BUILDING BLOCKS | PART 4 | SINGLE MOTHER SYSTEM and STELLAR EVOLUTION EFFECTS ON THE SYSTEM

THE HEAVENS AND THE EARTH...

Okay, need a help with an SMS? A Single Mother System, or CLASSICAL system, like our own, only one Star in the center.

The first thing I recommend is to draft your system in paper, a few lined circles should do the work, feel your system, edit if something doesn't feel right, add a moon aside, up or down the planet, or draw a inclined line across the planet to indicate any ring system you may like it to have...

Like this:

I have decided to keep it rather simple and add no moons for now, but we will do it later.

Now all we have is to name our planets and star:

It seems already good, let's put that to Scale, pick any planet from our Solar System and put it side to side with your planets, from known sizes of real planets we can figure out what sizes are our planets...

Heya, 2021 Valent here, sketching is cool and all, but never mind much about changing stuff as you learn more - it's part of the journey

Alright, everything okay with your planets?

Lets go back to the star, Vol.

Define its mass, and the other formulas will do the rest...

Here are the nominal parameters of Vol

It end up that this star is a G-type like our Sun, which means it's spectrum and composition are pretty similar to our Sun.

How similar? Well that depends quite a bit on the star's metallicity - for the Sun, that's about [Fe/H] ~ 0,0022.

The equation below will give you multiples of this value (1x, 2x, 3x...), based on star mass.

However, it will stop working when the mass is greater than 2,6 solar masses.

(because WHY would you need to go any higher?).

With metallicity in hand, we can start making some estimates for planet's around our star.

The mass of a terrestrial planet around our star can be determined based on Metallicity, Habitable Zone (HZ), and desired orbital distance (a) in AU, by:

If this sounds too much like a seven-headed serpent for you to solve, since Sun-like stars differ little in their mass-budget (as far as we can tell), we can simplify that to be hooked onto the Habitable Zone distance.

Now, for Gaseous planets there is no way to that in a simpler manner than:

For those of you that haven't noticed that yet - the less metallic, ie, the smaller the dust-to-gas ratio, the bigger are the gas planets around the star, and vice-versa.

Characteristics of most G-type stars are weaker Hydrogen lines, Calcium+ ions, ionized & neutral metals.

Bellow is a simulation of the Sun's spectrum:

And Vol's spectrum:

Notice how Vol's spectrum has more darker lines of Iron and Magnesium mostly, I opted for a high metalicity star cause I want very heavy-cored Ice giants along with a metal rich super-earth (Hool) to be explored. Helium lines are also stronger to 27% in contrast to the Sun's 24,85%.

Wanna estimate your star's age based on Hydrogen/Helium proportions?

The Sun currently fuses about 600 million tons of hydrogen into helium every second.

36 billion tons per minute.

2,160 trillion tons an hour.

51,84 trillion per day. 

18,91 quadrillion tons a year...

The Sun's mass is 1.988,55 septillion tons... 494,15 septillion tons are Helium...

Theoretically,  the sun produced ~87,175 septillion tons of Helium since its birth, 4,6 billion years ago, meaning that it was originally made of ~20,46% Helium.

Change is ~4% per 4,6 billion year.

~ +1% [He] per 1,15 billion years

If our star works at similar rate, and were initially made also of ~80/20... (Close G-type relative)

Change index is ~7%.

Then our star is  ~8,05 billion years old, 1,75x older than our Sun.

Then, if we want to date your star system's history, say like from the point we are now at 4,54Gyr, then all events in Paart's history will have happened about 3,5Gyr ago.

As it turns out, this star is old enough that any habitable planet around it could have evolved complex life from zero-point TWICE and a half (assuming it takes roughly 3 billion years for that), unfortunately it has only 3,6 billion years left, but it is enough so life could occur a 4th time before Vol becomes a blooming red giant.

(assuming somehow this planet biosphere died every 3 Gyrs  ugh  < .< ).

STELLAR EVOLUTION EFFECTS?

As we have covered in the last post, stars move through the HR Diagram as they age, our star is predicted to have a MS phase of 11,6 Gyr, being 8,05Gyr old, this takes our star to the far end of it's lifetime.

As such, it's predicted to be slightly cooler and larger than the Sun as it approaches the Red Giant branch.

Aged Vol parameters

Bellow, there is a chart showing both stars...

Whereas for T-Tauri Vol, it would have been way hotter but smaller and less luminous, at least half as luminous as the Sun.

Which means that planets would have formed much more closer to Vol compared to how far are the Solar System planet's from the Sun.

