Need astronomy/physics advice for planned planet

I've had a play around with the formulae on projectrho.com to come up with a suitable planet on which to set a story and I'd like some of the more astronomy-savvy tropers to check my calcs and reasoning, please.

I found a site that had Temp, Luminosity and Mass for Spectral Classes not recorded in the tables on projectrho and then I basically made a spreadsheet with the formulae and changed the value of received sunlight (within tolerable, habitable bounds) until I got numbers that "looked interesting enough for a story."

Here's the basic run down of what I've come up with and the assumptions I've made:

Star = G 1 V - about 1.03 x Solar mass, 1.1 x as much Luminosity and only a little larger (4583.5km greater diameter), according to the figures I found for a G1 Main Sequence star and the formula for calculating the diameter of a star.

At 1x the amount of insolation that Earth receives, the year wound up over 380 days long so I played with the insolation level as previously mentioned and got the following:

Planetary orbit = 1.02AU

Year = 372.175 Earth Days - which is near enough to 372.175 local days as the two are not significantly different (arbitrary slowing of planetary rotation to be close enough to Earth's so as to be negligible)

This means that every six years, there needs to be a "leap day" to realign the days. Every 120 years, another leap day needs to be added as the extra 0.04989 days (about 1.197 hours) every six years will gradually accrue. By the time they need further adjustment to mop up the balance, they'll've probably switched to a different calendar.

An Earth-born human living on that planet for 53 local years will be a little over 54 Earth Years older than when they arrived, having "gained" around 6.9 days over an Earth year with each local year.

Star appears only a smidge bigger in the sky than Sol appears from Earth (Angular diameter of .54 rather than .53 degrees) - not enough for the average immigrant to notice as who pays that much scrutiny to the sun?

Sunlight = 1.0519 x what Earth receives, I figure the mean temperature can be said to be around Earth normal - not noticeably hotter - depending on Bond Albedo and Greenhouse Factor differences between the planet and Earth. I played with both on the formula and leaving Bond Albedo equal to that of Earth but dropping the approximate Greenhouse Factor from Earth's approximate 1.1 to 1.09 brought the temperature down to around what I had previously calculated for Earth.

I'm sure that there's been enough variation in Greenhouse Factor on Earth to more than cover any insolation-related differences in Mean Temperature.

Any screw-ups in my numbers or assumptions? Anything I would need to be especially mindful of so far as differences between this world and Earth?

Axial tilt seems to be another "pick whatever value you like within reasonable bounds" (like insolation level and planetary rotational speed) so I was thinking of giving the planet a tilt of around 21-22 degrees from vertical which would give somewhat less variation in day length between midwinter and midsummer.

If anyone knows how to calculate solstice day/night lengths based on axial tilt or can point me to a suitable resource, that would be appreciated.

Next thing I've got to do is work out a decent moon for the planet!

The length of the day/night during the solstice depends not just on the axial tilt, but also on the latitude. If my math is correct, the length of the day/night (whichever is shorter) is given by:

 (solar day / 180) * arccos(tan(tilt)*tan(latitude)) 

The formula doesn't work for latitudes greater than the tilt, in those cases it's continuous day or continuous night.

Thanks for that. Yet another useful calculation for my growing spreadsheet.

Last night I found the calculation for sidereal period of a moon here and cross-cancelled until I could solve for r given T and M as I want to be able to give my planet a "month" of a suitable length to suit the year.

I recall that I once found formulae for calculating the orbits of moons and whether or not they would be tidally locked or free to rotate at various orbits but I can't for the life of me find them now.

Edit: What units do I use for solar day and get out? I tried 24 hours and got .209 as the result. Where did I screw up?

edited 20th Nov '17 10:07:17 AM by Wolf1066

Tiny little differences in initial conditions can have huge effects over the life of a planet. With that much extra solar energy hitting the planet, weather is likely to be a lot more volatile than we are used to. There might not even be any polar caps there. Not enough for a Venus, probably, but enough that the planet's surface will be constantly overcast and large scale storms common.

Far out, I didn't realise such a small amount of variance would have quite that level of result.

The rough and ready calcs for planetary temperature seemed to suggest that a bit of a "fudge" with greenhouse factor and/or Bond albedo should mitigate the changes.

It's like global warming, all the bad things that are coming (flooding of coastal cities, the decline of industrial agriculture, the loss of fresh water, increased hurricanes and wildfires, etc.) are all the result of a mere change of two or three degrees per year on average. Imagine what a five percent increase in total solar warming would do.

edited 20th Nov '17 6:12:20 PM by DeMarquis

Hmm. Cheers for that. Good thing about the spreadsheet is that I can change one figure and watch what happens to the other figures. Guess I'm going to have to aim for a lot closer to Earth-like insolation.

Cheers again.

OK I've done more mucking about and come up with the following:

Selected Spectral Class = G 1 V

Planet Sidereal Period = 386.503 Earth days

Received sunlight = 1.00023 Earth levels of insolation - 23/1000ths of a percent should be close enough to not matter much

Weeks in Year = 55.215 @ 7 Earth days per week = 55 weeks 1 day

Days more than Earth each year = 21.243

1 Earth year gained every 17.194 Local Years

Leap year every 2 years: 1 year = 386 days, next = 387 days

Leap cycle 773 days

2 Years (actual) = 773.006 days

Difference = 0.154 Hours

Second Leap Day each 156 Years

Moon Cycle – Full to Full

Moon Sidereal Period 27.4 Days or 657.6 Hours

Synodic Period: = 29.49 Days

Months in a Year = 13.106

I tweaked the moon's period to suit the longer year better. Solving for r with known sidereal period, the moon orbits at 60.426 Earth radii about the centre of an Earth-sized planet.

Does that seem any better than the previous attempt?

Edit: fixed my problem with the formula - seems my spreadsheet likes its values for TAN etc in radians rather than degrees so a little converting back and forth was all that was needed.

edited 22nd Nov '17 10:37:24 AM by Wolf1066