# How would this tidally locked planet be affected by its moon and would the moon have a deaccelerated orbit?

There is a terrestrial planet called Paveiha that orbits a small Red Dwarf star. It is the third planet in a system of 10 planets. Paveiha is close enough to the Sun that it is tidally locked and the planet itself has three moons. Two small irregular moons and one major spherical moon, Jeah, which is the focus of my question.

I have some statistics regarding the Sun, Paveiha and Jeah below. I don't know if this is enough information to accurately answer my questions, but at least confirming my suspicions that Jeah is in a deaccelerated orbit would be enough.

Information on the Sun, Paveiha and Jeah.

# The Sun

• Type: Red Dwarf
• Spectrum: M3.1 V
• Diameter: 373,136.28km. (26.8% the diameter of Earth's sun)
• Mass: 0.24119 solar mass.
• Age: 9.1 billion years.

# Paveiha

This map only shows the habitable (star facing) side of Paveiha. Clear white areas are water. The borders on the edges represent the beginning of the night side / icy region.

• Diameter: 8685.88km
• Mass: 0.31375 Earth mass.
• Density: 5.4628 g/cm3
• Axial Tilt: 0'28'30'68°
• Gravity: 0.6767g

• Perihilion: 0.07 AU

• Semimajor Axis: 0.07 AU
• Eccentricity: 0.011
• Orbital Period: 13.958 days.
• Orbital Speed: ?
• Roche Limit: 6446.83km

• Atmosphere Surface Pressure: 0.402atm

• Atmospheric Composition: • 48.2% oxygen (O2) • 41.2% carbon dioxide (CO2) • 10.4% nitrogen (N2) • 0.196 sulfur dioxide (SO2)

# Jeah

• Diameter: 1261.09km
• Mass: 0.00082409 Earth mass.
• Density: 4.7828 g/cm3
• Axial Tilt: 0'12'56'87
• Gravity: 0.084319g
• Perihilion: 17627.07km
• Semimajor Axis: 18181.17km
• Orbital Speed: ?
• Eccentricity: 0.30
• Orbital Period: 12 hours, 6 minutes, 37.31 seconds.

# I have two questions regarding Paveiha and its moon, Jeah.

1. Is Jeah in a deaccellerated orbit? Is it possible to determine how long it will take for Jeah to collide with Paveiha or spin out of orbit? How long?

2. How does Jeah's close orbit affect Paveiha? Would there be strong tidal forces?

2.1. Would it have any effect on its oceans?

2.2. Could the tidal forces disrupt life?

• Long story short, if the planet is close enough to the star to be tidally locked, the star's destabilizing influence will make the moons' orbits unstable and they will either escape or (more likely) crash into the planet, on timescale of centuries at best (next to the typical billions years of planet's existence). There's a reason why Mercury and Venus have no moons, and Earth has only one. – SF. Feb 27 '17 at 10:17
• Welcome to the Worldbuilding site, Noble. This is the best place for your questions, but we generally adhere to a one question per post policy, especially in your case since the questions cover radically different topics. For example, you should edit your post down to only contain the first question, and then I'm sure you will get some good answers. Once you have a good answer to your first post, you can ask the other questions. – kingledion Feb 27 '17 at 17:22
• To potential close voters: since this question was migrated recently, I recommend giving the author some time to revamp the post to meet site guidelines before spamming close flags/votes. – kingledion Feb 27 '17 at 17:23
• Thanks @kingledion for the advice, I will edit the post now. I'm new here so I thought it would be better for me to put all the questions in one big post instead of spamming multiple questions. update: edited post to only contain questions regarding Jeah, its orbit and the effects it would have on Paveiha – Noble Feb 27 '17 at 19:03
• Just so you know, I looked at some of your calculations and got Roche limit for Jeah to Paveiha of 5720 km; and a mean orbital speed of 55284 m/s (faster at perihelion, etc). – kingledion Feb 28 '17 at 19:22

# Simulation setup

I ran a simulation with your worlds in Rebound using Python. I have my setup on github if you want to take a look at it. The file is

orbit_noble_170301.py


# Results

I ran the integrator a few times with different time steps. For dt = ~12 hours, Jeah immediately left orbit of Paveiha and fell into orbit around the main star. Then after 4200 years, it had a close encounter with Paveiha and the last I was tracking it, it was about 0.7 light years away from the star and going fast.

I switched up the time steps and did some other modifications (not of the orbital parameters) but it never took more than a couple thousand years for Jeah to get ejected.

My thesis is that Jeah is just too light. Paveiha is 3 Mars's or half a Venus, but Jeah is a relatively puny Titania or Haumea size. It is about 1/20th the size of our moon. I was guessing that it was just too small; given that it wouldn't stay in orbit of the main plant (too close to the star I'm guessing), it was too light to stick around in the solar system.

So I tried increasing the size of Jeah by a factor of 10. This was a little better. Instead of getting ejected it tended to settle out in an orbit at around 12 AU (hope there's no gas giants!).

# Conclusion

I could not find a stable orbit for Jeah around Paveiha. I didn't even have to try integrating millions of years overnight; Jeah got stripped from the planet into an orbit around the star in a few decades.

If you want to give this a try by yourself, try to add yourself at my github and then we can talk there. I can try to help you set up rebound yourself, if I have the time.

Let me preface this by saying that, as a mortal, non-omnipotent being, I cannot know all outcomes. I will do my best to answer with what I as Worldbuilder think may happen, but keep in mind that what I say doesn't have to apply to your world. In other words, take what's I say with a grain of rice, and feel free to use your own interpretation.

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In regards to your queries, let's first take a look at your world, and compare it to our own Earth/Moon System.

Luna is approximately 27% the size of earth, and at its furthest is about 405,000km distant. This translates to about 1.985 x 10^26 N of gravitational force between the two objects.

Jeah, on the other hand, is about 14.5% the size of Paveiah, yet is only 17,000 km from its parent body. Considering the size ratio between parent body and Moon, your moon and planet have a size ratio half as much as the ratio between Earth and Luna, yet is also 27x closer. This translates to around 1.857 x 10^26 N of force.

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Given the calculations above, here are my conclusions.

1. No, Billy-Jeah isn't in danger of crashing down anytime soon.

2. Given the size ratio and distance between parent body and child body, Jeah's gravitational effect shouldn't be too different from the current tidal effects on Earth. Keep in mind, though, this is assuming that Jeah and Paveiah share Earth and Luna's makeup; if, say, Jeah was made completely of iron, then this estimate is off.

3. Gathering the increased level of oxygen, it's possible that Earth-style creatures would have increased energy. Big bugs, stronger animals, and more flammable areas. This, though, is assuming that the extra oxygen doesn't KILL them; too much of a good thing, after all...

4. Given the previous information, it's safe to say that the far side will definitely have permanent ice. But the nearest point to the star's light would receive the maximum amount of solar radiation it could get. Given that there's a huge hunk of land there, this'll likely mean that weather patterns will be driven partly by temperature differences, with hot air of the near side rushing away to meet the cool air from the far side. This should translate to a belt of vegetation between the two zones, and rainstorms would likely be frequent along this area.

5. That, I cannot answer adequately, I'm afraid. Because that would require me to make a whole host of assumptions about my species and its current level of technology. Even with humanity, we're only good enough to give a "maybe" for whether a planet even has liquid water on its surface. The fascinating point, really, is whatever you set it to be; beauty, as they say, is in the eye of the beholder.

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