For instance, gas giants could form at 2,16 AU because of how much close is the T-Tauri Vol's Frost Line - while rocky planets could have formed as close as 0,0723 AU.

Let's plot what those changes would look like:

I have plotted Paart's orbital distance drift based on what seems right in timescales, explicitly calculating the exact path requires radical changes to the model I have already built with my team - HOWEVER, it should be no problem to one that starts with this new knowledge in hand.

We have it's path and stellar evolution such that, by the rise of the complex life, it will drift towards the mean Habitable zone.

What I did for my system back in 2019?

None of that, though it happens to be excusable in my case, if we consider planetary migrations - which I will tackle in a future post about the pre-solar history of the Volar System.

What I did instead at the time - was to use a Keplerian Distribution

If we take a look at our solar system, we will notice how planets are spaced.

Mercury -    0,38 AU

Venus -       0,73 AU

Earth -        1,00 AU

Mars -         1,52 AU

Jupiter -       5,24 AU

Saturn -       9,50 AU

- -

Johannes Kepler when measuring the Solar System, noticed that if we begin a sequence at 0, 3, 6, 12, 24, 48, 96... and so on, added 4 and divided by 10.

4, 7, 10, 16, 28, 52, 100... /10  =  0,4 AU, 0,7 AU, 1 AU, 1,6 AU, 2,8 AU, 5,2 AU, 10 AU...

It matches around the same proportions as the known planet's orbit.

Although, no one had found the planet that lies at 2,8~3,2 AU yet, between Mars and Jupiter, Daniel Titius, another astronomer at the time said "But should the Lord Architect have left that space empty? Not at all."

Since then, many searched the skies for the missing planet of Kepler, as himself wrote “Between Mars and Jupiter, I place a planet"...

After the discovery of Ceres, that orbits in this zone, astronomers could finally set their telescopes down cause they have figured out the solar system...

... BUT ACTUALLY, NOT THOUGH.

They had also found out some of other objects in the same zone as Ceres, at the time, they also included them in map of the Solar System, as this map of 1846 shows:

For reference, Vulcan was still believed to exist due observation of the wobble in Mercury's orbit until Einstein came up with his Special Relativity Theory, Mercury wobble was nothing more than predictable space-time warp by the Sun's mass.

Astronomers dismissed their planets to asteroid-tier (aster = star; oid = similar; asteroid = star-looking), because they were absurdly small, even more than Charon, moon of Pluto.

This orbital proportions are due to orbital resonances and planetary migrations, but that's for other day...

You could come up with values between 0,2x and 2,0x the previous orbit, from innermost to outer planets, that might do the trick as well.

For the Vol System, I came up with 0, 2,5, 5, 10, 20, 40.

For the first, I added 3.

For the others, I added +0.1 point according to each position after the star, and sum the previous orbit value.

And divided everyone by 10.

0+3+0.1, 2,5+0.2, 5+0.3, 10+0.4, 20+0.5, 40+0.6.

/10

0,31 AU

0,58 AU

1,11 AU <- Paart fell inside the Habitable Zone, yay

2,15 AU

4,20 AU

8,26 AU

I have put that comet orbit at 2,15 AU, and made it very elliptical.

Distances to scale, it looks something like this:

And for today that's everything folks, bye.

- M. O. Valent, 20/02/2019

- M. O. Valent, last updated 02/06/2021

BUILDING BLOCKS | PART 3 | STARS MIRROR SYSTEM COMPOSITION

HOLD ON, LITTLE BUDDY...

I know last time we met I said "Lets go crazy an create the planets of our system :D", well, that is quite true, but there is some restrictions related to planet building around stars...

Remember Part 1?

Stars that are rich in carbon, oxygen and other metals live for some longer amount of time, even tho those elements are no more than 1% in the universe (99.9% of the universe are stars as well) or even less.

This not only means that by mass, nearly 70~75% of the Universe is Hydrogen plus 25~30% Helium, but as far 99% the Universe is made of Stars, obviously they mimic this recipe as well, varying a little bit.

There's the Sun composition bellow:

Then, there is the Solar System planets mass chart bellow: 

Saturn and Jupiter are gas giants made of... Hydrogen, plus some ices from Uranus and Neptune which is made of ALSO HYDROGEN with some Oxygen and Nitrogen.

The inner planets, Mercury, Venus, Earth and Mars, make only 1% of the orbiting mass around the Sun, they are made of metals. The other 99% is Gas and Ice giants.

As we can clearly see, the Sun mimics the Universe composition, and the Solar System planets kinda mimics the Sun's recipe.

