# How far out before some other star is brighter than the Sun? **URL:** \ **Category:** Factual Questions\ **Created:** [November 23, 2012, 5:28am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873 "2012-11-23T05:28:04Z")\ **Posts on this page:** 17\ **Page:** 4
**Author:** ![Gunslinger](https://avatars.discourse-cdn.com/v4/letter/g/4491bb/32.png) [@Gunslinger](https://boards.straightdope.com/u/Gunslinger)\ **Post date:** [May 4, 2017, 1:33pm UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/61 "2017-05-04T13:33:08Z")
> [@Senegoid](#): > > I read somewhere that, from the distance of one of our own outer planets (Neptune or Uranus or maybe Pluto), our own sun looks much like another star. > > Sorry, don’t know where I read that, or how reliable that source might have been, or even how literally it might have been intended. Probes to the outer planets have to have radiothermal powerplants, solar panels don’t work much beyond iirc Mars. But really all the questions posed in this thread are easily answered with rather complicated mathematical equations that I do not have the patience to work out. This guy, otoh: > [@Dr.Strangelove](#): > > One way of answering the question is to find out how far you have to go before the Sun looks like a point of light to the naked eye (like all other stars do from Earth). > > The angular resolution of the eye is about 1 arc-minute, or 2.91e-4 radians. The diameter of the sun is 1.38e6 km, so using the small-angle formula gives us a distance of 4.74e9 km. > > Pluto’s orbit varies from 4.44e9 to 7.31e9 km, so it’s in the right ballpark–from that distance, the sun would still be the brightest star in the sky, but still look like a point. > > Another way of looking at it: how far away do we have to get before the Sun is no brighter than the brightest (non-Sun) star on Earth? Well, the Sun has a magnitude of -26.74, while the next brightest star Sirius has magnitude -1.47. If my calcs are right, that corresponds to a distance of 113240 AU. That’s 1.79 light-years–a good distance but still less than halfway to the next star. For one example. > [@MikeS](#): > > (lower numbers mean brighter) Good ol’ science, back in the day a guy decided to number the stars he could see on a scale from 1-10 in order of decreasing brightness (it made sense at the time), and then the scale proved inadequate but was already entrenched. Cf all the temperature scales but Kelvin, etc. ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [May 4, 2017, 11:32pm UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/62 "2017-05-04T23:32:12Z")
> [@Gunslinger](#): > > Probes to the outer planets have to have radiothermal powerplants, solar panels don’t work much beyond iirc Mars. That used to be the case, but they now have high-efficiency multi-junction solar cells. NASA makes its own cells/panels at the [Glenn Reseach Center](https://en.wikipedia.org/wiki/Glenn_Research_Center) in Cleveland. Both the Dawn (asteroids) and Juno (Jupiter) missions run off them. For Juno, the solar panels are huge. > [@](#): > > Good ol’ science, back in the day a guy decided to number the stars he could see on a scale from 1-10 in order of decreasing brightness (it made sense at the time), and then the scale proved inadequate but was already entrenched. Cf all the temperature scales but Kelvin, etc. Nitpick: actually 1 to 6, with 1 being the brightest stars and 6 being barely visible with the naked eye. After they turned it into a real scale, that difference of 5 magnitudes means a factor of 100 in brightness. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [May 4, 2017, 11:54pm UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/63 "2017-05-04T23:54:14Z")
> [@dtilque](#): > > Nitpick: actually 1 to 6, with 1 being the brightest stars and 6 being barely visible with the naked eye. After they turned it into a real scale, that difference of 5 magnitudes means a factor of 100 in brightness. Huh. I didn’t realize the scale went back to the ancient Greeks. Lots of scales/units go through this pattern–they start off with some heuristic/qualitative system, and then when the instruments and analysis get better they curve-fit the scale to mostly match previous values. Time, temperature, distance, wind speed, and earthquake energy are examples here. And speaking of earthquakes, wikipedia has this to day about the Richter scale: _Richter derived his earthquake-magnitude scale from the apparent magnitude scale used to measure the brightness of stars.[4]_ Nifty. Though the moment magnitude scale is used now, which fixed some weaknesses in the Richter scale, while still giving similar numbers for the same quake. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 5, 2017, 12:11am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/64 "2017-05-05T00:11:02Z")
Another example of an originally-ad-hoc scale is the Mohs scale for hardness. There, though, something interesting happened when they quantified it: It turns out that materials 1 through 9 on the Mohs scale really are pretty close to linear… except that, on that linear scale, diamond ought to be about a 50, instead of the 10 the Mohs scale assigns it. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [May 6, 2017, 3:52am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/65 "2017-05-06T03:52:25Z")
