Can a sun rise and set on the same horizon?

[Razorback-PT]

Hello everyone.

I'm working on a video-game that takes place on a distant Earth like planet. A key part of the gameplay revolves around a special day and night cycle. I'd like this planet to be tidally locked to it's red dwarf star making it's habitable zone limited to the terminator.

Of course this would mean that the sun would be always fixed in the sky and no cycle could take place.

I'm here to ask you guys if there's any way to make it possible for the sun to rise up from the horizon slow down and then set again.

I've been searching and I've heard about this effect called libration. Would this make it possible? And how would that work?

Maybe you know of other possibilities. Would a large moon cause the planet to wobble slightly?

If it turns out that this is possible, what would be the shortest time for a day\night cycle to occur? I'd really like for this to happen in the span of a few hours so that the effect is noticeable for the player.

Any help is appreciated.

 

[Borek]

Have you seen this image:

[URL]http://upload.wikimedia.org/wikipedia/commons/b/ba/Lunar_libration_with_phase_Oct_2007_450px.gif[/URL]

That's how it works. Now, imagine you are on the Moon's terminator and you are looking at the camera that was taking the picture. The same will happen on your planet if you were looking in the direction of the sun.

 

[Phrak]

I'm not sure if what Borek said was clear. However, first take a planet with locked spin, so that one face of the planet always faces the sun. Now incline the axis of rotation to some large angle of inclination to the orbial plane. Near either pole the sun will apear to rise from the direction of the equator and set in the same direction. At an inclination of 90 degrees, the sun will rise to directly overhead and set at the same point on the horizon.

You might want to try a stick and ball model planet with a flashlight to convince yourself.

 

[Razorback-PT]

That picture was the thing that gave me hope this might be feasible. Imagining that the Earth was a star, I'd see it rise and set again if I where standing near the moon's terminator. But the time that takes seams to be linked to the duration of it's orbit, no? It would take a full orbit to see the full effect. Almost a month in case of the moon. My planet is close enough to it's star but it would still take about a month as well.

Phrak, I tried your experiment on http://universesandbox.com/" and it worked as you said. So it appears the libration is directly related to the angle of the rotation axis. At 90º the sun would rise above our heads. That's a bit to extreme though, I'm going for the constant twilight effect.

Still, a day night cycle would take a year on this place. About 30 Earth days.

Are there other alternatives to make the cycle much quicker? What would it take for the sun to rise and set in, let's say, 10 Earth hours? And what would that mean for life on this world?

 

[Travis_King]

A crazy wobbling unstable mess of a small moon/asteroid lol

If you want quick sunrise/sunset, have it revolve. If you want a habitable zone only in the terminator, have it locked (though for a red dwarf, I'm not so sure that would necessarily be the case. But it's for fiction, so you can say whatever you want.

It's a video game...I don't think you need to get that serious into the science. Even what you've done so far is more than most games consider.

 

[Razorback-PT]

I know pretty much no one will notice or care whether or not the game is scientifically accurate. Personally I feel like it needs to be. A story has a lot more resonance to me If I can look at it and say that it could actually take place in reality.

I see that I'm going to have to rethink a few things to make this work.

 

[Janus]

Another possibility is to give the planet an elliptical orbit. Being tidally locked does not mean that the planet must keep One face towards the Sun, just that the orbital period and rotational period be the same. Since a planet in an elliptical orbit slows up and down at different points of the orbit. the rotation period will alternately get ahead of or lag behind. This is another aspect of libration and the one that is responsible "side to side" swing in the animation Borek gave.

 

[Razorback-PT]

Interesting. I'll tinker with elliptical orbits on the simulators and see what I find. But my first guess is that the transition from night to day would still be pretty long. Twice a year, no? And then there's the problem with the planet getting out of the star's habitable zone occasionally.

How about this. Let's imagine that the star actually wobbles somehow. Maybe it's part of a binary system and has a barycenter beyond it's surface. I wouldn't want it to orbit another star though. Every time one of the stars would set, the other would already be visible creating perpetual day. Ok so what else could it be. Maybe a supermassive jovian planet? Or maybe even a small black hole? (Pretty sure that would mess things up). Let's just say it's a very dense small object.

