Distance Between Two F0 Stars: How to Calculate?

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In summary: I got 20/11.3=sqrt(d^2) so d is the square root of that. But I do not know how to input this into my calculatorIn summary, the problem involves determining the distance of a distant F0 star, given that it is 11.3 times less bright than a nearer F0 star with a stellar parallax of 0.05 arcseconds. Using the inverse square law, the distance can be calculated by forming a proportionality law and solving for the unknown distance variable. The final equation is 20/11.3 = sqrt(d^2), where d represents the distance in parsecs of the distant F0 star.
  • #1
Taylor_1989
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Homework Statement


A distant F0 star is 11.3 times less bright than a nearer F0 star that has a
stellar parallax of 0.05 arcseconds. What is the distance in parsec of the more distant F0 star?

Homework Equations


$$d=\frac{1}{D} {pc}$$
$$B_0/B_1 = 10^{\frac{(m_1-m_0)}{2.5}}$$

The Attempt at a Solution


I calculated the distance to the closet planet to be 20pc and the difference in magnitude to be 2.63. But what I can't seem to do is find the distance between the two planets. Could anyone please give me a nudge in the right direction.
 
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  • #2
Taylor_1989 said:
I calculated the distance to the closet planet to be 20pc and the difference in magnitude to be 2.63. But what I can't seem to do is find the distance between the two planets. Could anyone please give me a nudge in the right direction.

I think you mean stars, not planets.

Review the inverse square law for brightness versus distance. Your class notes or textbook should cover this. If not, a web search will turn up plenty of hits. For example:

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit1/bright.html
 
  • #3
gneill said:
I think you mean stars, not planets.

Review the inverse square law for brightness versus distance. Your class notes or textbook should cover this. If not, a web search will turn up plenty of hits. For example:

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit1/bright.html

I just had a look, so dose this mean that if it is 11.3 times less bright the if I take the square root of that and times it by 20pc I would get the correct ans. But surely that not correct because I need a proportionality constant right? It the less bright that is confusing me. Less bright in my notes means it a ratio, but I don't understand how that relates to the inverse square law
 
  • #4
If you have a proportionality law, then when you form a ratio using two instances the constant of proportionality will cancel.
 
  • #5
my second attempt, was this: $$11.3=\frac{1}{x^2}$$ , $$ x=\sqrt{\frac{1}{11.3}}$$
 
  • #6
What was the motivation? What does x represent?
 
  • #7
gneill said:
What was the motivation? What does x represent?
Okay so I drew it out from star 1. I said that if it is athe 1m then the brightNess would be B, I then said at 2m the brightness would be 1/2^2=1/4 because it has to cover and area of 4 squares, so by extending that I said at distance x it would be 1/x^2 the orginals brightness so the as I know the brightness to be a ratione of 11.3 I the said 11.3=1/x^2 and went from there.
 
  • #8
Okay. And what will you do with this value of x in order to answer the problem?
 
  • #9
gneill said:
Okay. And what will you do with this value of x in order to answer the problem?
I need to covert to parsec and then add to the 20pc. correct?
 
  • #10
I just had a throught could I not workout the intensity of the star 20pc aways from me then work it out from there using invelse square law.
 
  • #11
Taylor_1989 said:
I need to covert to parsec and then add to the 20pc. correct?
Your x is just a function of the ratio of brightness, and by itself contains no distance units. You need to use the known distance of the first star to set the distance scale. You would do better to write out the proportionality law for both cases and then form the ratio, solving for your unknown distance. That way the math takes care of all the logical steps.
 
  • #12
Taylor_1989 said:
I just had a throught could I not workout the intensity of the star 20pc aways from me then work it out from there using invelse square law.
The brightness is a measure of the intensity, and using the inverse square law to find the distance is what the problem intends. It seems that you've just realized what it's all about :smile:
 
  • #13
gneill said:
The brightness is a measure of the intensity, and using the inverse square law to find the distance is what the problem intends. It seems that you've just realized what it's all about :smile:

Ah okay: so I did this: 1/20 = 11.3/d^2 if I rearrange I get the ans correct?
 
  • #14
Not quite. You've squared one distance and not the other, so the units won't balance. Fix that and you'll be okay.

It really would be to your advantage to write out the proportionality law symbolically first, forming the ratio and solving for your unknown variable. Building equations using numbers and partial guesswork is fraught with peril; you shouldn't have to ask if what you're doing is going to work, since a clean derivation using symbols will demonstrate the correctness.
 
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  • #15
Sorry I ment to put the square in my bad.
 

1. What is the distance between stars?

The distance between stars can vary greatly depending on the specific stars being measured. Some stars are very close to each other, while others can be millions or even billions of miles apart.

2. How is the distance between stars measured?

The distance between stars is typically measured using a unit called a light-year. This is the distance that light travels in one year, which is equivalent to about 5.88 trillion miles. Scientists also use other units such as astronomical units (AU) and parsecs to measure distances between stars.

3. What is the closest star to Earth?

The closest star to Earth is Proxima Centauri, which is located in the Alpha Centauri star system. It is approximately 4.24 light-years away from Earth.

4. How far apart are stars in a galaxy?

The distance between stars in a galaxy can vary greatly, but on average, stars are about 5 light-years apart from each other. However, in the center of a galaxy, stars can be much closer together, while in the outer regions, they can be much further apart.

5. Can stars collide with each other?

Yes, stars can collide with each other. This can happen when two stars are in close proximity to each other, or when a star passes through a dense area of a galaxy. However, these events are relatively rare, as the vast majority of stars are too far apart for collisions to occur.

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