Fictional star and planet system

[Suprihen]

Hello, I'm new to this forum and, to go right to the point, I created a fictional solar system for a tabletop RPG, appointing some characteristics that I want it to have, but I can't handle the physics to bring up the numbers - so I came here. To simplify it, this system only have 1 planet, and 1 star.1. Here is what the star must look like to a person on the surface of the planet:

• 1a. Slightly smaller in appearance than the sun;
• 1b. Redder than the sun;
• 1c. Slightly less bright than the sun;

2. About the orbit:

• 2a. To complete an orbital period, the planet should take either 2.150 years or 25.800 years, the last one being preferable;
• 2b. Either way, each season should not surpass 10 years, ideally with 7 years.

3. About the planet:

• 3a. Identical to Earth (including 24h day/night).
• 3b. Posses a solo and dense ring around it (I have no idea if this is possible with smaller planets, but in regards to the story a ring is mandatory, so I'm abdicating on plausibility to keep this one, if necessary). In addition, the ring is always aligned right into the star's direction.
• 3c. Posses three natural satellites: one bigger than the moon (2x to 4x), one roughly the same size of the moon, and one smaller than the moon (4/5x to 2/5x).

4. About the star:

• 4a. Preferably, it should be larger than the sun – anywhere above 100 (one hundred) times larger in diameter will do, so I will set the ideal to 150 times larger in diameter. This information can be changed if it is impossible to achieve 1 and 2 with it;
• 4b. Must deliver roughly the same amount of anything the sun delivers to Earth (light, heat, radiation etc...) so that the fauna and flora of the planet keep similar to Earth’s.

Given the info above, and fulfilling the criteria as best as reality permits, what I need to know is, summarizing:
A -- How far away from the star should the planet stay, in au?
B -- What is the minimum and maximum range of the habitable zone?
C -- How much time will the planet take to complete one orbit around its star?
D -- How long will each season last?
E -- How would the ring be observable from the surface of the planet during day and night? Would it be clearly visible in the sky? Would it cast a shadow over the planet, or would the star's light simply overcome it?

Obs.: I brought a one planet one star system to don't overcomplicate, but if the addition of more planets is necessary to make the first planet reach the criteria proposed, it can be done.

Thank you for your time!

 

[Vanadium 50]

Can't do it. 1a, 1b and 1c contradict 4b.

 

[Suprihen]

I see, so considering that 4b is more important than 1a, 1b and 1c, I prefer to nullify those last three. Although, if the changes in life form on the planet where to be not so dramatic, in order to maintain at least similar cosmetics, I could go for that.

 

[Bandersnatch]

Hi Suprihen.

As mentioned by Vanadium, there are some issues with your setup, but before posting a lengthier response, I'd like to ask a few more clarifying questions:
Do you intend for the planet to have a natively evolved life, or is it a recently colonised world with little in terms of native life? (this will constrain the age of the star, and consequently many of its other properties).
What is the purpose of the size (radius) requirement for the star? Is it a hard requirement?
Are the desired revolution periods in thousands of years, or is it 2+ and 25+ years respectively?

 

[Loren]

Try this website. It will take you a few passes to sort everything out, but once you understand all the variables you can get some detailed and meaningful results. Essentially, it is a solar system generator or calculator.

The site author also provides the mathematics and physics behind his calculations.

Multiple moons is tricky. The interaction between them usually causes the system to become unstable. Your ring would be an example of such an instability gone bad. Rings do not last long, so a recent event (on geographical scales) would have caused the ring, so there would have to have been even more moons.

You might look at a program called Astrosynthesis. It will cost you $35, but you can model orbits of moons, planets, etc., fairly well. It will let you create your own solar systems and even multiple star systems if you want.

 

[Suprihen]

Thanks for your replies.

I would like to highlight here on the beginning that I ended up using more conservative figures for this fictional solar system, generated with this, this, and this; although I would still be glad to know if I interpreted correctly the numbers I got, if possible - I'm not sure if I should open a new thread about it, as the descriptions and questions on the last paragraph of this post deviates from the original post.

