Finding path difference of EM waves received by radio telecopes

In summary, the path difference of EM waves received by radio telescopes is used to determine the distance between the source of the waves and the telescope, aiding in the study of celestial objects. Scientists use interferometry to calculate the path difference, taking into account various factors such as atmospheric conditions and the strength of the waves. This information helps in creating detailed images and maps of celestial objects and detecting new objects in the universe. However, there are limitations to this method, such as decreased accuracy with distance and potential interference from external factors.
  • #1
songoku
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Homework Statement
Please see below
Relevant Equations
Trigonometry
1626158609238.png


My attempt:
1626158751799.png

I think ##x## is the path difference so by using trigonometry, I got ##x=d \sin \theta##

But my teacher said the answer is ##d \cos \theta##

What is my mistake? Thanks

Edit: Sorry, I found my mistake. My ##x## is not the path difference
 
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  • #2
OK, well done.

Tip: Always check a result for extreme cases (like here: ##\theta = 0## and ##\theta = \pi/2##)

##\ ##
 
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  • #3
songoku said:
My x is not the path difference
Well, it is the difference between the path lines, but not the path length difference.
 
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  • #4
Thank you very much BvU and haruspex
 
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1. How is the path difference of EM waves received by radio telescopes calculated?

The path difference of EM waves received by radio telescopes is calculated by measuring the difference in arrival time of the waves at two or more receiving antennas. This is done by using a technique called interferometry, where the signals from each antenna are combined and analyzed to determine the path difference.

2. Why is it important to find the path difference of EM waves received by radio telescopes?

Finding the path difference of EM waves received by radio telescopes is important because it allows us to accurately determine the direction and distance of the source of the waves. This information is crucial in astronomical studies and can help us understand the properties and behavior of celestial objects.

3. What factors can affect the accuracy of measuring the path difference of EM waves received by radio telescopes?

Several factors can affect the accuracy of measuring the path difference of EM waves received by radio telescopes. These include atmospheric conditions, the sensitivity and calibration of the receiving antennas, and any interference or noise in the signals.

4. Can the path difference of EM waves received by radio telescopes be used to determine the size of an object in space?

Yes, the path difference of EM waves received by radio telescopes can be used to determine the size of an object in space. By measuring the path difference and combining it with other information such as the frequency of the waves, scientists can calculate the size of the source object using mathematical equations.

5. Are there any limitations to using the path difference of EM waves received by radio telescopes?

While the path difference of EM waves received by radio telescopes is a powerful tool in astronomical studies, there are limitations to its use. For example, it may not be accurate for sources that are very far away or for objects that emit weak or intermittent signals. Additionally, atmospheric conditions and other external factors can also affect the accuracy of the measurements.

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