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So in my world there is a planet orbiting a star, which is in a far binary system with another star. Is there any formula to calculate when the distant star would be visible - times of year and/or day?

It only orbits one of the stars, the other is just at a distance. Also, I am not wondering about gravitational effects, only visibility.

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  • $\begingroup$ Bottom line: it depends on whether your planet orbits both stars or just one, or possibly switches between them. The prior question covers the first 2 scenarios very well including when the stars would be visible. $\endgroup$ – Willk Jul 4 '18 at 20:54
  • $\begingroup$ @Willk I'm not sure I see how it's a duplicate of the question you linked. $\endgroup$ – HDE 226868 Jul 4 '18 at 20:59
  • $\begingroup$ How is this a duplicate. I'm asking for when it will be visible, not what color it would be. $\endgroup$ – Derek Kaplan Jul 4 '18 at 21:59
  • $\begingroup$ Could two stars of equivalent mass/size form a binary system and be different colors? is about a planet orbiting a pair of stars, while this one is about a planet orbiting one of the stars in a binary star system. I don't see how this can possibly be a duplicate of that one; the settings are different, and the questions are asking about different things. $\endgroup$ – a CVn Jul 4 '18 at 22:08
  • $\begingroup$ @HDE226868 - since the accepted answer for the other one covered year length, sunrise, orbit types and star color types I thought it covered this question pretty thoroughly. But if you think not, I look forward to your answer! $\endgroup$ – Willk Jul 4 '18 at 22:29
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Possibility One:

In some S type systems the two stars are close enough and bright enough that each star will always be visible to the naked eye, even in daytime, from planets orbiting the other star - whenever the distant star will be above the horizon of the planet that orbits the nearer star. It is perfectly possible for the more distant star in an S type star system to be many times as bright as a full moon on Earth, for example.

So the more distant star will always be visible over half of the planet that orbits the nearer star. At any specific moment the more distant star will be visible in one hemisphere and invisible in the other hemisphere because the planet itself is in the way. And unless the direction to the more distant star is directly over one of the poles of the planet, the more distant star should be above the horizon, and thus visible, for part of the planet's day, and it should be below the horizon, and thus invisible, for part of the planet's day, as see from every point on the surface of the planet.

Possibility Two:

The more distant star might be distant enough, and dim enough, that it might never be bright enough to be seen with the naked eye in the day, but only visible to the naked eye during the night when the sky is dark enough not to drown it out. Thus the planet of the nearer star will have two hemispheres in regard to the more distant star, one where the distant star is above the horizon, and one where distant star is below the horizon. And the planet will have two hemispheres in regard to the nearer star, the day hemisphere and the night hemisphere.

So the more distant star will not be visible when it is in the planet's day hemisphere and also the facing away from the distant star hemisphere. And the more distant star will not be visible when it is in the planet's night hemisphere and also the facing away from the distant star hemisphere. And the more distant star will not be visible when it is in the planet's day hemisphere and also the facing toward the distant star hemisphere. The more distant star will only be visible when it is in the planet's night hemisphere and also the facing toward the distant star hemisphere.

In our solar system the planet Earth orbits the Sun at an average distance of one Astronomical Unit (1 AU), and the planet Uranus orbits the Sun at an average distance of 19.2184 AU, many times the orbital distance of Earth. As seen from Earth, the apparent magnitude of Uranus varies from plus 5.32 (brighter) to plus 5.95 (dimmer). This makes Uranus bright enough to be seen with the naked eye at night when conditions are good, but never bright enough to be seen in the day.

This makes the planet Uranus analogous to the more distant star. The more distant star in your solar system orbits around the nearer star at many times the distance that the habitable planet does, just as Uranus does in our solar system. And the more distant star in your solar system can have the brightness to be seen from the planet in the nighttime but not in the daytime, just as Uranus in our solar systems as the brightness to be seen from earth in the nighttime, but not in the daytime.

Thus the kind of computer program that could calculate when Uranus would be visible from a certain point on Earth could calculate when your more distant star would be visible from a certain point on your habitable planet. But instead of using the parameters for our solar system you would have to be able to enter the parameters for your fictional solar system.

Possibility Three:

The more distant star in your solar system might be so distant and so dim that it is never visible with the naked eye from your habitable planet. Thus nobody will ever see the more distant star in the sky of the habitable planet, unless they use a telescope to observe it. And perhaps people from Earth will know that the more distant star is there, but the natives of the planet will not have telescopes and won't ever have discovered it.

Possibility One Point Five.

There is also an intermediate possibility between Possibility One and Possibility Two, call it Possibility One Point Five.

That possibility is that the more distant star is sometimes bright enough to be seen with the naked eye in daytime from the planet, and some times is only bright enough to be seen at nighttime from the planet.

There is an example in our solar system. The planet Jupiter is sometimes bright enough to be seen with the naked eye from Earth during daylight - not bright daylight but when the sun is low in the sky, less than 10 degrees above the horizon. And at other times Jupiter is only bright enough to be seen at night. the same type of computer program that could calculate when Jupiter would be visible on Earth could calculate when the more distant star would be visible with the naked eye from the planet, if the correct variables were entered.

Possibility Two Point Five.

And there is also an intermediate between Possibility Two and Possibility Three, call it Possibility Two Point Five.

The more distant star in your system could orbit at so great a distance, and be so dim, that it was sometimes visible to the naked eye from the planet at night, and sometimes was not visible to the naked eye from the planet at all, even in the darkest night.

There is an example in our solar system. The asteroid Vesta is sometimes close enough to Earth to bright enough be visible with the naked eye from Earth a nighttime, and sometimes too far away and dim to be visible with the naked eye from Earth at nighttime.

So a computer program to calculate when Vesta is visible with the naked eye from Earth is the type of program that could calculate when the more distant star was visible from a point on your planet. But it would have to be a program that you could enter the data for your imaginary solar system into.

So you could use a program made for designing imaginary star systems and calculating when various objects are visible from a selected spot on a selected planet in that solar system.

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  • $\begingroup$ Great answer! Do you know of any good visibility calculators like you mentioned? $\endgroup$ – Derek Kaplan Jul 5 '18 at 13:05
  • $\begingroup$ Unfortunately I don't, but some of the people who post here probably do. $\endgroup$ – M. A. Golding Jul 5 '18 at 16:42

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