# Day length and orbital period + apparent luminosity

#### cbrons

1. The problem statement, all variables and given/known data
I am actually an MD student, but I have been working on writing a novel. I wanted to create exoplanets that were suitable for human habitation, and I had a guy help me over the summer come up with plausible numbers for a variety of variables. Where I am having trouble now is figuring out how long a year would be on these planets as well as the length of an individual day. I attached the data that the individual gave me on some other variables.

2. Relevant equations
If I wanted to figure out from this data:
- Apparent luminosity (at planet)
- Orbital period
- Day length

3. The attempt at a solution

- Apparent luminosity (at planet): 1.67657
- Orbital period: 0.715 Earth years
- Day length: ???

I am not certain that any of these is correct, and I don't even know how to begin to figure out the last parameter (day length).

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#### gneill

Mentor
Your data doesn't include the mass of star (although it will be constrained to some extent by its stellar classification) so you can't pin down the orbital period exactly. Use Newton's version of Kepler's third law to investigate. Use the web to investigate a suitable mass range for the star given its luminosity and type (G5).

The day length will be determined largely by the rotation rate of the planet on its axis of rotation, which is not fixed by the geometry of the orbit or the mass of the planet or star. Really, you can choose any day length you wish unless the system is so old (really, very, very old indeed) that it's day has become tidally locked to its year through tidal braking. Then you'd need to worry about how the star would still be a G5 after that long...

#### sozme

Your data doesn't include the mass of star (although it will be constrained to some extent by its stellar classification) so you can't pin down the orbital period exactly. Use Newton's version of Kepler's third law to investigate. Use the web to investigate a suitable mass range for the star given its luminosity and type (G5).

The day length will be determined largely by the rotation rate of the planet on its axis of rotation, which is not fixed by the geometry of the orbit or the mass of the planet or star. Really, you can choose any day length you wish unless the system is so old (really, very, very old indeed) that it's day has become tidally locked to its year through tidal braking. Then you'd need to worry about how the star would still be a G5 after that long...
Thank you so much. So I can basically choose any day and year length I want?

I.e. Day = 79344 seconds (equiv to 22.04 hours ... added the decimal to you know, make it seem more realistic). Then perhaps I can say a year = 262 days? Are these numbers ridiculous?

#### gneill

Mentor
Thank you so much. So I can basically choose any day and year length I want?
As I stated, there are some constraints on the year length because the mass of the star will be in a certain range and you've fixed the orbital radius. The combination of stellar mass and orbital radius determines the orbital period (Kepler's 3rd law).
I.e. Day = 79344 seconds (equiv to 22.04 hours ... added the decimal to you know, make it seem more realistic). Then perhaps I can say a year = 262 days? Are these numbers ridiculous?
Day length is much more flexible since it is effectively independent of the orbit.

I would recommend:
1. Pick a mass for your star (1 Sol would be convenient)
2. Determine the orbital period via Kepler's 3rd
3. Pick a day length to suit your story
4. Determine the number of local days in the planet's year.

Next you'll have to worry about the climate. You've set the luminosity of the star at 1.1 Sol, so it's putting out more energy than our Sun. You've also got the orbital radius significantly smaller than that of Earth, so it's going to be HOT on your planet. Think Venus type hot.

Did you do any research on the so-called "Goldilocks Zone" (also called the "Circumstellar Habitable Zone") for planets?

#### cbrons

Did you do any research on the so-called "Goldilocks Zone" (also called the "Circumstellar Habitable Zone") for planets?
Darn, I was hoping I had a habitable planet. Actually no, I paid a high school astronomy teacher and he came up with the data for the worlds I named. Maybe he meant to put a different star class. I can see now after your explanation why this would be way too hot for human habitation.

#### cbrons

Ok, I calculated the orbital period (but I am not sure it is correct.

To be clear, in my story, humans only visit this world. I'm not sure that these variables are correct, again, a high school science teacher I paid came up with most of these.

Is my calculated orbital period correct? (I double checked it, so unless I had my units wrong)
Do you think that temperature range seems incorrect given the other variables just by eyeing it?

The orbital period is enormous... a planet whose year is over 300 earth years? But its supposed to orbit close to the star? I dont know seems like I might have this wrong.

#### mfb

Mentor
The temperature range looks quite optimistic, with such a thick atmosphere and so close to the star a venus-like planet is much more likely. Your planet would get twice the solar intensity compared to earth, very similar to Venus.

The orbital period is way too long (even if it is supposed to be days instead of years), it should be less than half a year.

Also, it is unclear if that smaller planet can hold its thick atmosphere.

#### NTW

Check your numbers... In my calcs, the orbital period is much shorter...

#### gneill

Mentor
The numbers aren't consistent. The given planet mass and radius don't yield a surface gravity of 7.72 m/s2. It would be a bit higher than that.

You should show your calculations, not just the results.

#### cbrons

The numbers aren't consistent. The given planet mass and radius don't yield a surface gravity of 7.72 m/s2. It would be a bit higher than that.

You should show your calculations, not just the results.
8.11 is what I got when I re-did it

#### cbrons

I'm not sure what the person means "given Earth density" under radius.

#### cbrons

Check your numbers... In my calcs, the orbital period is much shorter...
Is it about 0.45 Earth years? thats what I got when I re-did it with correct units

#### mfb

Mentor
I'm not sure what the person means "given Earth density" under radius.
The assumption that the new planet has the same average density as earth.

0.45 earth years look right.

#### cbrons

I added K0 and then V... because I came up with the stellar mass via this table: http://www.atlasoftheuniverse.com/startype.html

Now you said that the temperature is incorrect. Any suggestions on the easiest way to cool this planet down by playing with the numbers?

#### mfb

Mentor
You can increase its orbital radius until the irradiation intensity (proportional to luminosity/distance^2) is roughly similar to the value of Earth.

Just a side-remark: the current atmosphere is toxic for humans. Too much oxygen.

#### cbrons

You can increase its orbital radius until the irradiation intensity (proportional to luminosity/distance^2) is roughly similar to the value of Earth.

Just a side-remark: the current atmosphere is toxic for humans. Too much oxygen.
Yes, I was going to ask if I can arbitrarily change the atmospheric comp as well as the pressure

#### mfb

Mentor
Oxygen without life is problematic, but good models about atmospheres of exoplanets are rare, so you can get away with many things.

#### cbrons

Oxygen without life is problematic, but good models about atmospheres of exoplanets are rare, so you can get away with many things.
Any suggestion for a better composition without oxygen? The humans who visit can bring breathing gear.

#### mfb

Mentor
Well, nitrogen is nice, you can have carbon dioxide (that will make the planet warmer), you might have some water vapour, some small amount of argon and smaller fractions of other noble gases. Oxygen... maybe.

With breathing gear, it does not matter much for the astronauts. As long as the pressure is below 10 bar, it will be fine.

"Day length and orbital period + apparent luminosity"

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