How do you Calculate the Surface Gravity for Gas Giants?

[StavraDev]

Hey, everyone! Recently I've been creating a mod that adds multiple gas giants. The answer to my question may seem obvious, but remember: Jool only has a surface gravity of 0.8g due to the fact that the Kerbol System is scaled 1:10 (for context, I intend to scale the system curently in development to 1:5). If anybody can help, please let me know! 

[Leganeski]

Hello and welcome to the forums, @StavraDev!

Surface gravity is generally not affected by the scale factor, regardless of the type of planet. For instance, Kerbin and Earth have the same surface gravity despite being at very different scales. To get the surface gravity of a 1/5 scale planet, you just need to calculate the surface gravity that a real-life planet with 5 times the radius would have.

2 hours ago, StavraDev said:

Jool only has a surface gravity of 0.8g due to the fact that the Kerbol System is scaled 1:10

This is not actually caused by the 1/10 scale factor. Jool's surface gravity is indeed lower than what it would be in real life, but this is because the stock KSP system was created without too much attention to whether the densities were exactly realistic. (Eve is 45% denser than the otherwise similar Kerbin, a difference so substantial it would be very hard to explain in the real world.)

In order to find out what Jool's surface gravity should be, we could compare it to Saturn. Jool has just over 1/10 the radius of Saturn, which has a mean surface gravity of 1.065 g, so Jool's surface gravity should be slightly higher: somewhere around 1.1 or 1.2 g.

Real gas giants never get much larger in radius than that, unless they're rotating quickly or puffed up by heat from a very close star. As the mass of a planet increases beyond about that of Saturn, it starts getting compressed, and nearly all of the new mass ends up increasing the surface gravity rather than the radius. For example, Jupiter has 1.2 times the radius of Saturn, but 2.4 times the surface gravity because it is so much more compressed. Above 10 times the mass of Saturn, the radius actually starts shrinking as more mass is added!

The following chart (taken from here) shows the relationship between mass and radius for a range of different compositions. Typical gas giants are near the dotted light blue line, which represents a composition of mostly hydrogen with some helium.

To get the surface gravity, divide the mass by the square of the radius. Everything on the chart is relative to Earth, so it should come out in gees.

 

Finally, I might mention that 1/4 real scale tends to be more commonly used than 1/5 in the KSP modding community. (For example, JNSQ's planets were constructed at 1/4 scale, and BDB's rockets were balanced at that scale.) Of course, the scale of your mod is entirely up to you, but choosing 1/4 scale could potentially lead to better integration with other mods.

[StavraDev]

Thank you so much for the response! Now I just gotta recalculate the light curve for the star at a 1:4 scale. 

Edited July 9, 2023 by StavraDev
typo

[RevanX_LSR]

The density of gas giants also depend on the material that they are made of. Ice giants consists of higher density gases which gives them higher density. Jool has an unusually low gravity due to its lack of realism especially for a jupiter remake. it is better to base planets of their IRL equivalents rather than KSP equivalents, especially when dealing with stars.