As from research (http://jtgnew.sjrdesign.net/solsys_sun.html):

Because the sun is well over 99% of the mass of the solar system, the sun's composition is effectively the solar system's composition, as well.

Individual objects, however, do vary from the solar composition, with some specific elements enriched relative to others (for example, even though silicon is a much smaller component of the sun than carbon, silicon is highly enriched in Earth's crust relative to carbon)

So, if a star lacks any Oxygen, Iron or Sodium in its spectrum, there is NO REASON why these elements should appear in the planets of its system.

Another conclusion we can take of is that, Metal-Rich stars, ie, the ones with a large Metallicity index can have denser and larger planets made of those materials rather than the ones with smaller index.

The index works in the following logarithmic power of 10:

Sun is 10¹ in metals. Ie, near 1,8% by mass of the Sun is metals (non-H/He).

Star that is 10^+1, is 10% by mass made of metals.

Star that is 10^-1, is 0,1% by mass made of metals.

Star that is 10^-2, is 0,01% by mass made of metals.

The first stars might had -6 index, less than 0,000001% or none by mass made of metals.

The Red Giant Arcturus in Boötis, have index of −0.52, ie 30% of the Sun's metal index, in other words, nearly ~0,54% of Arcturus by mass is made of metals.

As we can also deduce, cool stars like red dwarfs do not produce enough energy to rapid intense fusion, so, like we find in gas giants, we may find molecules like silicates, ammonia and methane vapor in its atmosphere spectrum, on the other hand, in violent fast living stars, most of those elements are in mono-atomic plasma state, ie, instead of silicate compounds, there is free Oxygen and Silicon in spectrum.

This turn out to be true as we observe the spectrum of metal-rich stars and metal-poor stars.

The darker line is from a star called Pristine-221, as you can see, its spectrum has peaks at Hydrogen and at Calcium lines but it remains pretty continuous, in contrast, our Sun has varied peaks from various metals, including a great prominence in Hydrogen/Helium ones.

We can see lack of any metals in Pristine-221, carbon-free almost, and it is very unlikely this star ever has/had any planets.

We can see now see WHY  we choose stars F to M as candidates for harboring planets with life.

The exact proportion for our star is 99.8% of the system mass is the Sun, and the other 0,2% are the planets.

Lets call this ~0,25% value our SOLAR AVERAGE.

And take the 1% as MAXIMUM MASS OF PLANET SYSTEM.

Well, given what we now know about stars, and the physics of whatever system they may have, lets go to some examples:

Your star is a Red Dwarf with 450x the mass of Jupiter, the largest a system can get around it is ~1%, or 4,5 Jupiter masses in total mass. Solar Average is 1,1 Jupiter mass

Your star is a Orange dwarf with 0,75 the mass of the Sun, the largest a system can get around it is ~1%, or 7,5 Jupiter masses in total mass. Solar Average is 1,8 Jupiter mass.

For reference, Jupiter and the Sun are roughly the same density (same materials duh), 1 mass of Jupiter is equal to 0,001 Solar Mass.

Expect the summarized mass of your comets and asteroids max out at 15% the mass of the Moon. For reference, all asteroids in the Solar System are 4%.

Use what you've learned here to check IN and OUT your planets, next time we will see how to arrange them in a single-star system.

- M.O. Valent, 19/02/2019

BUILDING BLOCKS | PART 2 | PLANETS

LET THERE BE DRY LAND...

Planets are the main background in our stories, like dimensions in a magical universe, each planet is a different world, containing different many environments in itself...

The planets in your stories could be of all types, from rocky hot Mercuries, cold deserts like Mars, or hot Jupiters, or similar to Earth in some extent...

Whatever planet or moon you may choose, keep in mind that everything can be written down to math.

All values, for Density, Mass, Radii and Volume will be given in Earth relatives, ie, Earth values are equal to 1.

For reference, Earth density is around 5,51 g/cm³. Is very recomended your density wander in the realm of solid stuff like silicates and metals, unless you are building a Waterworld or a Gas giant.

Theoretically, habitable worlds "comfy" stats goes as:

g = 0,68 ~ 1,5

M = 0,4 ~ 2,35

R = 0,78 ~ 1,25

But could go as far as these, if you extrapolate habitability for settling:

g = 0,4 ~ 1,6

M = 0,1 ~ 3,5

R = 0,5 ~ 1,5

These last Extensive values includes worlds as small as Mars in mass, gravity and radii, just for comparison.

As for density, you can easily solve through directly crunching the numbers into average values, for rocky planets, use densities similar to Earth, or go through material densities, if they are abundant.

