Size of fictional planet based on gravity and density

[rdanner3]

Given a planet of the same (relative) density as Earth, and a G-force on said planet of 1.916G, what is the procedure to determine the radius and surface area for such a planet, given it having only 57% water coverage?

I will admit that I am working on this for a book series I started in 2002, but my initial calculations obtained a ridiculously large planet size (17x Earth's surface area). Clearly, my own efforts were (at the time) incorrect equations, but I will admit that my math skills may not be up to the task, although much of the data I originally based the calculations on have been lost. Other planets in my series are Earth-type, albeit different due to the stars they orbit being far different from our Sun.

I want to ultimately be able to explain why such a planet would have a rotational period of 100,000 seconds, and an orbital period of 1,000 of those rotations (roughly 3.17 Terran years), yet be habitable.

Bear in mind that I am not requesting that someone do the work, just help me obtain the knowledge needed to do the work myself for this project.

 

[zhermes]

Awesome project. Have you considered issues concerning the Habitable Zone?

The surface area of a planet is given by the radius (to good accuracy at least). Thus you just need the radius which is included in the equation for Newton's[/PLAIN] Law of Gravity:
$$F_g = G_N\frac{M_p m}{R^2}$$
Where $G_N$ is Newton's constant; $M_p$ is the mass of the planet, and $m$ is the mass of the secondary object (e.g. a person feeling the force), and finally $R$ is the radius of the planet.
From Newton's second law:
$$F = F_g = m a$$
where 'a' is the gravitational acceleration (on Earth this is usually called 'g'; what you called 'G').
You can combine these equations to remove 'm'. Also, you want $a = 1.916 g$.
The only other thing you need to solve for is the total mass of the planet, which is determined by its density and size:
$$M_p = \frac{4\pi}{3} \rho R^3$$
where $\rho$ is the density (which you can look up on wikipedia for the earth---the amount of surface water won't make any noticeable difference).

 

[rdanner3]

Awesome project. Have you considered issues concerning the Habitable Zone?

Yes, I have, but finding correct data on the different star classes (or an actually-working visual calculator!) has been interesting.

The surface area of a planet is given by the radius (to good accuracy at least). Thus you just need the radius which is included in the equation for Newton's Law of Gravity:
$$F_g = G_N\frac{M_p m}{R^2}$$
Where $G_N$ is Newton's constant; $M_p$ is the mass of the planet, and $m$ is the mass of the secondary object (e.g. a person feeling the force), and finally $R$ is the radius of the planet.
From Newton's second law:
$$F = F_g = m a$$
where 'a' is the gravitational acceleration (on Earth this is usually called 'g'; what you called 'G').
You can combine these equations to remove 'm'. Also, you want $a = 1.916 g$.
The only other thing you need to solve for is the total mass of the planet, which is determined by its density and size:
$$M_p = \frac{4\pi}{3} \rho R^3$$
where $\rho$ is the density (which you can look up on wikipedia for the earth---the amount of surface water won't make any noticeable difference).

Okay, that does make sense, insofar as I actually understand what you've mentioned. I would be incorrect if I said I understood all of this. :-) And I acknowledge your near-rebuke regarding g and my incorrect use of the uppercase G for it. LOL

 

[rdanner3]

The only Habitable Zone "calculator" I've seen at all is useless for what I need; it only shows three very-general star types (basically, small, medium, super-huge) and is leaving me totally unable to figure out other critical data in re: the star classes of these star systems. Based on what I know (the orbital year of two of the planets), I expect one of the stars is a close cousin (so to speak) of the star we ourselves orbit. The one for Regelis, on the other hand, appears to be much hotter, as the HZ is obviously much further out from the star.

Based on the apparent ecology and temperature spreads I have created for Regelis (and the fact that their hurricane classification system has 10(!) steps, not 5, as ours does) I expect that Regelis is closer to the inner edge of its system's HZ than Earth is.

Worst directly-referenced hurricane (in the novels) has been a Class 7, although class 10s have been indirectly referred to, largely in historical context. (Either one would be intensely dangerous, probably destructive beyond anything we have concept of, to be honest.) Closest I can figure for the Class 7 is somewhere around 2000km across, with wind speeds exceeding 250mph, although meterology is decidedly not my strong suit. Been trying to research certain data from well-known storms now for several hours, to little effect. :-\

 

[pmacias]

As a scientist, my best advice would be to start by reviewing and gathering all relevant data and equations related to planetary size, density, and gravity. This would include researching the effects of different G-forces on planetary bodies and how they impact their size and surface area.

Once you have a solid understanding of the principles and equations involved, you can then apply them to your fictional planet. Start by determining the mass of the planet, which can be calculated using its density and surface area. From there, you can use the formula for gravitational force (F=G(m1m2)/r^2) to solve for the radius of the planet.

To take into account the 57% water coverage, you can use the average density of water (1 g/cm^3) and subtract it from the overall density of the planet. This will give you a more accurate mass and therefore a more accurate radius.

As for the rotational and orbital periods, you can use Kepler's laws of planetary motion to calculate the orbital period based on the planet's mass and distance from its star. The rotational period can then be calculated based on the planet's size and rotational speed.

It is also important to consider other factors such as the planet's atmosphere and composition, as these can also affect its habitability despite its size and gravity.

Overall, it will take a combination of research, understanding of relevant principles and equations, and careful calculations to determine the size and characteristics of your fictional planet. Good luck with your project!