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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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