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Recently, I've been using a site called "The WorldSmith 3.03" in order to calculate some of my planet's physical characteristics:

Now, when it comes to the planet's gravity there is something that confuses me. There are two values that I need to fill in, in order to get my planet's surface gravity: Mass & CMF (Core Mass Fraction). I was always under the impression that a planet's gravity is only determined by its mass, so if I make my planet have a mass of 2 M Earth (twice that of Earth) then the gravity of the planet should also be 2 g. However, when i put in a value for CMF (39% for instance) then the calculations put my world's gravity at 1.408 g. Why is that?

Let me clarify, I have no problem with these values, I think they work just fine for my world. I just want to make sure if they are true and if yes then I want to understand how exactly does the value of CMF effect a planet's surface gravity?

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  • $\begingroup$ physics.stackexchange.com/questions/195676/… $\endgroup$
    – Goodies
    Commented Dec 28, 2022 at 11:14
  • $\begingroup$ Knowing the core mass fraction is insufficient; you also need to know the average density of the core and of the envelope. It may be the case that the calculator makes the unspoken assumption that the planet is sort-of like Earth, with a core of iron and an evelope of silicates. $\endgroup$
    – AlexP
    Commented Dec 28, 2022 at 13:31
  • $\begingroup$ I can't access the website. $\endgroup$
    – KEY_ABRADE
    Commented Dec 28, 2022 at 21:16
  • $\begingroup$ Surface gravity depends on the mass and the radius of the planet. Presumably, a planet with a higher CMF will have a higher density, and hence a smaller radius for the same mass. That will make it have a higher surface gravity. (Posting as a comment because I haven't used this site and don't know for sure that this parameter behaves as I would expect.) $\endgroup$
    – N. Virgo
    Commented Dec 29, 2022 at 1:14
  • $\begingroup$ The surface gravity felt by people standing on the surface depends on the mass and the radius of the planet. The escape velocity, vital for retaining atmosphere, also depends on the mass and the radius of the planet. But a change in the mass and radius will not change the surface gravity and the escape velocity in the same proportion - they have to be calculated seperately $\endgroup$ Commented Dec 30, 2022 at 22:59

2 Answers 2

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In the Newtonian theory, the gravity given by a certain mass M at distance R is given by $g=$$GM\over R^2$

if I make my planet have a mass of 2 M Earth (twice that of Earth's) then the gravity of the planet should also be 2 g.

only if you are not changing the radius of the planet. If you are changing it, gravity will change accordingly.

The core mass fraction tells you only how big is the core with respect to the rest of the planet, or in other words, what is the ratio between light and heavy elements in the planet, considering that heavier elements tend to sink in the core while lighter elements tend to float in the crust.

Such a parameter can at most influence the gradient of the gravitational field when going inside the planet, not at its surface.

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    $\begingroup$ The core is denser than the rest of the planet, so a planet with a high core mass fraction will be denser overall and have a higher surface gravity for the same overall mass. I suppose working in terms of core mass fraction (and modeling the resulting core and overall density from it together with the mass) makes it easier to avoid unrealistic density values. $\endgroup$ Commented Dec 28, 2022 at 16:22
  • $\begingroup$ Presumably, the core mass fraction parameter affects the radius of the planet and affects the surface gravity that way. $\endgroup$
    – N. Virgo
    Commented Dec 29, 2022 at 1:12
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A planet's gravity is determined by its mass.

The WorldSmith site would appear to be using core mass fraction as a proxy for density. If it assumes that the core is mostly iron, and the rest is mostly silicates, and picks an average density for both types of material, then calculating the density is simple.

You supply mass and CMF as inputs, and presumably WorldSmith converts CMF to density. With mass and density, it's then easy for the program to calculate volume and surface area for your planet. Those are important numbers for any planet, although they mostly affect stuff happening on the planet, rather than in the dynamics of the star system.

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    $\begingroup$ No. CMF is the DISCTRIBUTION of density within the planet $\endgroup$
    – Hobbamok
    Commented Dec 28, 2022 at 20:21

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