Why is it called Rigel Centaurus and not Rigel Centauri, Rigel Al Centaurus, etc? ---
**Author:** ![The\_Man\_In\_Black](https://avatars.discourse-cdn.com/v4/letter/t/bcef8e/32.png) [@The\_Man\_In\_Black](https://boards.straightdope.com/u/The_Man_In_Black)\ **Post date:** [May 7, 2017, 1:51am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/66 "2017-05-07T01:51:29Z")
> [@Chronos](#): > > Sirius is currently about 8 ly away, so bringing it in to 1 ly would make it 64 times brighter. It’d be a very pretty light at that brightness, somewhat brighter than Venus, but still nowhere near enough to read by. What would VY Canis Majoris look like at 1 light year? ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [May 7, 2017, 10:38pm UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/67 "2017-05-07T22:38:36Z")
[I made a picture](http://scottcutler.net/images/local_stars_40ly.png). A 40 ly cube coded by which star is locally the brightest. This didn’t turn out quite as well as I’d hoped, mainly because it’s really hard to get a set of colors that works, and because the rendering quality of the program I used isn’t great. But it still a bit nifty. - Sol is the small bluish ball at the exact center - Rigil Kentaurus is the larger reddish one to the lower-right - Sirius is the transparent cyan ball that both are embedded in - Canopus is the entire transparent volume that’s otherwise unoccupied - Arcturus is bright yellow - Vega is bright magenta - Capella is the tan ball on the upper left - Fomalhaut is the steel gray ball to the upper right - Altair is the dark magenta patch on Vega, and slightly behind Fomalhaut - Pollux is the dark gray one on the lower left - Miscellaneous other stars are in light gray ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [May 7, 2017, 11:48pm UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/68 "2017-05-07T23:48:17Z")
\*Tres \*cool. That’s really neato. Thanks for putting in the effort. It also shows clearly how complicated the OP’s question really is. We’re embedded in a more or less randomly distributed field of stars of more or less random brightness across a massive range of brightnesses. The only plausible outcome is a foam of overlapping, disjoint, and concentric bubbles of varying sizes. But seeing it makes that a lot more obvious. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 8, 2017, 12:11am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/69 "2017-05-08T00:11:54Z")
Are those regions actually spheres? It seems like they shouldn’t be, especially not where they overlap (like the ones on the edge of Canopus). ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [May 8, 2017, 12:29am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/70 "2017-05-08T00:29:14Z")
I haven’t fully figured out what the shapes should be intuitively. If you have two stars, one huge and the other smaller, the small one will definitely look pretty close to a sphere: the falloff from the larger one means the background brightness is close to uniform, and so the isosurface of the small star should just be a uniform distance from the center. What about when the smaller star is a bit larger? I’m not sure, but it would not shock me if it were still a sphere, albeit not necessarily centered around the star. Projections can be funny this way (slightly reminiscent of the counterintuitive fact that a cone intersected with a plane makes an ellipse, and not some weird egg shape). What about when two stars intersect, with both embedded in a uniform background (like Sirius and Capella in my picture)? I’m not totally sure, but I think what you’ll get are two spheres, and then the intersection will be another section of a sphere, but with a different radius. If the two stars are equal, you get a flat plane (i.e., infinite radius). If one sphere is smaller, it “pushes” harder on the larger one since the falloff is faster, and you’ll get a bulge in that direction. So I think the cutout in Capella is not quite at the same curvature as Sirius, but somewhat less. Hard to tell from just the pic, of course. All of this is largely guesswork; unfortunately, it’s not exactly easy to reverse engineer the “true” shapes from the volumetric dataset. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [May 8, 2017, 12:36am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/71 "2017-05-08T00:36:59Z")
> [@LSLGuy](#): > > The only plausible outcome is a foam of overlapping, disjoint, and concentric bubbles of varying sizes. But seeing it makes that a lot more obvious. Yup. Also, really drives home the fact that there are some real monsters out there. Gives me a Lovecraftian vibe, actually; despite our seemingly powerful sun, we’re just a tiny blip embedded in a huge space, and if we ever left the confines of our home we’d see some unimaginably huge beasts, with no concern for life, human or otherwise. They’re out there, looming over us, and we only get away with existence by being no insignificant so as not to be worth attention. Sorry, got distracted there for a moment… ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [May 8, 2017, 12:53am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/72 "2017-05-08T00:53:32Z")
