Hello,
have you always wondered how could you possibly plan a realistic planet in a fictional setting respecting the law of physics to make it feel real? Wonder no more, follow these steps and you too will be able to plan your personal planet and star B-)
STAR AND GOLDILOCKS ZONE
The first thing you need to decide is how's your star made and how CHONKY it is.
Decide in a percentage of solar masses; for my example I'll take a 1,01 solar masses star, in the fictional manticorae constellation, called eta manticorae. That makes our star tally a total mass of 1,01* 1,989*10^30 kg, around 2,008*10^30 kg. That's not much of a CHONK, in stellar standards
Now, look online for an habitable zone calulator and fiddle with the parameters until you get some numbers you're happy with. Inputs include (mine in parenthesis):
metallicity (0,02)
Helium to metal enrichment ratio (standard=2)
Equilibrium temperature of outer boundary (200°K)
albedo of planet (0,25) (how much the planet reflects incoming light; high for a planet shiny like a mirror, low for a planet that absorbs light like a mofo. Earth is 0,3 if I recall correctly)
You will get results like these
Diameter of longer habitability dm=1,42AU (astronomical units, look it up)
time of longer habitability tm=10,62 Gyr (Giga-years, or billion years)
Width of half habitability zone W=0,84 AU
Internal radius ri=0,94AU
External radius re= 1,96 AU
This means that a planet 1,42 AU away from Eta Manticorae would be suitable to live on for 10'620'000'000 years, a planet distant 1,42±(0,84/2)AU from Eta would be habitable for at least tm/2=5'310'000'000 years, and between 0,94 and 1,96 would be habitable for at least 4'000'000 years
I decided randomly and the planet ended at 1,51AU
GRAVITATION AND PERIOD
The universal constant of gravitation is6,67408*10^-11
Multiply that for the mass of your star and you'll get the gravitational constant of the star.
For Eta is 1,34*10^{20}
To calculate the period:
put the distance from the planet you calculated in meters
Elevate to the third power
Divide for the gravitational constant
take the square root
multiply by 2*pi
the result will be in seconds
I get P=5,828*10^7 sec
Converting into hours that makes 16189, slightly less than mars period
DAYS AND YEARS
Now you need to figure the arrangement of hours per day, days per month and months per year
16189 is prime, so I take 16188, that means the calendar will skip a beat every 16189 years. We'll live.
Looking at the factors of 16188, we can do 426 days of 38 hours each or 852 days of 19 hours. To not get crazy with months and day per month I pick the former. Days are extremely long but no matter. The planet turns proportionally slowly, so that means we need a beefy planet to keep an atmosphere and a magnetic field
426= 2*3*71, so my options are 2 months of 213 days each, 3 months of 142 days or 6 months of 71. None of them seems viable, so I decide to pull a sneaky and do even months of 36 days and odd months of 35 each.
Given the same number of months I can keep the names as they are, otherwise you might change it
APSIS
Now we need to determine when the planet is at the nearest point from the star (periastron), and the farther (apoastron)
I determined casually the periastron taking a random number between 1 and 16188, getting hour 3209; doing the math that results to be the 17th hour of day 84, or two hours from noon of the 13th of "march".
Logically, adding half a year I'll get the apoastron, that means 3209+(16188/2)= 11303 hour. As expected that'll be the 17th hour of day 297, i.e. 13th "september"
EQUINOXES AND SOLSTICES
Now we need to determine solstices and equinoxes. Taking a random number for the first equinox I get hour 2172, that is 6:00 of day 57, or February 22nd.
Adding a quarter of year each time and doing the math:
equinox 1: 22/02 h 6:00
solstice 1: 21/05 h 25:00
equinox 2: 22/08 h 6:00
solstice 2: 21/11 h 25:00
Now, if we assume, on the contrary of planet earth, an omogeneous distribution of emersed land between the northern and southern emisphere, the harshness and distribution of the seasons will be determined only by the position relative to Eta Manticorae.
AXIS AND SEASONS
To determine the inclination of the rotation pole from the perpendicular to the orbit's plane, I take a random number between 45° and -45°. I get -9°.
That settles three things:
since the inclination is less than half than earth's, that means Eta's light hits the planet a whole lot more consistently through the course of the year; that means seasons are milder.
On the other hand, that means that the equator gets much more heat and the poles much less. That in turn signifies that the equator areas are likely Savannas and deserts, while the polar zones are cold deserts and tundras. This also entices a more fierce temperature regulation: stronger north-south winds and a more likelihood for violent precipitation.
A negative value indicates an opposite behavior from earth's own climate. The planet during the first solstice is oriented "the other way" compared to earth. The first equinox is the day of minimum radiation for the northern hemisphere and maximum for the southern; vice versa for the second solstice.
In summary, the northern hemisphere's seasons are as following:
22/02 - 21/05 autumn
22/05 - 21/08 winter
22/08 - 21/11 spring
22/11 - 21/02 summer
Now we need to consider the distance of the planer from Eta related to seasons. The periastron is reached march 13th, in the northern autumn. That means the northern autumn/ southern spring are warmer than the earth's counterpart, while the northern spring/ southern autumn is colder than what we used to.
This is turn means that the seasons are even milder than we thought before, and the northern hemisphere is the 'cold' one, while the southern is the 'warm' one
Given to the duration of the day, we have two possibilites:
the planet turns at half speed compared to earth and it has roughly the same mass; I want to avoid this becasue that'll mean it hasn't enough mass and spin to keep an atmosphere
the planet has half speed and double mass. This means a thicker mantle and a thicker crust. The magnetic field I think would be comparable to earth's.
LIFE?
To be inhabitable by humans, the planet need to have loose oxygen in the atmosphere. This means that anaerobic microorganisms need to develop in the water, to free the oxygen from the other gases like ammonia vapors, methane and others that tend to form on planets
From there life could have formed but nothing says it went the same way earth life did. It all depends to which ancestral specie won the land rush. Maybe none did and the planet is still barren, or without 'grass', or without 'wooden' plants
CONCLUSION
Thank you for reading, I hope this was informative and gave you the right knowledge to plan your own planet. Feel free to share/ discuss the topic in the comments :)
Nick out, peace