How do we know the density and such of Saturn?

Question

How do we know all of this? What specific tools, and procedures, and other things did we use to find such info?
Info from Wikipedia.

Saturn is an oblate spheroid, i.e. it is flattened at the poles and bulging at the equator; its equatorial and polar diameters vary by almost 10% (120,536 km vs. 108,728 km). This is the result of its rapid rotation and fluid state. The other gas planets are also oblate, but to a lesser degree. Saturn is the only one of the Solar System's planets that is less dense than water, with an average specific density of 0.69. This is a mean value; Saturn's upper atmosphere is less dense and its core is considerably more dense than water.

Answer 1

We're able to detect it in several ways. First, we can see how Saturn interacts with the other planets, its moons, and the sun, gravitationally. This allows us to calculate its total mass.

With its mass in hand, we can measure how big around it is using telescopes to see it directly. With its height and width and breadth measure, along with its mass, we can calculate its density.

The finer measurements, such as how we know its more dense at its center than high up in the atmosphere, come from special instruments that were put on spacecraft that orbited Saturn at close range. With radar, we can measure the composition and density of clouds, and with other instruments that measure gravity, we can get a good reading of the core density if we can get fairly close to the planet, like with a few million miles or so.

Answer 2

In fact, you can get the average density of Saturn without knowing the planet's mass. All you need is a telescope, a filar micrometer, and an accurate clock. You basically time the periods of Saturn's moons' orbits and determine the ratio of each moon's semimajor axis to Saturn's average radius.

P^2 = 4 pi^2 a^3 / (GM)
M = rho volume = rho (4/3) pi R^3
rho = (3 pi / G) (a / R)^3 / P^2

See? All you need is the radius ratios and the satellite periods, and you can nail down the average density of the planet.

You'll probably catch Saturn with the ring plane at an angle to your line of sight. Assume the rings would be circular if you saw them at 90 degress aspect and determine the tilt of the ring plane (hence the satellites' orbital plane) with your filar micrometer.

Tilt angle = Arcsin {(ring narrowest) / (ring widest)}

The same angle is used to predict where the moons (Enceladus, Dione, Tethys, Titan, Hyperion) will be, roughly, in relation to Saturn, with reference to a working coordinate system having the major axis of the ring projection as the x axis and having a perpendicular y axis through the center of Saturn.

Once you have the projected picture of where the satellites are, you can correct that to an overhead view with a rotation around the x axis by (pi/2 - tilt angle). If your professor is a really MEAN guy who won't let you assume any a priori knowledge about the satellites' orbits, you can still get a decent answer by assuming that they are circular and that the orbital speed is constant.

Answer 3

A planet's mass can be calculated from its orbital characteristics.

It's size can be easily measured.

Therefore, its density is just a matter of:

Mass divided by volume.

Answer 4

One way is spectral photogaphy. Each element absorbs a certain amount of light and when filtered through a spectrum, can be identified. Once the elements are identified, an objects mass can be identified. Since saturn is mostly hydrogen and other light elements, it has a low mass.

Answer 5

We know its volume by simply looking at it with telescopes and measuring its size. We know its mass by watching how its moons orbit it under the influence of its gravity. We calculate density as mass divided by volume.

Answer 6

Just because I weigh the same as a log of wood, doesn't mean I'm made out of wood.

Answer 7

on the same topic

If mass is known, by orbit size calculation, but direct resolving cant give a size, size can be estimated by estimating the rock/ice make up of the object.

Answer 8

mass divided by volume is one way