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I have a planet orbiting one star in a binary system. When the planet is exactly between the two stars it will experience a double day; when the primary sun sets the secondary one rises, no overlap. (My second star sheds enough light to make a difference on the planet.) When the planet is on the opposite point in its orbit the primary star occludes the secondary, so it's as if there were one star, lighting-wise. I'm trying to figure out the stuff in between.

The planet orbits A at a distance of 1AU. Answers on the linked question suggest that the distance between A and B should be 10-20AU for this to be viable. The planet's orbit is meant to be viable; feel free to treat it as circular despite the drawing.

I'm having trouble working out what days look like on the planet for the points in between the two marked positions. I think at the halfway points it'll get overlapping days, but I don't know how long (as a ratio of the rotation period). It's probably a simple matter of geometry, but adding the rotation of the planet to the orbit is causing me problems.

What I'd really like is a chart showing the progression of the day -- time of first sunrise, second sunrise, first sunset, second sunset -- for the four main points and perhaps the four in between those (so I can understand the transitions), at the equator and at what we'll call 45deg N. Treat times as relative to star A -- noon is when A is directly overhead, regardless of where B is.)

I know we're going to need some axial tilt to make this planet have seasons; pick and declare any reasonable-seeming number that makes your calculations easy, or default to Earth's for the sake of comparison. I'm trying to visualize what days and nights look like on this planet; I don't have precise numbers in mind.

We're also going to need a rotation period. For the sake of the question let's assume 24 hours like on Earth. In practice, once I know what the proportions look like, I'll adjust the rotation to suit the needs of my inhabitants (because we're worldbuilders and we can do that :-) ).

I have a planet orbiting one star in a binary system. When the planet is exactly between the two stars it will experience a double day; when the primary sun sets the secondary one rises, no overlap. (My second star sheds enough light to make a difference on the planet.) When the planet is on the opposite point in its orbit the primary star occludes the secondary, so it's as if there were one star, lighting-wise. I'm trying to figure out the stuff in between.

The planet orbits A at a distance of 1AU. Answers on the linked question suggest that the distance between A and B should be 10-20AU for this to be viable. The planet's orbit is meant to be viable; feel free to treat it as circular despite the drawing.

I'm having trouble working out what days look like on the planet for the points in between the two marked positions. I think at the halfway points it'll get overlapping days, but I don't know how long (as a ratio of the rotation period). It's probably a simple matter of geometry, but adding the rotation of the planet to the orbit is causing me problems.

What I'd really like is a chart showing the progression of the day -- time of first sunrise, second sunrise, first sunset, second sunset -- for the four main points and perhaps the four in between those (so I can understand the transitions), at the equator and at what we'll call 45deg N. Treat times as relative to star A -- noon is when A is directly overhead, regardless of where B is.)

I know we're going to need some axial tilt to make this planet have seasons; pick and declare any reasonable-seeming number that makes your calculations easy, or default to Earth's for the sake of comparison. I'm trying to visualize what days and nights look like on this planet; I don't have precise numbers in mind.

We're also going to need a rotation period. For the sake of the question let's assume 24 hours like on Earth. In practice, once I know what the proportions look like, I'll adjust the rotation to suit the needs of my inhabitants (because we're worldbuilders and we can do that :-) ).

I have a planet orbiting one star in a binary system. When the planet is exactly between the two stars it will experience a double day; when the primary sun sets the secondary one rises, no overlap. (My second star sheds enough light to make a difference on the planet.) When the planet is on the opposite point in its orbit the primary star occludes the secondary, so it's as if there were one star, lighting-wise.

The planet orbits A at a distance of 1AU. Answers on the linked question suggest that the distance between A and B should be 10-20AU for this to be viable. The planet's orbit is meant to be viable; feel free to treat it as circular despite the drawing.

I'm having trouble working out what days look like on the planet for the points in between. I think at the halfway points it'll get overlapping days, but I don't know how long (as a ratio of the rotation period). It's probably a simple matter of geometry, but adding the rotation of the planet to the orbit is causing me problems.

What I'd really like is a chart showing the progression of the day -- time of first sunrise, second sunrise, first sunset, second sunset -- for the four main points and perhaps the four in between those (so I can understand the transitions), at the equator and at what we'll call 45deg N. Treat times as relative to star A -- noon is when A is directly overhead, regardless of where B is.)

I know we're going to need some axial tilt to make this planet have seasons; pick and declare any reasonable-seeming number that makes your calculations easy, or default to Earth's for the sake of comparison. I'm trying to visualize what days and nights look like on this planet; I don't have precise numbers in mind.

We're also going to need a rotation period. For the sake of the question let's assume 24 hours like on Earth. In practice, once I know what the proportions look like, I'll adjust the rotation to suit the needs of my inhabitants (because we're worldbuilders and we can do that :-) ).

I have a planet orbiting one star in a binary system. When the planet is exactly between the two stars it will experience a double day; when the primary sun sets the secondary one rises, no overlap. (My second star sheds enough light to make a difference on the planet.) When the planet is on the opposite point in its orbit the primary star occludes the secondary, so it's as if there were one star, lighting-wise. I'm trying to figure out the stuff in between.

The planet orbits A at a distance of 1AU. Answers on the linked question suggest that the distance between A and B should be 10-20AU for this to be viable. The planet's orbit is meant to be viable; feel free to treat it as circular despite the drawing.

I'm having trouble working out what days look like on the planet for the points in between the two marked positions. I think at the halfway points it'll get overlapping days, but I don't know how long (as a ratio of the rotation period). It's probably a simple matter of geometry, but adding the rotation of the planet to the orbit is causing me problems.

What I'd really like is a chart showing the progression of the day -- time of first sunrise, second sunrise, first sunset, second sunset -- for the four main points and perhaps the four in between those (so I can understand the transitions), at the equator and at what we'll call 45deg N. Treat times as relative to star A -- noon is when A is directly overhead, regardless of where B is.)

I know we're going to need some axial tilt to make this planet have seasons; pick and declare any reasonable-seeming number that makes your calculations easy, or default to Earth's for the sake of comparison. I'm trying to visualize what days and nights look like on this planet; I don't have precise numbers in mind.

We're also going to need a rotation period. For the sake of the question let's assume 24 hours like on Earth. In practice, once I know what the proportions look like, I'll adjust the rotation to suit the needs of my inhabitants (because we're worldbuilders and we can do that :-) ).