<p>It tells you that Arcturus is a long way away and very bright. It was not realised just how far away and how bright stars were until the 17th century, and accurate calculations didn't come until the 18th. There are still many objects for which we only have a rough idea of of how distant and how bright they are. Even well known stars like Betelgeuse have not had their distance measured with great accuracy. </p>

<p>You have a formula for Flux, (which you understand to be a formula for "apparent brightness") and you know that distant light bulbs can appear as bright as stars so you can make an equation:</p>

<p>$$L_{\mathrm{bulb}}/(4\pi D_{\mathrm{bulb}}) = L_{\mathrm{star}}/(4\pi D_{\mathrm{star}})$$</p>

<p>You know the L and D for the bulb, and in the first question you assume a value of the L for Arcturus, and deduce a distance. Substitute known and assumed values and solve for $D_{\mathrm{star}}$, taking care to get the units consistent (change everything to SI units: for this exercise). </p>

<p>In the second question you use parallax to calculate $D_{\mathrm{star}}$ (distance in parsecs = 1000/(parallax in mas)). You substitute this value to get the value for the Luminosity.</p>

CC BY-SA 3.0
2018-02-03T12:18:18.663Z
2018-02-03T12:18:18.663Z
James K
<p>From the rooftop, certain lights look roughly as bright as Arcturus. If these lights emit a power of 10 W and are 5 km away. What does that tell you about Arcturus?</p>

<p>If you assume all stars are equally luminous*, how far would Arcturus be?</p>

<p>If you measured the parallax to Arcturus, 90 mas**, how luminous would Arcturus be?</p>

<p>I am struggling with solving this problem. I realize that I might need the formula: $F = L/(4\pi D^2)$ for flux vs. luminosity and distance, but I do not know how to solve it. Please walk me through the solution.</p>

<p>*The luminosity of the Sun is 3.86e26 W</p>

<p>** 1 Parsec = 3.08e16 m</p>

CC BY-SA 3.0
2018-03-05T17:26:12.327Z
I'm voting to close this question as off-topic because it is a very basic astronomy homework problem.
ProfRob
CC BY-SA 3.0
2018-02-01T20:36:06.183Z
If this is homework, can you acknowledge that in the question. I'd also like to see your response to the very first question (as that doesn't involve maths)
James K
<observational-astronomy>
Parallax and luminosity question about Arcturus, compared to terrestrial light?
Roceofiron
# Parallax and luminosity question about Arcturus, compared to terrestrial light?

(Asked by: username_0 on 2018-02-01)

From the rooftop, certain lights look roughly as bright as Arcturus. If these lights emit a power of 10 W and are 5 km away. What does that tell you about Arcturus?

If you assume all stars are equally luminous\*, how far would Arcturus be?

If you measured the parallax to Arcturus, 90 mas\*\*, how luminous would Arcturus be?

I am struggling with solving this problem. I realize that I might need the formula: $F = L/(4\pi D^2)$ for flux vs. luminosity and distance, but I do not know how to solve it. Please walk me through the solution.

\*The luminosity of the Sun is 3.86e26 W

\*\* 1 Parsec = 3.08e16 m

**Tags:** observational-astronomy

> **Comments:**
> **username_2**: If this is homework, can you acknowledge that in the question. I'd also like to see your response to the very first question (as that doesn't involve maths)  
> **username_1**: I'm voting to close this question as off-topic because it is a very basic astronomy homework problem.  

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## 1 answers

### Answer by username_2 on 2018-02-03. Score: 1

It tells you that Arcturus is a long way away and very bright. It was not realised just how far away and how bright stars were until the 17th century, and accurate calculations didn't come until the 18th. There are still many objects for which we only have a rough idea of of how distant and how bright they are. Even well known stars like Betelgeuse have not had their distance measured with great accuracy.

You have a formula for Flux, (which you understand to be a formula for "apparent brightness") and you know that distant light bulbs can appear as bright as stars so you can make an equation:

$$L\_{\mathrm{bulb}}/(4\pi D\_{\mathrm{bulb}}) = L\_{\mathrm{star}}/(4\pi D\_{\mathrm{star}})$$

You know the L and D for the bulb, and in the first question you assume a value of the L for Arcturus, and deduce a distance. Substitute known and assumed values and solve for $D\_{\mathrm{star}}$, taking care to get the units consistent (change everything to SI units: for this exercise).

In the second question you use parallax to calculate $D\_{\mathrm{star}}$ (distance in parsecs = 1000/(parallax in mas)). You substitute this value to get the value for the Luminosity.


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