So our planet would be orbiting both the star and the object. They'd be very close and orbiting each other very fast. (Once every 24 hours?)

The planet would still be locked to that system, so only the wobbling would cause the star to show up above the horizon. I only need to the star to show up slightly and then go back down again.

What do you guys think?

 

[skeptic2]

If you were at the North Pole, the sun would both rise and set on the southern horizon. Of course it might not even set at all.

 

[Razorback-PT]

I've worked out a working simulation. It's not really a binary system. I need the star to orbit a sufficiently dense object.

This particular object is 18 suns in mass but only 500000kms in diameter. It has a density of 500g/cm^3

Is this object a black hole?

If not, could there be an object like this but dark?

So the star orbits this black hole in 8 hours which is great for what I need. The planet would orbit the black hole as well but would still fit snuggly in the star's habitable zone. (see attachment. Green is habitable.)

If someone where to stand on the planet's equator and terminator, the star would go up and down at the horizon level just like I wished.

Are there any problems that I missed?

 

[Razorback-PT]

Thinking about it, the central object definitely needs to be a black hole. I've made it about 15 suns in mass, but only 30 kms in diameter.

In order for the star to orbit this black hole in about ten hours, It would need to be pretty close to it.

I'm guessing a star orbiting that close would get sucked into the black hole. Forming an accretion disk and two crazy jets.

A star wouldn't survive that close, right?

 

[Janus]

Thinking about it, the central object definitely needs to be a black hole. I've made it about 15 suns in mass, but only 30 kms in diameter.

In order for the star to orbit this black hole in about ten hours, It would need to be pretty close to it.

I'm guessing a star orbiting that close would get sucked into the black hole. Forming an accretion disk and two crazy jets.

A star wouldn't survive that close, right?

The BH would be 90 km in diameter.

At ten hours, the star would be within the Roche limit for the the BH and be torn apart.

 

[Razorback-PT]

Thanks, I thought as much. I looked into calculating the roche limit, but that sort of math is really beyond me.

So, how far away am I from getting a stable system here? Keeping that short orbit period is the only thing that I really need, I can change everything else.

What direction should I be going? Making the black hole less massive?

Something else occurred to me, perhaps a happy accident. Red dwarfs are known to be dangerous for life due to their violent flare storms. Wouldn't a black hole keep the planet safe by consuming those coronal mass ejections?

 

[Travis_King]

I still think that you are going too far into the physics. A good story only needs a plausible scenario. Unless your character is an astrophysist or your narrator (if you have one) thinks he's talking to one, nobody is going to know much about your system beyond the input they get

 

[Janus]

Thanks, I thought as much. I looked into calculating the roche limit, but that sort of math is really beyond me.

So, how far away am I from getting a stable system here? Keeping that short orbit period is the only thing that I really need, I can change everything else.

What direction should I be going? Making the black hole less massive?

Something else occurred to me, perhaps a happy accident. Red dwarfs are known to be dangerous for life due to their violent flare storms. Wouldn't a black hole keep the planet safe by consuming those coronal mass ejections?

Forget what I said, I had forgot that your star was a Red dwarf, (I was assuming a star like our own), and that changes everything.

Fiddling with the size of the BH, won't change anything, because interestingly enough, the orbital period of a body at Roche limit distance is independent of the primary body's mass. What it does depend on is the density of the orbiting object. The denser the object, the shorter orbital period it can have while remaining outside the Roche limit. And a Red Dwarf would be considerably denser than our Sun.

You should have no problem getting a 10 hr orbit around that BH.

As far as coronal mass ejections go, some of more powerful ones would still be able to reach the planet, but they will have lost a good amount of their punch climbing out of the Black hole's gravity well.

 

[Razorback-PT]

Thats great, thanks Janus!

Travis King, I get your point, and if the astronomy wasn't such a vital part of the plot I'd agree with you. In this case, characters will actually discuss elements such as these.

But there's something else I've come to find when writing stories and doing research like this. By digging deeper I often find things that end up enhancing the story. The black hole turned out to be a blessing for many reasons. Keeping the flare storms in check is only one example.