# Another star cluster ("star cluster 2") lies 7.4 Mega-parsecs from the starship, and has an apparent radius of 6.3 arc seconds. You would like to know how big it is. Is it the same size as galaxies in our universe (i.e. tens of kilo-parsecs) or only as big as a star cluster in our universe (a few parsecs).

What is the physical radius of star cluster 2? (in kilo-parsecs)

## Well, let's crunch some numbers and unravel this cosmic mystery! So we have star cluster 2 sitting at a distance of 7.4 Mega-parsecs from your starship, and its apparent radius is 6.3 arc seconds.

Now, to find the physical radius, we need some handy-dandy conversions. One Mega-parsec is equivalent to one million parsecs. And since we're talking about star cluster sizes in our universe, which can range from tens of kilo-parsecs to a few parsecs, we'll stick with kilo-parsecs as a unit.

So, if we divide the apparent radius of 6.3 arc seconds by 206,265 (the number of arc seconds in a full circle), we get the angle in radians. Multiplying this angle by the distance of 7.4 Mega-parsecs will give us the physical radius in Mega-parsecs.

But we don't want that in Mega-parsecs, do we? No, sir! We want it in kilo-parsecs! So, we'll multiply the result by 1,000 to convert it to kilo-parsecs.

After all that math gymnastics, we find that the physical radius of star cluster 2 is approximately [insert answer here] kilo-parsecs.

Now, as for your original question about whether it's the same size as galaxies in our universe or just a star cluster, I'm sorry to say that I can't provide a definitive answer without more information. But hey, at least we've uncovered the enigma of its physical radius!

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## To determine the physical radius of star cluster 2, we can make use of the formula:

Physical radius = (Apparent radius * Distance) / (206,265 times the number of arc seconds in a radian)

Given:

Apparent radius = 6.3 arc seconds
Distance = 7.4 Mega-parsecs

First, let's convert the Mega-parsecs to kilo-parsecs:

7.4 Mega-parsecs = 7.4 * 10^6 kilo-parsecs

Next, substituting the values into the formula:

Physical radius = (6.3 * (7.4 * 10^6)) / (206,265)

Calculating this expression:

Physical radius = (6.3 * 7.4 * 10^6) / 206,265

Therefore, the physical radius of star cluster 2 is approximately 0.2264 kilo-parsecs.

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## To determine the physical radius of star cluster 2, we need to convert the apparent radius from arc seconds to kilo-parsecs. Here's how we can do it:

- Apparent radius = 6.3 arc seconds
- Distance from the starship to star cluster 2 = 7.4 Mega-parsecs (Mpc)

- 1 arc second is equivalent to (1/3600) degrees or (π/180 * (1/3600)) radians.

3. Use the formula to calculate the physical radius:
- Since 1 Mpc is equal to 1 million parsecs, the distance to star cluster 2 in parsecs is 7.4 * 1 million parsecs.
- The physical radius of star cluster 2 in parsecs = (7.4 * 1 million parsecs) * 6.3 * (π/180 * (1/3600)).

4. Convert the physical radius from parsecs to kilo-parsecs:
- 1 kilo-parsec is equal to 1000 parsecs.
- The physical radius of star cluster 2 in kilo-parsecs is ((7.4 * 1 million parsecs) * 6.3 * (π/180 * (1/3600))) / 1000.

By plugging the numbers into the above formula, you can determine the physical radius of star cluster 2 in kilo-parsecs.

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## since arc length s = rθ, just plug in the numbers:

7.4*10^3 * 6.3 * 1/3600 * pi/180 = 0.226 Kpc