During a close flyby, the Cassini spacecraft yielded a new...

During a close flyby, the Cassini spacecraft yielded a new estimate of the mass of Enceladus of $1.08 \times 10^{20} \mathrm{kg}$. Given that Enceladus's diameter is $499 \mathrm{km}$, calculate its density. The larger satellite Tethys has a density of about $1.0 \mathrm{kg} / \mathrm{L}$. What does this density suggest about Enceladus's composition relative to Tethys's? How might this account for Enceladus's unusual surface features?

Key Concepts

Satellite Composition Inference

Comparing computed densities to those of known materials allows scientists to infer the makeup of celestial bodies. A density higher than that of pure ice suggests a significant proportion of rocky material, whereas a lower density indicates a dominance of ice. This approach helps determine whether a satellite is more rocky or icy in composition.

Internal Heating and Surface Activity

The internal composition of a satellite affects its thermal evolution and geological activity. A higher rock-to-ice ratio can facilitate internal heating through tidal interactions, which in turn can lead to geological processes such as cryovolcanism and resurfacing. These processes are often manifested as unusual surface features like fissures and active plumes.

Density Calculation

Density is determined by dividing an object's mass by its volume. For spherical bodies, the volume is calculated using the formula V = (4/3)?r³, where r is the radius. This calculation is fundamental in planetary science to derive an object’s bulk composition from observed mass and size data.

Transcript

00:01 Okay, so this is problem 29 and we're going to study the eugen's probe that was landed in saturn's moon titan.

00:11 So a couple of things we know about titan.

00:15 We know its diameter is 5 ,150 kilometers.

00:21 But what we're interested here is always is the radius.

00:25 So i like to keep putting tricks in tricks like that and the questions.

00:32 Because that is most often what people fall for.

00:37 Their difference between diameter and radius, right? so radius is the diameter divided by 2.

00:44 And here we want to divide 5 ,000 and 150 kilometers by 2.

00:51 So that's 200 and 557 kilometers.

00:59 Or i'll actually write, oops, let's write it in meters, which would be 2 .575 times 10 to 6 years.

01:17 So as a general rule, every time you have a distance like that, turn it into meters and beware of diameters because often what you will want is the radius.

01:31 Okay, we know how much the probe weight on earth and we will.

01:34 Want to know what it weighs on the surface of titan.

01:39 So the probe weighted 3 ,120 newtons on earth.

01:50 So that would be equal to its gravitational force.

01:56 And on earth, we can cheat because we know this is simply equals to m -g.

02:02 This is only valid on the surface of the earth, with g equals 1 .9 meters per second square, right? so from this, we can extract the mass of the satellite, which i will just write m, and this would be 3 ,120 2d, divided by 9 .8 meters per second square.

02:29 And sure, let's run those numbers down.

02:38 That would be 318 kilograms.

02:43 All right and now we want to know the wave on titan.

02:52 So on titan i'll drive in green.

02:56 The weight is the gravitational force again.

02:58 You could use a w as a variable.

03:01 This is the same.

03:04 And we know it's equal to the gravitational force, which will be m, the mass of the satellite times, let's call it mt, the mass of titan over r, which is the mass of the satellite, the radius of titan, so might as well write a little t.

03:24 Just to make it clear that it's the radius of the satellite, of titan, which is also a satellite...

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