern and equation 8 from the link above and calculate T_{sun}with the data that we have gathered we receive T_{sun}= 600K.

(Our method of calculation being to subtract the input power of a measurement of the sky from a measurement with the sun in the center).

If instead of guessing that our power pattern falls towards zero we estimate that it tapers to a value of, say, -33dB at θ_{crit}and then stays at that value from [θ_{crit},π] then we get much closer to the real temperature of the sun. An ideal value would be for the power pattern to fall to -33.45dB of maximum, but fluctuations of a mere 0.1dB around that value throws off the temperature by ~120K. So even if we set out to measure our power pattern we would need to be VERY exact in those measurements for it to be of benefit to us. That is, if we use this method of calculating T_{sun}.

Is there a better way for us to get a good value of T_{sun}that does not require us to measure our power pattern?

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