Calculating the size of planets from length of days.

[conrad141]

So I'm not huge when it comes to physics. In fact I only created and account in order to ask this question. I'm am trying to figure out a way to calculate the approximate size of a planet based on how long it's day/night time cycle is. There is a lot of variability involved here. I think I understand that the rotation speed of planets is related to how it was formed, larger planets being faster. So I need to figure out the circumference of a hypothetical planet that has 20 minute days ( 10minute day, 7 minute night, 3 minutes of transition period.). It has a sun and one moon and is very similar to Earth in that it is the perfect distance from the sun to support life.

https://www.physicsforums.com/showthread.php?t=310920
This thread helped me understand somethings.

So what would be the size of this planet. If you have to assume for any of the variables, assume they are the same as that of earth.

So how should I go about doing this?

 

[fillipeano]

What you're asking is hard to determine (for me, at least).
Venus, which is pretty much like Earth, rotates extremely slowly. One day is a bit less than 250 Earth days. Looking at Mercury, a day is 58 Earth days.

 

[conrad141]

So what you're saying is that planet size doesn't directly correlate to rotation speed? What does correlate to speed then? Would distance from the sun, presence of a moon, or number of moons be easier to calculate with? What data could actually be used to determine planet size other than direct measurements?

 

[Borek]

So what you're saying is that planet size doesn't directly correlate to rotation speed? What does correlate to speed then? Would distance from the sun, presence of a moon, or number of moons be easier to calculate with? What data could actually be used to determine planet size other than direct measurements?

I don't think there is any correlation. Perhaps during planet formation from the initial cloud, but later it gets lost for many reasons. I think Venus is tidally locked to Sun, like Moon and Earth. Also collisions of protoplanets can change their rotation speed.

So IMHO you have to measure.

 

[Nik_2213]

We used to think the rule was small rocky planets inside the 'ice line' and gas giants outside.

The number of 'Hot Jupiters' showing up, some in eccentric and/or retrograde orbits has put paid to such simplicity.

Worse, it seems that forming planets can interact with their nebula's dust-disk and migrate-- Inwards or outwards. IIRC, the fuzzy edges of Kirkwood gaps in asteroid belt may be due to Jupiter migrating some-what...

IIRC, once planetismals begin to collide and merge into planet cores, size, day-length, even rotation direction and axial alignment are effectively random.

Then you have tidal interactions: IIRC, our Moon formed much closer to Earth than we see it, then tidal dissipation slowed the Earth from estimated ~6 hr day and eased the Moon's orbit outwards-- Thanks to lunar retro-flectors and laser ranging, we know both processes continue...