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? $\endgroup$– user151558Apr 25, 2016 at 22:28
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5$\begingroup$ 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 HammenApr 26, 2016 at 0:46
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$\begingroup$ 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. $\endgroup$– userLTKApr 26, 2016 at 5:14
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$\begingroup$ @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. $\endgroup$– userLTKApr 26, 2016 at 5:20
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3$\begingroup$ @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. $\endgroup$– ProfRobApr 27, 2016 at 6:42
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1 Answer
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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? $\endgroup$ Jan 23, 2017 at 0:40
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$\begingroup$ I don't have any information about Ganymede's density or surface gravity --- I'd have to look it up. $\endgroup$– robJan 23, 2017 at 0:59
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$\begingroup$ No, the problem is you said "larger therefore less dense". This does not always hold $\endgroup$– TosicOct 18, 2020 at 12:43
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1$\begingroup$ @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. $\endgroup$– robOct 18, 2020 at 20:57