I think you can see what I was describing with the star intersecting Sirius just to the right of the 12:00 position (of Sirius’ boundary). You can see that both outside and inside are pretty close to sections of a sphere, but with different radii. The smaller star “wins” in that is pushes into the volume of Sirius, but not with full force, and so it doesn’t bulge inward quite to the extent as it would if it were a full sphere. There’s no discontinuity, of course; the circle of intersection with Sirius matches up with both the inside and outside parts of the smaller star, so you end up with what looks like two partial spheres glued together with a seam. Reminds me a bit of refraction–you know, like how a pencil in water changes (the apparent) angle at the surface, but the two parts still meet at the boundary. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [May 8, 2017, 12:59am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/73 "2017-05-08T00:59:15Z")
… Not to be worth attention. Until something somewhere decides to GRB and scrapes this biofilm off the top of this rock along with the smidgen of gaseous pollution clinging to the surface just now. Blink. All gone. We truly are as nothing in all this vastness. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [May 8, 2017, 1:16am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/74 "2017-05-08T01:16:13Z")
Just a little plausibility proof about what I was describing. Consider a 2d plane for a moment (just looking at the z=0 plane). Suppose we have two stars, one with brightness 1 at r=1 and coordinates (0, 0) and the other with brightness 2 at r=1 and coordinates (1, 0). What is the curve of intersection? Our two brightness formulas are: 1/(x^2 + y^2) 2/((x-1)^2 + y^2) They intersect where they’re equal, so: 1/(x^2 + y^2) = 2/((x-1)^2 + y^2) Some manipulation: 1\*((x-1)^2 + y^2) = 2\*(x^2 + y^2) x^2 - 2x + 1 + y^2 = 2x^2 + 2y^2 x^2 - 2x + 1 = 2x^2 + y^2 0 = x^2 + 2x - 1 + y^2 2 = x^2 + 2x + 1 + y^2 2 = (x+1)^2 + y^2 So it’s still a sphere (circle) of intersection, with coordinates (-1, 0) and radius sqrt(2). Which roughly makes sense to me. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [May 8, 2017, 4:07am UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/75 "2017-05-08T04:07:57Z")
Working it out with full generality: We can assume WLOG that we have one star at (0, 0) and the other at (1, 0) (pick the units and coordinate frame appropriately). We can also assume that the first star has brightness 1 and the other brightness b. Set equal: 1/(x[sup]2[/sup] + y[sup]2[/sup]) = b/((x-1)[sup]2[/sup] + y[sup]2[/sup]) Cross-multiply: x[sup]2[/sup] - 2x + 1 + y[sup]2[/sup] = bx[sup]2[/sup] + by[sup]2[/sup] More rearrangements: 0 = (b-1)x[sup]2[/sup] + 2x - 1 + (b-1)y[sup]2[/sup] 0 = (b-1)(x[sup]2[/sup] + 2/(b-1)\*x - 1/(b-1)) + (b-1)y[sup]2[/sup] 0 = (x[sup]2[/sup] + 2/(b-1)\*x - 1/(b-1)) + y[sup]2[/sup] 1/(b-1)[sup]2[/sup] + 1/(b-1) = (x[sup]2[/sup] + 2/(b-1)\*x + 1/(b-1)[sup]2[/sup]) + y[sup]2[/sup] 1/(b-1)[sup]2[/sup] + 1/(b-1) = (x + 1/(b-1))[sup]2[/sup] + y[sup]2[/sup] That’s the equation for a sphere (well, circle, but it doesn’t matter). We don’t have to consider more than two stars since the surface between any two is just a function of those two, not any others (other stars will change the extent of the surface, but not the shape). And you can see one thing easily; for equal brightness (b=1), the surface becomes a “sphere at infinity” (i.e., a plane). For b\<1 it curves to the left, and for b\>1 it curves to the right, also as expected. So yeah, everything is made up of sections of spheres. Isolated stars are complete spheres while others may decompose into several sections. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 8, 2017, 1:03pm UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/76 "2017-05-08T13:03:09Z")
OK, yeah, that was about what my intuition was telling me. I just wasn’t seeing a seam in some of those. And **LSLGuy** , I know that it’s popular to talk about a GRB flash-sterilizing the entire planet, but it can’t happen. Gamma ray bursts have a duration of at most a few seconds, and they can’t penetrate through an entire planet. So you could flash-sterilize half of the planet (or at least, half of the land area-- The deep oceans would also be protected), but the other half would be (initially) untouched. Now, I’m sure that there would be severe long-term ecological consequences to the other half, and the flash would probably also produce opaque nitrogen oxides that would severely cut down sunlight for several years, but those are things that at least some life (probably even some humans) would still survive. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [May 8, 2017, 2:24pm UTC](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873/77 "2017-05-08T14:24:07Z")
Cool. Thanks for the additional details. I hate being somebody that propagates the misconceptions “everyone knows”. In sorta-related news, bonobos aren’t the chimp counterpart to human free love hippies either. [Previous page](https://boards.straightdope.com/t/how-far-out-before-some-other-star-is-brighter-than-the-sun/641873.md?page=3)