Here is a list of metal densities for use:

Element	Symbol	Density g/cm3
Actinium	Ac	10
Aluminum	Al	2.70
Antimony	Sb	6.68
Barium	Ba	3.62
Beryllium	Be	1.85
Bismuth	Bi	9.79
Cadmium	Cd	8.69
Calcium	Ca	1.54
Cerium	Ce	6.77
Cesium	Cs	1.93
Chromium	Cr	7.15
Cobalt	Co	8.86
Copper	Cu	8.96
Dysprosium	Dy	8.55
Erbium	Er	9.07
Europium	Eu	5.24
Gadolinium	Gd	7.90
Gallium	Ga	5.91
Gold	Au	19.3
Hafnium	Hf	13.3
Holmium	Ho	8.80
Indium	In	7.31
Iridium	Ir	22.5
Iron	Fe	7.87
Lanthanum	La	6.15
Lead	Pb	11.3
Lithium	Li	0.53
Lutetium	Lu	9.84
Magnesium	Mg	1.74
Manganese	Mn	7.3
Mercury	Hg	13.53
Molybdenum	Mo	10.2
Neodymium	Nd	7.01
Neptunium	Np	20.2
Nickel	Ni	8.90
Niobium	Nb	8.57
Osmium	Os	22.59
Palladium	Pd	12.0
Platinum	Pt	21.5
Plutonium	Pu	19.7
Polonium	Po	9.20
Potassium	K	0.89
Praseodymium	Pr	6.77
Promethium	Pm	7.26
Protactinium	Pa	15.4
Radium	Ra	5
Rhenium	Re	20.8
Rhodium	Rh	12.4
Rubidium	Rb	1.53
Ruthenium	Ru	12.1
Samarium	Sm	7.52
Scandium	Sc	2.99
Silver	Ag	10.5
Sodium	Na	0.97
Strontium	Sr	2.64
Tantalum	Ta	16.4
Technetium	Tc	11
Terbium	Tb	8.23
Thallium	Tl	11.8
Thorium	Th	11.7
Thulium	Tm	9.32
Tin	Sn	7.26
Titanium	Ti	4.51
Tungsten	W	19.3
Uranium	U	19.1
Vanadium	V	6.0
Ytterbium	Yb	6.90
Yttrium	Y	4.47
Zinc	Zn	7.14
Zirconium	Zr	6.52

Lets say the planet I want to build is 70% Iron, 20% Titanium, 5% Tungsten, 3% Bismuth, 1% Nickel and 1% Water Ice, because I want a very cold metal world, like a mining colony for instance.

ρ = %(ρ A)+%(ρ B)+%(ρ C)+%(ρ D)

ρ = 0.7*(7.87)+0.2*(4.51)+0.05*(19.3)+0.03*(9.79)+0.01*(8.90)+0.01*(0.92)

ρ = 7.7679g/cm³  or  1,4x Earth's density

 

Even tho you might already know what to make, I wanna show you new possibilities:

Super-Mercury

You know the planet Mercury is very dense, it could be summarized to being a big iron ball with a thin layer of rock over it. Know what's better than making a Mercury-like world in your system? Make it real BIG, a Super-Mercury.

Super-Earth

The planet Earth is cool, may universe hide smaller versions of Earth, like Venus would have been in the past, but why not make it big? Most of the terrestrial exoplanets found are Super-Earths, larger, heavier, but still habitable having not so strong gravity and lots of land and sea to conquer.

Puffy Worlds

The opposite of a Super-Mercury, a puffy world is a planet made of light material, like silicates and aluminum, rather than Iron and Nickel. Imagine a world the size of Earth, but with 2/3rds as Earth's gravity.

Helium Titans

Gas giants are huge, take Jupiter for instance, the entire Earth could fit inside its Great Red Spot, but what if some gas giants were made from heavier materials? The second most abundant element is Helium, with the mass of 2 Hydrogens in itself, so it's not rather possible, but totally likely that any gas giant might form not from only Hydrogen but maybe 20% to 90% Helium, imagine, a Jupiter sized giant, but weighting twice as Jupiter, this could lead to some crazy heavily packed systems. Imagine explorers around a new discovered planet, smaller than Saturn with apparently way more moons and heavier ones than it could theoretically hold, but ends up that by being made of Helium, and having half radii as Jupiter, having the same mass, its gravitational pull would be 4x as powerful as our king of the planets.

Now, lets go crazy an create the planets of our system :D

- M. O. Valent, 19/02/2019