# Facing difficulties with radio telescope measurements

• Stargazing
Mange313
Hi

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 TA, so how do we proceed?

We have looked at the following article to gain some insight:
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 ΩA which figures in the equation as well. Ideally we would like to have the power pattern function and divide the Tsource up into 3 parts: Tsun, Tsky and Tground which would simply give us an equation with one unknown (Tsun) 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 Tsun with the data that we have gathered we receive Tsun = 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 θcrit and then stays at that value from [θcrit,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 Tsun.

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

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Gold Member
• A Gaussian is, indeed, a common approximation to the pattern of a parabolic dish, so I wouldn't hesitate to use that. The expression $e^{-2\theta^2}$ is certainly wrong, however. You need to have a normalization constant in the exponent that introduces the beam width, which is a function of both aperture diameter and wavelength.
• The temperature of the sun should be around 6000K (or more during periods of high sunspot activity), so I don't think that 120 degrees here or there matters at all. You have a very large discrepancy.
• The sun's apparent temperature depends on frequency (or wavelength), so you should know your frequency. Here's a reference that shows the dependence. It has a simple expression for the integral.
I wouldn't use their power pattern expression, however. It applies to an untapered aperture, which is highly unusual. Virtually all dishes use a taper. (On the other hand, the fact that they get reasonable results with this pattern shows how unimportant are the details of the function that you choose.)
• Without seeing all your calculations and reasoning, and how you calibrated the thermal noise and losses in your system, it will be difficult to help you. In fact, a web forum is a poor medium for discussing and diagnosing a complicated experimental and theoretical problem like this. Physics Forums works best for straightforward problems like homework problems.
• The fastest and easiest way to get help is to ask your professor.