# Astronomy question: Interstellar distances **URL:** \ **Category:** Factual Questions\ **Created:** [April 23, 2005, 1:45am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714 "2005-04-23T01:45:20Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![SpectBrain](https://avatars.discourse-cdn.com/v4/letter/s/a87d85/32.png) [@SpectBrain](https://boards.straightdope.com/u/SpectBrain)\ **Post date:** [April 23, 2005, 1:45am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/1 "2005-04-23T01:45:20Z")
Last evening I was laying out on my deck gazing at the sky. It was just past dusk and the stars were becoming visible. Almost directly overhead I spotted three stars forming a triangle. (I know, I know any three points will form a triangle) Two of the stars were about 5 degrees apart. My question: Assuming that the stars are about the same distance from Earth, what would be the distance from one star to the other? Light minutes or light days or light years? ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [April 23, 2005, 1:50am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/2 "2005-04-23T01:50:31Z")
> [@SpectBrain](#): > > Last evening I was laying out on my deck gazing at the sky. It was just past dusk and the stars were becoming visible. Almost directly overhead I spotted three stars forming a triangle. (I know, I know any three points will form a triangle) > Two of the stars were about 5 degrees apart. My question: Assuming that the stars are about the same distance from Earth, what would be the distance from one star to the other? Light minutes or light days or light years? If D is the distance to the stars then they would be 5_pi_D/180 apart in the same units as D. ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [April 23, 2005, 1:54am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/3 "2005-04-23T01:54:59Z")
The exact answer is 2_D_sin(angle/2). The formula in the above post works fine for angles like 5[sup]o[/sup] ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [April 23, 2005, 1:57am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/4 "2005-04-23T01:57:30Z")
Dave I am pretty sure that gives you the arc length of a circle with radius D. The distance between the stars should be 2\*sin(2.5 degrees)\*D. ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [April 23, 2005, 1:58am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/5 "2005-04-23T01:58:54Z")
> [@treis](#): > > Dave I am pretty sure that gives you the arc length of a circle with radius D. > > The distance between the stars should be 2\*sin(2.5 degrees)\*D. Great minds and so on and so forth. ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [April 23, 2005, 2:12am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/6 "2005-04-23T02:12:01Z")
I think my angular size calculator would come in handy here: [http://www.1728.com/angsize.htm](http://www.1728.com/angsize.htm) Let’s suppose the stars are 5 degrees apart and the distance is 20 light years, then their distance from each other would be 1.75 light years. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [April 23, 2005, 5:04am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/7 "2005-04-23T05:04:17Z")
Certainly, though, what you were seeing was Saturn (the brighter of the three) next to the twin stars of Gemini, Castor and Pollux. Castor and Pollux are 4 1/2 degrees apart, but Castor is 52 lightyears away and Pollux is only 32 lya. That makes them 20 lightyears apart, no matter how close they seem to be. Saturn was 6 1/2 degrees from Pollux, but it is only a little more than a light_hour_ away. 🙂 ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [April 23, 2005, 8:34am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/8 "2005-04-23T08:34:40Z")
> [@treis](#): > > Dave I am pretty sure that gives you the arc length of a circle with radius D. > > The distance between the stars should be 2\*sin(2.5 degrees)\*D. I don’t know about this method. My trig teacher would have had a tizzy! Funny, in the trig I was taught, you’d NEVER use degrees to determine arclength! I think you’re getting the straight-line “equivalent” approximating the length of arc. And, for small angles, it’s probably nit-picky. So, shouldn’t you be using radians to find arclength? - Jinx ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [April 23, 2005, 1:46pm UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/9 "2005-04-23T13:46:17Z")
> [@Jinx](#): > > I don’t know about this method. My trig teacher would have had a tizzy! > Funny, in the trig I was taught, you’d NEVER use degrees to determine arclength! I think you’re getting the straight-line “equivalent” approximating the length of arc. And, for small angles, it’s probably nit-picky. > > So, shouldn’t you be using radians to find arclength? > > - Jinx Multiplying degrees by the fraction pi/180 converts to radians. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [April 23, 2005, 2:47pm UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/10 "2005-04-23T14:47:32Z")
> [@David Simmons](#): > > Multiplying degrees by the fraction pi/180 converts to radians. but then you’d just multiply that by D That is, 5 degrees times pi/180 times D But, that 5 degrees is off by more than the error in using the sine function, and as I mentioned the stars are not at the same “D” ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [April 23, 2005, 3:14pm UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/11 "2005-04-23T15:14:20Z")
