The day/night cycle of Refuge

Ok, the day/night cycle on a moon that circles a gas giant is going to be complex.

You live on Refuge.  You get up in the morning, the sun, Oasis, is rising in the Eastern sky.  The day is going to be a beautiful green!  The sun rises higher and higher in the sky toward Ember, who is in the exact same spot as it is every day.   The Sun nears Ember, and 11 hours and 51 minutes after the sun rose it disappears behind Ember for 99 minutes.  Just over an hour and a half later it reappears, only to set 11 hours and 51 minutes later.  As the sun sets, however, Refuge is moving between the sun and Ember which is making Ember brighter in the sky, so night is lit up with a gas giant blazing away overhead.  Not that it's MUCH light, because as a class IV gas giant Ember only reflects 3% of the light that reaches it.  An interesting day night cycle that would change seasonally as the plane that Refuge orbits Ember in tilts relative to the Sun.  Sometimes there might not be a shortnight at all, other times it might only be a few minutes.

Refuge is tidally locked to Ember.  I've decided on Ember as the name for the gas giant, Hades is just a bit to cliche.  So Ember it is.


The mass of Ember is:  2.12576E+1028  (figured as 11.2 Jupiter Masses)
The mass of Refuge is:  1.84342E+1025  

I calculated the mass of Refuge by deciding I wanted it to be a large world.

20,800 kilometers in diameter.  

I wanted it to have a livable surface gravity.

1.16g

So with 1.16g and a 20,800 mile diameter I came up with

F=GmM/r²

F=ma, the little m's cancel out.  GM/r²=a

M=ar²/G

a=11.368 (1.16x9.8)  Which is the increased gravity of Refuge over Earths 9.8m/sec²
r=10,400
G is the gravitational constant, or 6.67x 10E-11)

11.368 x 10400000²/(6.67 x 10E-11)

M= 1.84342E+1025   (how annoying it is that there is no code for superscripted numbers over 3?)

Earth's mass, by comparison, is  5.972E+1024   
  
This gives Refuge a density of......

D = mass/volume

We have the mass above.  Volume is determined by 4/3πr³

So the volume of Refuge is 4/3π(1040000000)³ or 4.71181E+1027 cubic centimeters  (the radius is listed in centimeters)


Earth has a density of 5.52g/cm³
Refuge has a density of 3.91g/cm³


So Refuge is significantly less dense than Earth, mainly because it's very metal poor.  Silica rocks tend to have a density of around 3 times water, metals tend to be much more dense.  Refuge has a nice iron core, however, kept fluid by the huge planet wrapped around it like a blanket.  This creates the magnetic field that keeps the surface safe from radiation.  Along with the dense atmosphere.


But we're here to discuss the day night cycle, and make any changes necessary to the location of Refuge's orbit around Ember to give it a reasonable day/night cycle.


Ok, I'm going to cheat a bit.  I'm using an online calculator for this, but here is the link.


http://www.calctool.org/CALC/phys/astronomy/planet_orbit


I give Refuge a semimajor axis around Ember of 1,100,000 kilometers.  In the place of mass of sun I input 3561.5 using the measurement of Earths, because that's how massive Ember is relative to Earth.  I did the same thing with mass of planet using 3.11, because that's how much more massive Refuge is than Earth.


I come up with an orbital period of 2.22551 days.  I had roughly done the math in my head for about 2.5 days, so this works for me.  Refuge orbits Ember in roughly 53.4 hours.


Why is this important?  Because Refuge is tidally locked to Ember, its day relative to Oasis (the sun) is also 53.4 hours.  That means 26.7 hours of daylight, followed by 26.7 of night.  That would take some getting used too!  But in the 10-12,000 years humans have been on the planet, they adapted.


So what's a shortnight?  That's the time that Refuge is technically in its 26.7 hours of day, but passes behind Ember.  This would be the darkest time of all for the locals, as the sun would be hidden behind Ember, and Ember would not show any sunlit surface at all to those on the ground of Refuge.  The only light would be the glowing red of iron rain clouds on Ember, the other moons in the sky that orbit Ember, and the tapestry of the Milky Way 19,000 light years away.  Talk about an interesting night sky!


So Ember is 180,000 kilometers in diameter.  How long does shortnight last?

We'll treat Refuge's orbit as a circle.  The circumference of the orbit is π * diameter, the diameter is 2,200,000 kilometers.  So π * 2,200,000 is  6,911,503 kilometers.  It covers this in 53.4 hours, so 6.911.503/54.3 = 127,283 kilometers per hour, or /3600 =  a stately 35.356 kilometers per second.

Let's say that Ember is oblate like Jupiter, with a polar diameter of 180,000 but an equatorial diameter of 210,000 kilometers.  That means Refuge passes behind ember in 5,939 seconds.  99 minutes.

So shortnight is 99 minutes!

This is a lot of math (which I hope I got right, I'm not a physicist) to determine that a shortnight on Refuge is just over an hour and a half. But it's important to the story, it's important to consider if the moon would experience any significant cooling during the time it was in Ember's shadow... it all pertains to making the story more real.  I would feel like I was ripping off my reader if I didn't try to get the details as accurate as possible.

How big is the burning rage of Ember in the night sky during shortnight?

Using this calculator, the data says that Ember will be 9.3448 degrees of sky pole to pole, and 10.905 degrees of sky at the equator.  By comparison, the moon is about .5 degrees in our night sky on Earth.  So Ember would rage 20x larger than the moon in our sky.

http://www.1728.org/angsize.htm