Bandersnatch, I was indeed too specific on a subject I have no clue about, but now after a few days digging on it, I can see more clearly some of these impossibilities that you and Vanadium indicated. About the radius, the requirement of it being large was all about the star fitting, from the perspective of humanoids on the planet, into a circular shape in the sky (described below), while still providing enough luminosity and heat to sustain life, so I figured (wrongly, I suppose) that increasing the radius would allow the star to be more far away from the planet, thus reducing its apparent size while keeping a Sol like effects on it.

In regards to the forms of life on the planet, they are both natively evolved and colonized, with the latter happening approximately 26.000 years ago. Although there is another major force propelling evolution and probability of life, besides natural selection, I had intended for the age of the star, and consequently the planet, to be a close fraction from our sun and earth, which now seems impossible for this (yes, expressly) 2+ thousand years and 25+ thousand years revolution period, which I suppose that would demand a very distant orbit, and additional implications to the star in order to maintain it's desired effects, possibly including mass, and if so, correct me if I'm wrong, reducing too much it's life span. I didn't brought the reasoning behind the requirements before to not over length the post, besides, I was more inclined into hard science fiction, so the fantasy bits were intended to be an add on rather than a major factor.

Loren, I will definitely be looking at these tools, specially for the next solar systems I may create as the story progresses. About the stability of the moons and the ring duration you mentioned, I'm now going to take the easy path and use the anomaly at the center of the circular shape I mentioned before to justify it.

What I have got now for this fictional solar system, all calculated on these two web sites I mentioned, is a star with a initial mass 50% greater than the sun, with a planet 2,93 au away from it. The revolution period is 1497 days, thus approximately 4 years. The planet is expected to go through about 1/4 of the period of time that Earth has inside the habitable zone. The luminosity is almost 5 times greater than the sun at the beginning, when the planet is on the outer edge of the habitable zone, and between 7 and 8 times when approaching the end. In addiction, if I got the numbers right, the apparent magnitude of the star is -34,18, while the sun's is -26,64, so I'm assuming, and I need confirmation, it looks bigger in the sky than the sun, even being almost 3 au from the planet. As a result I had to stretch the perceivable length of the circular shape on the sky, which is, to be more accurate, an eye shaped structure formed by a bifurcation on the trajectory of the ring. Being always aligned between the center of mass of the star and the center of mass of the planet, the 'pupil' of the eye becomes the star from terrestrial perspective, generating a distinctive view when one of the moons eclipses it. These eclipses are now replacing the 365 days, 2.150 and 25.800 time marks that I initially settled for the orbit of the planet. As a direct implication of the 1497 days orbit, I'm assuming that I have now four seasons during a more eccentric orbit than Earth's (caused by the other planet's interference), with, respectively, 390, 240, 390 and 477 days - I didn't determined the eccentricity or calculated the seasons numerically, so these differences in days might just be too high to keep the planet within the habitable zone. Additionaly, I increased the axial tilt of the planet, which I'm assuming that causes a greater climate change between seasons. To put it in numbers, the seasons are looking like this on the temperate zone:

1) 390 days; North: 12ºC; South: 23ºC
2) 240 days; North: 26ºC; South: 42ºC
3) 390 days; North: 12ºC; South: 23ºC
4) 477 days; North: -25ºC; South: 0ºC

For the time being, I don't know where to put the solstices and equinoxes, or if the ring, being dense, is in fact casting a shadow on the planet, so I could use some hints.

 

[Bandersnatch]

if I got the numbers right, the apparent magnitude of the star is -34,18, while the sun's is -26,64, so I'm assuming, and I need confirmation, it looks bigger in the sky than the sun, even being almost 3 au from the planet.

This bit is incorrect. The apparent magnitude of the star at 3 AU must be the same as that of the Sun as seen from Earth - if you want the planet to have the same irradiation. A -34 magnitude would indicate over 300 times more energy reaching the planet than what we're getting here.
(Apparent magnitude is just another measure of energy flux (or irradiation) at a given distance.)

