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Reading on Wikipedia I saw that Titan is 80% more massive than the earth's moon but has only 85% the surface gravity. Why is this?

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  • $\begingroup$ Titan is less dense than the moon? $\endgroup$ – user151558 Apr 25 '16 at 22:28
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    $\begingroup$ As a more extreme example, Uranus' mass is over 14.5 times that of the Earth, but Uranus' "surface gravity" is about 89% of Earth's surface gravity. $\endgroup$ – David Hammen Apr 26 '16 at 0:46
  • $\begingroup$ The Moon is is basically rock, Titan is made up of about 50% ices. Most of the outer moons and Ceres contain a significant amount of ices/water, so they have much lower density than the inner planets and our moon. $\endgroup$ – userLTK Apr 26 '16 at 5:14
  • $\begingroup$ @user151558 While this is generally correct, it's a very brief and unsatisfying answer. Surface gravity is a function of mass and radius (and sometimes speed of rotation). Density is relevant, but it's not a complete answer. $\endgroup$ – userLTK Apr 26 '16 at 5:20
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    $\begingroup$ @userTLK The comment is not generally correct. It is the specifically correct answer to this very elementary question. $g \propto \rho^{2/3} M^{1/3}$. Though saying that the radius of Titan is much bigger would have been equally valid. $\endgroup$ – ProfRob Apr 27 '16 at 6:42
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Surface gravitational acceleration on an object with mass $M$ and radius $R$ is given by $$ g = \frac{GM}{R^2} \propto G\rho R $$ where $\rho \propto M/R^3$ is the density of the object. If one body has smaller surface $g$ than another, it must have smaller density $\rho$, smaller radius $R$, or both. Titan is larger than Earth's Moon, so your observation about its surface gravity means Titan must be less dense than the Moon. Wikipedia confirms:

  • $R_\text{Titan} = 1.5 R_\text{Moon}$, but
  • $\rho_\text{Moon} = 3.34\rm\,g/cm^3$ while Titan has only $\rho_\text{Titan} = 1.88\rm\,g/cm^3$.
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  • $\begingroup$ So by that logic, Ganymede, the largest of our moons, is also the lightest? $\endgroup$ – JohnWDailey Jan 23 '17 at 0:40
  • $\begingroup$ I don't have any information about Ganymede's density or surface gravity --- I'd have to look it up. $\endgroup$ – rob Jan 23 '17 at 0:59
  • $\begingroup$ No, the problem is you said "larger therefore less dense". This does not always hold $\endgroup$ – Tosic Oct 18 '20 at 12:43
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    $\begingroup$ @Tosic Oh! That wasn't what I meant (note that Earth is larger than and denser than either the Moon or Titan). I've added a sentence which hopefully clarifies. $\endgroup$ – rob Oct 18 '20 at 20:57
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This does at first seem strange because Ganymede's gravity is lower than the moon but higher than titan...

I believe the difference in gravity is not a function of it's volume but of it's density. This means that it depends on what it is made of: how much iron versus how much methane... Clearly iron has far greater mass by volume than any gas...

For example :

  • With an average density of 1.936 g/cm$^3$, Ganymede is most likely composed of equal parts rocky material and water ice. gravity of 1.428 m/s$^2$ diameter of 5,268.2 km
  • The moon's density is 3.34 g/cm$6 3$. The Moon is made of rock and metal. gravity of 1.62 m/s$^2$ diameter of 3,474.2 km.

So, clearly a celestial body that has lots of water or gas will have a lower density than a body of equal size but made up of rock and metal. If Ganymede were to be made up of the same stuff as the moon then it would have gravity at about 45 percent that of earth (9.807 m/s²) or about 4.5m/s²... the moon is about 1/6th.

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  • $\begingroup$ Hello and welcome to the site. I made some edits to your post. Feel free to rollback if you feel like I transfigured what you were trying to say. $\endgroup$ – usernumber Oct 18 '20 at 14:36

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