Astronomy on Titan: the Saturn system

So once we are floating in a balloon atop Titan’s haze, we will get to see lots of interesting things. I will start with the Saturn system.

Saturn is an obvious place to start, because of its prominence. Its angular size is about that of a fist at arm’s length, much greater than anything else that one will see in its system. We will be able to see its atmospheric zones and belts, and near its poles, its auroras. We will also notice that it is flattened at the poles, with its flattening being about 1/10.

Saturn’s rings will also be visible, though even at their best visibility, they will be very close to being edge-on, and one may need a telescope to resolve them.

Several of Saturn’s moons will be visible to the unaided eye, and one will also see some of them being eclipsed by Saturn and some of them casting shadows on Saturn. It will take a telescope to resolve them, with only Rhea being even borderline resolvable without a telescope.

There are lots of interesting things that one can discover by observing them.

Titan’s shadow on Saturn is large enough to be visible by the unaided eye. Its angular size is 14 m of arc, about half that of the Sun and the Moon from the Earth. From its size, one can deduce Saturn’s size and distance — equatorial radius: 60,000 km, polar radius 54,000 km, and distance 1,222,000 km.

We would see several moons orbiting near Saturn, orbiting in nearly circular orbits nearly coplanar with the rings. Eclipses by Saturn would make it evident that their orbits are centered on Saturn. Plotting their distances and Titan-relative periods would give a good approximation of Kepler’s third law:

(period) ~ (distance)^(3/2)

with some departures for the farther moons, especially the farthest inner moon, Rhea.

Some moons would be seen to orbit in the orbits of some moons much bigger than them, notably Tethys and Dione, orbiting either 60d ahead or 60d behind.

Of the outer moons, only Hyperion and Iapetus are readily visible. Iapetus would be seen to have a roughly circular, constant-speed orbit, while Hyperion’s Titan-relative orbit is roughly shaped like a three-petal flower, with one of the petals being directed toward Titan.

But then some wise guy asks: what if Titan is like the inner moons, moving around Saturn? What if it is the Sun or the stars that is stationary? One then finds that Kepler’s Third Law is successfully fit by not only the inner moons, but also Titan, Hyperion, and Iapetus as well. One would also find that the inner moons’ orbits have slow precession effects, and that Hyperion’s orbit is an ellipse with Titan catching up to Hyperion about every 4 Titan orbits for each 3 Hyperion orbits.

This wise guy might also try calculating the precession rates for the inner moons, and relative to the stars, they’d find a fit to a law similar to Kepler’s third law:

(period) ~ (distance)^(7/2)

These periods run from 1 (Earth) year for Mimas to 36 years for Rhea, a little over the Sun’s apparent period. Extrapolating to Titan gives 750 years, and with good enough observations, one may be able to observe a bit of Titan’s precessions.

This would suggest that it is the stars that are nonrotating. So we would conclude that the Universe is not centered on Titan, but instead on Saturn, with the Sun moving around it, like all the other objects that move around Saturn.

Kepler’s third law would suggest Newton’s inverse-square law of gravity, though applying that to the moons’ interactions takes a lot of complicated calculations. But one would find that Titan controls Hyperion’s orbit orientation, that Mimas and Tethys pull each other alternately forward and backward from their 2:1 resonance, and that Enceladus and Dione do likewise. Also why some moons orbit in some other moons’ orbits 60d ahead or behind (Lagrange points L4 and L5).

One would also find that Saturn’s equatorial bulge has its own gravitational field, a field that makes the inner moons’ orbits precess. So with that and Saturn’s flattening, one would conclude that Saturn is much more dense close to its center than near its surface.

The Sun would be an enigma.

Iapetus’s Titan-orbit parallax would be readily observable at 20d, while the Sun’s would be 3m, difficult without a telescope. Also, from Newtonian mechanics, one would find that Titan’s mass is about 1/4200 Saturn’s, and that Saturn’s other moons are much less massive. But the Sun’s great distance would imply that it has a linear size about 12 times greater than Saturn’s, and that is mass is about 3500 times larger.

So would Saturn be moving around the Sun?

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