How do I explain the formation of my world scientifically?
For my science fantasy story, I need a particular setting for my world. I need a planet (Earth or earth-like), habitable and with complex life forms like our planet. However, over time, this planet gets tidally locked with another celestial body (either a moon or another planet). I don't mind it covering millions of years to achieve this result, provided it doesn't affect the lifeforms drastically (at least a handful of them). So how should I proceed to building this world to make this possible?
The final version of my world would be a planet/moon tidally locked with a celestial body which occupies substantial space in the sky, and with the day-night cycle of around a week.
There are three probable scenarios I could think of to achieve the result:
1. Our current Earth gets locked with its Moon
I've thought of Earth getting locked with the moon, but this option does not seem feasible. The Moon seems to drift away from the Earth gradually, while I'd want it to get closer to Earth for it to look larger in the Earth's sky. Even if the Earth gets locked with the Moon naturally over millions of years, the day-night cycle would be nowhere around a week. Meanwhile, the Sun would turn into red giant and engulf both Earth and the Moon, rendering the entire process useless. If somehow the Moon gets closer to Earth without destabilizing its orbit with each other while simultaneously drifting away from the Sun, this scenario could work to achieve the desired outcome.
2. Locking Earth in Jupiter's orbit as its Moon
Locking Earth in Jupiter's"‹ orbit is also an option, but still not feasible. A series of highly unlikely but possible events, (like passing of an asteroid in Earth's orbit, in perfect planetary alignment) could make Earth drift out of its orbit and get captured by Jupiter. However, I suppose, this process would have apocalyptic effect on the Earth's lifeforms. If somehow this entire process happens in a way such that it least affects the habitability, and the new Earth continues to support complex lifeforms as it does now, this option seems most viable.
3. Creating a fictional solar system
Another option is creating a fictional solar system with earth-like planet to achieve this scenario. In this case, necessary tweaks could be made in the size and position of the planets, such that the earth-like planet (with conditions similar to that of the Earth) to make the transition of the planet with minimal impact to the planet's habitability.
Which of the above scenario sounds realistic enough to be possible?
Is it even possible to achieve any of these scenarios (hypothetically)?
I prefer to get this outcome by manipulating the natural behaviour of celestial bodies even if it is highly unlikely to happen, but possible. If not, I'd settle with human intervention to make this possible. I'm really not considering handwavium at this moment, but I'm open to ideas.
I'm not looking for hard numbers, but just a way to explain my world scientifically.
This post was sourced from https://worldbuilding.stackexchange.com/q/87422. It is licensed under CC BY-SA 3.0.
1 answer
The formula for the time a body $B_1$ orbiting another body $B_2$ of mass $m_2$ will become tidally locked to $B_2$ is (see Gladman et al. (1996), Equation 9) $$t=\frac{\omega a^6I_1Q}{3Gm_2^2k_2R_1^5}$$ where $\omega$ is the initial spin rate, $a$ is the semi-major axis, $Q$ is something called the dissipation function, $k_2$ is the second Love number, and $R_1$ is the radius of $B_1$. The second Love number for Earth, is around $0.3$ to $0.35$; one analytical model found $k_2=0.360932$. I'll be a bit more conservative and say $k_2\simeq0.325$. Assuming that $B_1$ is Earth and $B_2$ is the Sun, I plug in all the relevant parameters:
- $\omega=3\times10^{-4}\text{ rad/s}$, assuming an initial day of 6 hours.
- $a=1.50\times10^{11}\text{ m}$
- $I_1=1.378\times10^{47}\text{ kg m}^2$
- $Q\simeq100$
- $m_2=2\times10^{30}\text{ kg}$
- $R_1=6.371\times10^6\text{ m}$
I then get $t\sim10^{32}\text{ s}$, which is way too large.
What if we change things around? Let's say Earth orbits Jupiter, where $m_2=2\times10^{27}\text{ kg}$. If we set $a=10^9\text{ m}$, then I get $t\sim10^{14}\text{ s}$, which is about 3 million years. Not bad! That's a timescale that fits nicely into the age of the Solar System.
Let me review the three options:
- Option 1 (Earth locked to Moon) is probably not good on small timescales, and as you said, the Moon is drifting farther away.
- Option 2 (Earth locked to Jupiter) is possible on the right timescale. You'd need to figure out a source of energy, although tidal heating always gets me excited. Alternatively, perhaps you modify things so that Jupiter migrates into the inner Solar System (sending planets tumbling, of course). This means that Earth could still be in the circumstellar habitable zone.
- Option 3 is arguable the best - the modifications to Jupiter's orbit might fall into this category. Earth being tidally locked to the Sun is definitely not going to work - you'd need a much smaller semi-major axis, which would lead to Earth being cooked like a fried egg!
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