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# Quick Astro Question!- Do you understand this? watch

1. hi,
This is from the jan 04 paper Q2, for astro aqa a.

there's 2 stars, with the same apparent magnitude, one of spectral class A and the other of spectral class G.

it's asks for which spectral class the smaller star belongs to? the answer is G.

but i'm confused as i thought that as A is hotter, and the power output of each are the same, that surface area would be smaller for A? - using stefan's law.

Any help appreciated.
thanks
2. Temperature decreases along the horizontal axis of the Hertzsprung-Russell diagram.

Stefans law P = stefans constant A T^4 = kAT^4 (or something like that...been a while since my astronomy module lol)

P/kT^4 = A

So area is inversely proportional to T^4

So the star with the higher temperature is the smaller. So it should be class A unless we're both missing something...
3. just double checked G is definitely the answer. ???
4. Basically, (I know this may be naff all help to you now, but let's give it a shot anyway), first consider what apparent magnitude actually is - the apparent brightness of a star from Earth. I'm slightly worried that they use apparent magnitude with absolute - if you ever get back, recheck that. I'm going to assume they're relatively similar distances from the Earth, as we don't have any other info to go on.

With that in mind, if these two stars have the same apparent magnitude, then they both appear to have the same brightness.

The classification of stars from hottest (and thus, brightest due to higher power output) to coolest is OBAFGKM . Hence, A will be hotter than G.

Let's bring all this together. If A is hotter than G, then it has a higher power output per unit surface area. G has a lower power output per unit surface area.

In order for these two to appear of the same brightness, then A has to have a larger surface area, so it's intensity is equal to that of the other star. Hence, the smaller star is G.
5. (Original post by chidona)
Basically, (I know this may be naff all help to you now, but let's give it a shot anyway), first consider what apparent magnitude actually is - the apparent brightness of a star from Earth. I'm slightly worried that they use apparent magnitude with absolute - if you ever get back, recheck that. I'm going to assume they're relatively similar distances from the Earth, as we don't have any other info to go on.

With that in mind, if these two stars have the same apparent magnitude, then they both appear to have the same brightness.

The classification of stars from hottest (and thus, brightest due to higher power output) to coolest is OBAFGKM . Hence, A will be hotter than G.

Let's bring all this together. If A is hotter than G, then it has a higher power output per unit surface area. G has a lower power output per unit surface area.

In order for these two to appear of the same brightness, then A has to have a larger surface area, so it's intensity is equal to that of the other star. Hence, the smaller star is G.

Seems I decided to completely ignore the whole apparent magnitude bit haha. My mistake. Good answer though!
6. ohhhh i get it. so is power output a measure of temperature or brightness or both???

7. Power output can be a measure of both, i believe, but someone feel free to contradict me. Usually in astro questions they'll just probe you about brightness, so don't worry =]

8. No the mark scheme is wrong, i checked this question with my teacher
As P = sigma A T^4 and P is constant (because Absolute magnitude is constant) then if T is larger A must be smaller
Hense the hotter star, the A class star, is the smallest

If you check the examiner's report it says that ' the best answers said that the smallest star was in spectral class A'

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