Is the Surface Gravity of Mu Arae-c Miscalculated?

In summary, the conversation discusses the density and mass of a possible giant rocky planet and its origins. The hypothesis suggests that if it was once a gas giant, its current radius could be 0.6 Jupiter and its mass could be 10.5 Earths, resulting in a low density of 189.74kg/m^3. However, there is speculation that the radius estimate may be incorrect and that the planet may have eroded from a larger gas giant, leading to a more reasonable density of 1240kg/m^3. There is also confusion about the mass estimates and whether the hypothesis is accurate.
  • #1
Researcher X
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I was wondering about the possible surface g of this giant rocky planet, and I found this one origin hypothesis on wikipedia.

"If an eroded gas giant, the sun would have boiled the planet from a larger protoplanet, of 20 Earth masses up to half Jupiter's mass. If the latter, its current radius could be as high as 0.6 Jupiter."

With this radius/volume estimate, and the mass (10.5 Earths), put into a density calculator, we get a puny and utterly impossible 189.74kg/m^3. If it's the remaining solid core of a gas giant, shouldn't it be incredibly dense? And it simply cannot be this diffuse.
Balsa wood can sometimes be heavier than this. This is 0.034385647 x Earth's density. Even Saturn is about six times denser.
Using this mean density with the estimated maximum radius, I get only 0.2g.

Before I mixed up kg/m for g/cc and got the g to 34.385646974g and with the early 14e mass of the planet, I got the ridiculous figure of 310g.

So, I've got it either way too heavy or way too light. Where have I gone wrong? Or is the radius estimate on wiki waaaaaaay off. I wouldn't expect it to be that large after all.

I've seen 3.5g for this planet before, but I don't know how that was come to.
 
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  • #2
"If an eroded gas giant, the sun would have boiled the planet from a larger protoplanet, of 20 Earth masses up to half Jupiter's mass. If the latter, its current radius could be as high as 0.6 Jupiter."

Note "if the latter", which means half Jupiter's mass. If we use that as the mass, the density comes out to a reasonable 1240 kg/m^3.
 
  • #3
I see, but that is odd because it was already penned at 14 Earth masses, and then revised to 10.5. When it says "20 Earth masses to 1/2 Jupiter's mass". it means that it eroded from that mass of a gas giant down to the current terrestrial planet mass of 10.5.

1240 kg/m^2 would make more sense though. Even still, not entirely, because that would make it less dense than Earth, and we're not talking about a gas giant, we're talking about a solid planet that may have eroded from a gas giant. It's current density should be a lot greater, which is why I also can't console 0.6 Jupiter diameters (the claim for its current diameter) with 10.5 Earth masses (the current mass estimate). It just doesn't add up, and gives it an impossibly low density for a solid planet of that size. If it was 0.6 Jupiter diameters it would be much more massive than 10 times the Earth. Does this mean that that hypothesis is completely wrong?
 

1. What is the surface gravity of Mu Arae-c?

The surface gravity of Mu Arae-c is estimated to be 2.5 times that of Earth's surface gravity, which is equivalent to 25 meters per second squared (m/s²).

2. How is the surface gravity of Mu Arae-c calculated?

The surface gravity of a planet is calculated using its mass and radius. In the case of Mu Arae-c, its mass is estimated to be 13.6 times that of Earth, and its radius is estimated to be 2.5 times that of Earth. By plugging these values into the equation for surface gravity (g = GM/r²), we can estimate that Mu Arae-c has a surface gravity of 25 m/s².

3. How does the surface gravity of Mu Arae-c compare to other exoplanets?

Mu Arae-c has a surface gravity that is slightly higher than that of Earth. However, there are other exoplanets that have much higher surface gravities, such as the gas giants in our own solar system, which can have surface gravities up to 10-30 times that of Earth.

4. What factors can affect the surface gravity of a planet?

The surface gravity of a planet is primarily determined by its mass and radius. A planet with a larger mass and/or a smaller radius will have a higher surface gravity. Other factors that can affect the surface gravity include the planet's composition, rotation rate, and atmospheric pressure.

5. How does the surface gravity of Mu Arae-c impact its habitability?

The high surface gravity of Mu Arae-c would make it difficult for humans to live and move around on the planet. It would also have a significant impact on the planet's atmospheric conditions and potential for liquid water. However, the impact of surface gravity on habitability is still being studied and is not yet fully understood.

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