The star, with its 1.5 solar mass, has barely over 1.2 times solar radius (the mass-radius relationship is approx. proportional to $M^{9/19}$). The mass also dictates higher temperature and ~7* times solar luminosity, which means that it emits much more energy per surface area than the Sun does. As a result, to keep the total energy received by the planet comparable to Earth's, the star has to be farther away (the ~3 AU you got). A disc of 1.2 solar radii at 3 times the distance between Earth and Sun would have 1.2/3 times the angular diameter of the Sun on the sky (i.e., approx. 0.2 degrees). It would be a rather quite smaller disc, but blazingly bright.

A star in the main sequence with that mass would also look much whiter in colour than the Sun does, perhaps with a slightest tinge of blue. I'm not sure if you still hold the redness of the star as a requirement, but if you do - you should drop it. The only stars that are red and are not in their death throes (i.e. red giants), are the least massive, dim ones.
You could still get a reddish tinge to the way the star looks by having an atmosphere with lots of dust (like on Mars?), or just very, very thick (think how the Sun looks at sunsets). But then again, that'd pose more questions - why is it so thick? How does it change the climate? etc.

*(you should assume it's near the latter parts of its life, so that despite the short lifespan of ~3 billion years the evolution of native life would sound plausible)

I'm not entirely sure I understand what the setup is with the rings and how they conspire with the star to produce the 'eye', so I'm not going to tackle the planetary bits now.

 

[Loren]

More on planetary rings.

Any planet in the habitable zone will likely be too close to its parent star to maintain a ring. Tidal forces will tear them apart.

As I stated before, they need to be a geologically recent event such as a moon in an orbital decay where it finally came within the Roche's limit and was torn apart.

They would make a spectacular display for those planet bound. Imagine a great white arc subtending across the day lit sky, perhaps even banding within the ring might occur. At sunset the rings would probably take on a blazing reddening color. At night they would occlude sections of the sky, blotting out stars where that part of the ring falls within the planet's shadow.

At the equator or at least along the ring's equatorial plane it would be all but invisible, so the further north or south of the equator, the better the view.

Latitudes above the tropical zones on the planet during the winter time would experience additional loss of sunlight due to the rings blotting out a significant portion of the solar energy. Winter could be pretty brutal.

 

[Suprihen]

To set this arrangement of star and planet as definitive, I will summarize the present features, along with the points that require further clarification.

So, the specific features are these:

Planet distance from the star: 2,94 au.

Current age of the system: 2.5 billion years. The planet is expected to support life for another 140
million years, according to the simulator.

Orbital period: 4,11529 years.

Star mass: 1.5 Msun.

Star radius (2.5 billion years after star system formation):
- Bandersnatch, you mentioned 1.2 Rsun, while the simulator gave me 2.45 Rsun, any clue on what could be the source of divergence.

Star luminosity (2.5 billion years after star system formation): 7.52 Lsun.

- I am having trouble picturing what this luminosity implies. I can cover our current solar disc and its corona with the palm of my hand. A >7 Lsun means that I would not be able to do that? Or it means that the brightness would simply be more intense (like the comparison between a common lantern to burning magnesium )?
- Furthermore, during day light, a >7 Lsun would make everything on the surface of the planet look like it is under dozens of reflector lights, or would this luminosity just resume to the aspect of the star on the sky (since the planet is ~3 au and presumably getting similar amounts of energy)?

Spoiler: Landscape brightness

- Basically, supposing the picture on the left is Earth, will the landscape on this planet look like the picture on the right during day light?
- Yes, I've dropped the redness of the star.​

Star temperature (2.5 billion years after star system formation): 6140 K.

Planetary ring: Formed only 1 million years ago, from a fourth moon that slowly approached and, eventually, entered the Roche’s limit, collapsing into a ring around the planet.

