Calculating the distance between the clusters

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In summary, the conversation discusses the measured flux and distance of two stars, Blue star 1 and a similar colored star in star cluster 1. The flux falls off proportionally to \frac{1}{r^2}, and using this information, it can be determined that the distance of star cluster 1 is 2 Mega-parsecs away from Blue star 1.
  • #1
CaptCoonoor
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Blue star 1 is 1.36 parsecs from you, and has a measured flux of 9.6×10−9Wm−2.

The similar colour star in star cluster 1 has a measured flux of 9.5×10−21Wm−2.

How far away (in Mega-parsecs) is star cluster 1?

Can anyone tell me how to start off? I'll do the rest
 
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  • #2
The flux falls off proportional to [itex]\frac{1}{r^2}[/itex]. Is this enough of a hint?
 
  • #3
a little bit more please
 
  • #4
Suppose I said the flux from a light bulb 1 meter away is [itex]I_0[/itex] Then I move the light bulb until the flux is [itex]\frac{I_0}{4}[/itex]. How far away is the light bulb now?
 
  • #5
phyzguy said:
Suppose I said the flux from a light bulb 1 meter away is [itex]I_0[/itex] Then I move the light bulb until the flux is [itex]\frac{I_0}{4}[/itex]. How far away is the light bulb now?
2 m?
 
  • #6
OK, good. Now apply this same logic to the stars. By what ratio has the flux decreased? So what is the ratio of the distances?
 

1. How is the distance between clusters calculated?

The distance between clusters is typically calculated using a mathematical formula known as the Euclidean distance. This formula takes into account the coordinates of each cluster and calculates the straight-line distance between them.

2. What is the purpose of calculating the distance between clusters?

The distance between clusters is an important measure in cluster analysis, as it allows us to determine the similarity or dissimilarity between different groups of data points. This information can then be used to identify patterns and relationships within the data.

3. Can different distance measures be used to calculate the distance between clusters?

Yes, there are several distance measures that can be used in cluster analysis, such as Manhattan distance, cosine distance, and Mahalanobis distance. The choice of distance measure may depend on the type of data being analyzed and the specific goals of the analysis.

4. How does the number of clusters affect the distance calculation?

The number of clusters can have an impact on the distance calculation, as it can affect the overall structure and distribution of the data. In general, increasing the number of clusters can result in shorter distances between clusters, while decreasing the number of clusters can result in longer distances.

5. Can the distance between clusters be used to determine the optimal number of clusters?

The distance between clusters is just one factor that can be used to determine the optimal number of clusters. Other methods, such as the elbow method or silhouette analysis, may also be used to identify the most appropriate number of clusters for a given dataset.

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