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Which spacecraft will be the first for which the Sun would become the second brightest object in the sky?

When that will happen and how far?

What would be the most efficient direction to fly in order to achieve that goal?

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  • $\begingroup$ That’s at least two separate questions. $\endgroup$ – chirlu Sep 4 '17 at 1:35
  • $\begingroup$ @chirlu, Thank you for the suggestion. My questions are closely related, I believe it is appropriate to phrase them the way I did. $\endgroup$ – user3715778 Sep 4 '17 at 1:39
  • $\begingroup$ Do you mean the brightness of a rocket during launch, or during propulsive maneuvers in space, or during re-entry, or passively reflected sunlight during orbit, or actively reflected sunlight as part of some art or energy production project? I guess standing below (and to the side of) a rocket in the first 30 seconds of launch, it would always be brighter than the moon, maybe 20 seconds for LOX/LH2 so in that case "first" would be over a half-century ago. Also, the tags pioneer, new-horizons, voyager, and interstellar-travel do not make sense. $\endgroup$ – uhoh Sep 4 '17 at 5:22
  • $\begingroup$ @utoh, No, I mean an apparent brightness of a celestial object from the perspective of the spacecraft. For all the listed probes so far, the brightest object in the sky is still the Sun, but inevitably at some point in the future, the Sun will become the second brightest object in the sky. $\endgroup$ – user3715778 Sep 4 '17 at 5:58
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    $\begingroup$ OK obviously others understood the question better than I did. It's probably the word "sky" in the title that threw me off; it sounded terrestrial to me. $\endgroup$ – uhoh Sep 5 '17 at 0:07
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As a reference, part of this question I answered at Astronomy.SE. The closest point at which the Sun would not be the brightest object in the sky is if we headed directly towards Sirius A, at a distance of 1.46 light years.

The fastest object leaving the Solar System right now is Voyager 1. It's speed right now is about 38026 miles per hour, or about 5.7534471e-5 light years/ year. If it was heading in the right direction (It's not), the time would be about 25,000 years. Of course, Voyager will be slowing down over that period of time, but not significantly. In 40,000 years it will pass fairly close to a star, mostly because the star is moving towards us, called AC +79 3888.

Voyager 2 is actually heading vaguely in Sirius's direction, so it might be the first. It will take about 30K years for Sirius to be the brighest star in it's view, however.

Of course, it is HIGHLY likely that a spacecraft will be sent to a neighbor sooner than that, that will be much quicker. How long will it take? Well, that depends on technology of the future, which I can't fathom to guess at this point in time.

Bottom line, it's going to take quite a while, but we will eventually have a spacecraft that the Sun isn't the brightest star in the sky.

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    $\begingroup$ In other words, the answer is: a future spacecraft that is not yet designed. I like the optimism of your answer. $\endgroup$ – Lesser Hedgehog Sep 4 '17 at 18:52
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    $\begingroup$ If we can't get a spacecraft to another star in 30,000 years, I think we have failed as a society. $\endgroup$ – PearsonArtPhoto Sep 4 '17 at 19:13
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    $\begingroup$ It becomes quite complicated, Voyager 1 is faster than Voyager 2, but heading in a 'wrong' direction. Sirius is brighter, but Alpha Centauri is closer. Both Sirius and Alpha Centauri approaching the Sun, however, Alpha Centauri almost 6x times faster than Sirius. $\endgroup$ – user3715778 Sep 4 '17 at 20:09
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To answer the second part of your question, we have to look for a bright and close star. Close, because the closer you are, the faster it changes its apparent brightness when approaching it. I guess (didn't prove it), Sirius and Alpha Centauri are the only candidates here as Sirius is the brightest star and only 8.6 ly away, while Alpha Centauri is 4.4 ly away.

The brightness of a star scales inversely with the square of the distance, i.e. $I \sim 1/x^2$. Sirius has an absolute magnitude of 1.42 while the sun has 4.83. That means, the ratio of their absolute brightness is $100^{(4.83-1.42)/5} = 23$. So, the brightness of the two stars at any point between them is $$I_{Sun} = \frac{1}{x^2} = \frac{23}{(8.6-x)^2} = I_{Sirius}$$ Solving for x gives us a distance of 1.48 ly from the Sun where Sirius starts to get brighter. Even when travelling in the opposite direction, i.e. straight away from Sirius, there is a point where Sirius gets brighter, namely at -2.26 ly from Sun.

Now let's look at Alpha Centauri: It has an absolute magnitude of 4.38, very similar to the Sun's. It will seem brighter than the Sun at about halfway between the stars, precisely at a distance of 1.98 ly.

In summary, the closest point to us where any star seems brighter than the Sun itself is about 1.98 ly in the direction of Alpha Centauri, or 1.48 ly in the direction of Sirius. Regardless of direction, the furthest possible distance where Sun is still the brightest object in the sky is 2.26 ly.

Unfortunately, all these distances are so huge and travel times are long so that we have to take the relative movement of stars with respect to Sun into account. At the moment, Alpha Centauri is approaching us faster than Sirius, so it could be the "most efficient" way to go is in the direction of Alpha Centauri, depending on the speed of the probe.

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  • $\begingroup$ Your calculation of the ratio of their absolute brightness seems to be wrong, I get 23.12 instead of 24. Rounded to the nearest integer is 23, not 24 $\endgroup$ – Uwe Sep 4 '17 at 11:41
  • $\begingroup$ @Uwe Thanks, looks like a typo. The other values were fine. $\endgroup$ – asdfex Sep 4 '17 at 13:36
  • $\begingroup$ @asdfex, Thank you, we have to look not only for bright and close stars but also for fast one as well. $\endgroup$ – user3715778 Sep 4 '17 at 14:54

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