- Loren, you mentioned that the event originating the ring system must be geologically recent, with the tidal forces of the star tearing it apart as time goes on. Now on top of that, I’m picturing the eccentricity of this planet’s orbit to be generated by the influence of other planets, maybe gas giants. Accounting for these two factors: the star and the other planets influence, would the ring system hold itself for at least 300.000 years? Knowing that anatomically modern human beings date from at least 200.000 years, I would like that the native intelligent life coexisted for, if not all, at least a great length of the ring system’s life span.
Aside from this initial ring formation, I’m planning for it to leave its natural aspect due to the approximation of an anomaly that will alter it’s original form as shown below:

Spoiler: Ring system evolution

- I’m assuming the 3rd stage, and final form, does not have that much of an impact on the temperate zone’s climate, as you mentioned for the 1st stage ring system, due to it’s much thinner width. Additionaly, with the 3rd stage cylindrical shape, I’m also assuming it is now visualized equally from any given location on the surface of the planet.​

Life on the planet:

Spoiler: Not crucial to the topic. May give a clue about what I have in mind.

This universe is supposed to be a very close reflection of our own: there is only one single universe, but it has multiple ‘frequencies’, all tied together, but almost undetectable from each other. The actual human civilization evolved on one of these frequencies, becoming a multitude of individual engines that shelter conglomerates of consciousness (brains in a jar) harvesting the energy of the stars to power their survival, along with their individual and detail-rich virtual realities, in which they lived self-generated dreams.

Although at this stage the civilization already had inconceivable amounts of knowledge, the impossibility of reaching information about the other frequencies of the universe reflected into various uncertainties regarding quantum level phenomena. Some of those phenomena, combined, escalated inside a few of the conglomerates of consciousness (CC) - pretty much like a virus - to bring back the reproductive behavior of the human sub consciousness. When this happened, the ‘infected’ ones started multiplying uncontrollably. While some of the CCs managed to switch off from the virtual realities, most of the others began to grow exponentially through the whole universe, spreading and harvesting every single star in just a couple of millions of years.

The remaining minority of the switched off and non-infected branch of humanity assumed the form of the classical gray alien – the last ancestor of the Homo sapiens sapiens capable of natural reproduction. They had huge life spans and even greater intelligence, which was used to design a way out of the current frequency while defending the last solar systems from the voracious infected CCs. The result of this technological leap were the ‘emissaries’. These engines were activated using a colossal amount of energy retrieved from captured CCs, and were able to escape the present frequency and enter a new one, in which takes place the game’s campaign setting. The points from which the emissaries came into the new frequency of the universe are the anomalies that I’m referring. These are undetectable oddities with unpredictable effects over matter and energy. While both the old and the new universe frequencies (abbreviated OF and NF) assumed a rare Earth hypothesis, were the probability of occurrence of life is extremely shallow, a different factor plays on the NF: the ‘cindra’.

It is a substance (not energy, not matter) that flows from another dimension, aside from the four space and time dimensions, and interacts weakly to anything that is composed of complex molecules organized into some kind of pattern. Additionaly, it interacts much strongly with anything that manifests awareness – or consciousness – of it’s surroundings, although only being reported on biochemical brains. The cindraimpulsionantes life towards complexity and once the organism becomes conscious, the cindra starts taking the shape of an ‘anima’, much like a soul, that incorporate itself mostly inside the individual’s freudian ‘Id’, and vestigially into its ‘superego’. When thrown at life and death situations, the anima will learn and adapt, propelling the species physically and biochemically towards the apex of its evolution, along with that specific individual’s fitness, which translates into incredible mental and physical prowess – this explains why some characters have superhuman capacities. As a result, the NF has a similar origin of life probability than the OF, but once it does emerge, the complexity of this life explodes much faster.

Consequently, the native life on the planet evolved in just about 0,95 billion years, which includes 8 different intelligent and civilized life forms, along with 6 different species descendants from the original Homo sapiens sapiens ancestor that arrived 25.800 years ago, brought by the emissaries through the anomaly. New and sensible to the ‘cindra’, they diverged very fast originating these 6 distinctive species. In the process, they lost their ‘gray alien’ appearance and became essentially similar to modern day humans, with one of them being indeed cosmetically very close to the humans we know.

