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Can a rocky planet have these qualities and exist:
half of earth's gravity
4/5 earth radius
a magnetic field capable of retaining an atmosphere
a slightly slower rotation than earth
can sustain life
I am trying to create a world where a normal human will seem superhuman.
The short answer is yes, it is possible. Your premise is quite similar to John Carter of Mars, a series of stories published in the 1910's which were then made into a movie in 2012. An American Civil War veteran is transported to Mars, where due to the lower gravity, he is essentially superhuman. I do encourage you, however, to attempt your own take on the theme. There's no reason to assume you won't come up with something new and compelling.
Long answer. For 4/5 Earth radius and half gravity, you just need a planet of appropriate density. Know, however, that being that low density means it would probably be mineral-poor. For a magnetic field, you just need a rotating planet with a molten core, and there is no reason it can't rotate at a rate slightly slower than Earth.
As for sustaining life, after the above considerations it just needs to be in the habitable zone of a star. It could be a moon of a gas giant in the appropriate zone, or a planet in its own right. At that point it's really up to you. If you would like to expand your knowledge of what makes a planet habitable, I suggest looking up articles on: The Fermi Paradox; the Drake Equation; Habitable Zones of stars; the Great Filter Theory; and technological intelligence.
Your two basic equations are for gravity and for density:
$$a = GM/r^2 \text{ and } \rho=3M/4\pi r^3$$
And you are given a = 5.0 (roughly half of Earth) and r = 5100000 m (roughly 0.8 of the Earth)
So solving gives a mass of about $1.9\times 10^{24}$ and a density of 3500 kg/m^3. The Earth has a density of about 5100.
Here is where your problems start, as you want a powerful magnetic field, and that needs a liquid iron core. But your planet has a density that is substantially less than that of the Earth. Iron cores are heavy. If you have a heavy iron core, but are still have a density of 3500 you need a lot of lighter stuff, like water to compensate. But you now have a "water world" with 300km deep oceans covering the surface (I haven't done the detailed calculation here)
This is your basic problem. We can turn this around: if we fix $\rho$ at 5000, then this gives a planet with a radius of 3500km
With low gravity, it is going to have a hard time holding on to its atmosphere, even with a magnetic field, but perhaps this can be handwaved away.
Let's go through your requirements.
- a slightly slower rotation than Earth
Surely possible, there is no constrain on this.
- half of earth's gravity
- 4/5 earth radius
The two above mean that the planet is poor in heavy elements such as iron. Based on our understanding of Earth science, a molten iron core is needed to have
- a magnetic field capable of retaining an atmosphere
Without an atmosphere it's pretty hard to
- sustain life
You can try to go around this problem by visiting the planet when it's still young, and therefore the smaller core is still molten and can sustain a magnetic field and then retain an atmosphere.
More or less like Mars in the early history of our solar system.
I think the bigger dilemma is not whether such a planet can exist, but whether humans on it would really be super human. Remember that in less gravity you will need less strength to do the day to day tasks of human life.
Since you need less strength and there is less gravity, both your bones and muscles will atrophy. So you may have a planet where humans from Earth may seem superhuman if they are just visiting, but anyone who lives on this new planet for more than a few weeks is quickly going to become weak. They will quickly become just normal humans again relative to this planet, but extremely fragile by Earth standards.
Since the purpose of the planet is to make humans seem superhuman, the qualities of humans themselves may pose a problem.