> [@RM Mentock](#): > > but then you’d just multiply that by D > > That is, 5 degrees times pi/180 times D > > But, that 5 degrees is off by more than the error in using the sine function, and as I mentioned the stars are not at the same “D” All I can do is point to [my first post in the thread](http://boards.straightdope.com/sdmb/showpost.php?p=6086589&postcount=2) which contains the equation. And point out that the OP said to assume the stars were at “about the same distance” from the observer. ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [April 23, 2005, 6:16pm UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/12 "2005-04-23T18:16:10Z")
**Jinx** But in this case we are _not_ calculating arc length. Let’s suppose there is a circle 12 inches in diameter. The 2 points at the ends of the diameter are 12 inches apart. If we viewed this circle “edge-on” from a distance of 50 feet, the diameter would have an _angular size_ of 1.15 degrees. And the distance between the 2 points is still 12 inches. The _arc length_ between the 2 points would be 18.85 inches. We are not concerned with the arc length in this type of problem so the value of 18.85 inches is meaningless. ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [April 23, 2005, 7:42pm UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/13 "2005-04-23T19:42:58Z")
Just so the OP can decide whether or not he wants to look up sines or just use the angle for small angles - For the 5[sup]o[/sup] of separation at distance D the difference between computing arc length by the formula in my first post and the exact answer by the formula in my second or **treis’** first post is 3.17380306291026 parts in 10000 according to my Mathcad. For angles out to 8.8[sup]o[/sup] the difference is less than 1 part in 1000. ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [April 23, 2005, 7:59pm UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/14 "2005-04-23T19:59:07Z")
> [@RM Mentock](#): > > Certainly, though, what you were seeing was Saturn (the brighter of the three) next to the twin stars of Gemini, Castor and Pollux. Castor and Pollux are 4 1/2 degrees apart, but Castor is 52 lightyears away and Pollux is only 32 lya. That makes them 20 lightyears apart, no matter how close they seem to be. > > Saturn was 6 1/2 degrees from Pollux, but it is only a little more than a light_hour_ away. 🙂 Erhm no it doesn’t. By my calculation they are 20.255 light years apart. ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [April 23, 2005, 8:24pm UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/15 "2005-04-23T20:24:27Z")
> [@treis](#): > > Erhm no it doesn’t. By my calculation they are 20.255 light years apart. That’s quite a quibble. (Especially since the distances he quoted probably aren’t precise to within 1/1000th of a light year.) The point, I think, was that close objects in the sky are likely to vary widely in their distance from us, and that these differences probably account for more of their mutual seperation than the angular distance that we can see. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [April 23, 2005, 9:53pm UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/16 "2005-04-23T21:53:26Z")
> [@treis](#): > > Erhm no it doesn’t. By my calculation they are 20.255 light years apart. 20.255 lightyears _is_ 20 lightyears, in that case 🙂 ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [April 23, 2005, 10:56pm UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/17 "2005-04-23T22:56:07Z")
> [@chrisk](#): > > That’s quite a quibble. (Especially since the distances he quoted probably aren’t precise to within 1/1000th of a light year.) > > The point, I think, was that close objects in the sky are likely to vary widely in their distance from us, and that these differences probably account for more of their mutual seperation than the angular distance that we can see. Bah with that attitude I hope you’re the one aiming the super death at Earth. You’ll miss the entire solar system 😉 ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [April 23, 2005, 11:02pm UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/18 "2005-04-23T23:02:33Z")
What we need are more sig fig debates. ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [April 24, 2005, 12:00am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/19 "2005-04-24T00:00:41Z")
> [@treis](#): > > Bah with that attitude I hope you’re the one aiming the super death at Earth. You’ll miss the entire solar system 😉 Nah… I’ll just realize that for that kind of application, I’ll probably need more precise figures than earth astronomers have about distant stars, at the moment. 😃 My ‘attitude’ is that sometimes precision is important, and sometimes it ain’t. ---
**Author:** ![ralph124c](https://avatars.discourse-cdn.com/v4/letter/r/8797f3/32.png) [@ralph124c](https://boards.straightdope.com/u/ralph124c)\ **Post date:** [April 24, 2005, 12:12am UTC](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714/20 "2005-04-24T00:12:09Z")
Aren’t we in a pretty sparsely endowed region of the galaxy? I recall that the nearest star to the sun id Barnard’s Star (4.5 LY distant?). In the center of the galaxies, are stars a lot closer together? That is where most likely, interstellear travel is taking place. [Next page](https://boards.straightdope.com/t/astronomy-question-interstellar-distances/300714.md?page=2)