Summarizing, native complex life evolved on the planet within 0,95 billion years, including 8 intelligent native species and 6 intelligent outsiders that arrived 25.800 years ago.

Orbital eccentricity of the planet, axial tilt and seasons: As mentioned before, both the planet’s orbit and its axial tilt are greater than Earth’s, with the intent of having asymmetric and sharply different climates between them. Although its not a priority to achieve precise figures for these parameters, I need to know if the numbers I’ve got sound plausible – four seasons on the temperate zone, with 390, 240, 390 and 477 days and their respective temperature variations. Aside from that, here are some other issues:

- The Kepler’s Laws are bugging my brain about where to place the solstices and equinoxes. To illustrate the question:

Spoiler: Seasons and eccentricity

- Unless I’ve understood something wrong, our actual seasons are divided conventionally to match the solstices and equinoxes. I preferred to set the season divisions exactly at the middle of such events, so that the coldest point of winter would be at it’s middle, and the hottest point of summer too. With an eccentric orbit, however, it got unclear to me where these solstices and equinoxes should be. Looking at the picture, it seems like the solstices would happen right in the spatial middle of the seasons they refer to, namely, around the day 120 of the season 2, and the day 238 of the season 4. Supposing that logic is right in the first place, I still don’t know where should the equinoxes be.
- I’m still very clueless about how the weather will be near the equator. Supposing a axial tilt of 35º, for example, will that mean that the equatorial belt will have less time of direct perpendicular light hitting it during the course of a full orbit, in comparison to our ~23,5º?​

Natural Satellites: moon S (0,9 moon masses); moon F (0,4 moon masses); moon A ( 1,8 moon masses).
- Is it possible for moon F to have an elliptic orbit, and/or perhaps an occultation by the other moons that would cause it to be clearly visible only from time to time? For example, only for 15 days in each 75 days period.

Eye on the Sky: To clarify what I have in mind, here is a schematization:

Spoiler: Eye structure

- Consider that the center of the eye structure is always aligned exactly between the planet’s and the star’s centers of mass. Is there a combination of the width of the eye structure and it’s distance from the planet that allows the star to be, from the perspectives of observers on the ground from points A to G, always inside the eye structure? I know a simple way to do that would be expand the eye to a width above that of the planet, but, maintained the proximity, that would also make it surround most of the sky, thus loosing it’s ‘eye’ similarity.​

Any question answered greatly advances my setting’s details and verisimilitude, so thanks again for your replies.

​

 

[Loren]

Wow. I can't speak for the luminosity and other characteristics you cite, but the rings disturb me.

What mechanisms cause the diversion? Even shepherding moons would not do something so strange.

Each particle in the ring obeys orbital mechanical laws, so imagine a spaceship in orbit following that twisted path. Each deviation in the orbit requires energy to turn it out and then back in. Where is that energy coming from?

If it is the planet, then something must give due to the law of conservation of energy.

I think a standard ring would be fine for the ages you describe, but I can't wrap my arms around what you propose.

 

[snorkack]

Planet distance from the star: 2,94 au.
Star radius (2.5 billion years after star system formation):
2.45 Rsun

Star luminosity (2.5 billion years after star system formation): 7.52 Lsun.

- I am having trouble picturing what this luminosity implies. I can cover our current solar disc and its corona with the palm of my hand. A >7 Lsun means that I would not be able to do that?​

That depends on star radius, not luminosity!
And on apparent radius - not actual radius.
Divide the radius - 2,45 - with the distance to it - 2,94.
What I get is 0,83.
The disc would look smaller, not bigger

Or it means that the brightness would simply be more intense (like the comparison between a common lantern to burning magnesium )?
- Furthermore, during day light, a >7 Lsun would make everything on the surface of the planet look like it is under dozens of reflector lights, or would this luminosity just resume to the aspect of the star on the sky (since the planet is ~3 au and presumably getting similar amounts of energy)?

The luminosity would be dimmer - even though more intense.
Divide the absolute luminosity - 7,52 Lsun (was it visible or bolometric?), with square of distance. I get 0,87.