It is interesting and instructive to consider what the Solar System looks like from elsewhere in it, and I have focused my efforts on Titan, Saturn's largest satellite, and the only satellite in the Solar System with a sizable atmosphere. I had originally posted most of this in another messageboard; I am reposting it here because it may be of interest to you people. And there is a nice Wikipedia article on this subject in general, Extraterrestrial skies. It covers not only the Solar System, but also extrasolar planets.

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If one could not see beyond its clouds, one could still deduce that it is round, if one can do surveying over a large enough area (its radius is about 2575 km).

Polygon angle-sum excess = (Polygon area)/(Radius)^2

Or in general, (Curvature)*(Polygon area), and if one can measure enough polygons across Titan's surface, one would eventually conclude that its surface curvature is approximately constant over its surface.

Once that is done, one might want to try the Foucault pendulum experiment. It detects how Titan rotates underneath the swinging pendulum, which it does at a period of nearly 16 Earth days. Its actual rate and direction will depend on the latitude:

(Foucault rotation rate)
= (rotation rate)*((upward direction).(rotation-axis direction))
= (rotation rate)*(sin(latitude))

Once one can detect the Foucault rotation, one can then measure it in different places to test the hypothesis that Titan is a rotating sphere.

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Titan's atmosphere is essentially opaque in visible light, though there are some regions of the infrared spectrum where it is close to transparent - some windows near 1 micron and a 5-micron-wide one near 20 microns. But the resolution will be lower, because of the longer wavelengths. To be able to see beyond Titan in visible light, one must go above the main haze layer, whose top is at altitude 250 km. There is a layer of detached haze at about 300 - 350 km up, but it is much thinner. (Some sources: The Atmosphere of Titan and Titan's Haze)

The atmospheric pressure at the top of the main haze is around 1 mbar, as compared to 1000 mbar at the surface (around Earth's); getting up there by balloon will require a balloon volume of around (100 m)^3 for each ton of payload, with the balloon material having a surface density of at most around 10^-3 g/cm^2 (10-micron-thick plastic). But that balloon can be flimsier than its Earth counterpart; Titan's surface gravity is less than 1/7 that of Earth.

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But once once does so, one will see Saturn in the sky, about 5 deg across (10 times the Moon from the Earth). It will stay in essentially the same position in the sky, though it will move in the sky a little bit due to Titan's orbital eccentricity and inclination. Its rings will also be visible, but will always be very close to edge-on. However, their shadows will be easily visible on Saturn, especially near Saturn's solstices.

Saturn's larger inner moons, Janus, Mimas, Enceladus, Tethys, Dione, and Rhea, will be readily visible, though they will stay close to Saturn; Rhea gets only 26 degrees from Saturn, and the others less. They also orbit faster, Rhea making 3.53 orbits per Titan day and Janus 23 orbits. Their orbits are nearly circular and coplanar, and near Saturn's equinoxes, they cast shadows on Saturn, and in turn enter Saturn's shadow. Titan's eclipse season lasts only 1/16 of a Saturn year, while the nearer ones have longer eclipse seasons. From these observations, one can easily show that those objects are orbiting Saturn and not Titan, and that Saturn is much larger than Titan by a factor of 23, which is in turn larger than those objects (Rhea, the largest, is 1/3 Titan's size). One can even discover Kepler's Third Law from their motions, and perhaps infer from that that Saturn and not Titan is the center of the Universe.

Observing Mimas, Enceladus, Tethys, and Dione over the long term reveals that Mimas and Tethys, and likewise Enceladus and Dione, interact with each other, one speeding up while the other slows down, and vice versa, in a pendulum-like fashion. This "orbital resonance" effect is due to the fact that Tethys's orbital period is twice that of Mimas, and Dione's twice that of Enceladus.

And though one will be able to see some of Saturn's surface detail, one won't be able to see much detail of those satellites without a telescope; Rhea's average angular size is 4' and its largest angular size is 8' (1/8 and 1/4 that of the Moon from the Earth), and that's the biggest one.

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Looking outside of Titan's orbit, the first satellite one comes across is Hyperion, which would present a serious puzzle. Relative to Titan, orbit is shaped like a three-lobed circle centered on Saturn, with Hyperion slowing down at the corners of the lobes and speeding up in between. One lobe points to Titan, and as a result, Hyperion spends only 1/10 of its time away from Saturn in angular direction from Titan.

Since it is difficult to get precise direct distance measurements, this would be a bigpuzzle until Hyperion's eclipse season, when one can use those eclipses to get additional constraints on its positions. These would demonstrate that Hyperion's orbit is an ellipse and that it sweeps out a constantly increasing area as it moves (Kepler's First and Second Laws). And that odd Titan-relative shape would be due to an orbit resonance with Titan, with Hyperion's orbit period being very close to 4/3 times that of Titan, and with Hyperion being at its farthest distance from Saturn when Titan is in its direction. Its average orbit distance is 1.21 that of Titan and its eccentricity 0.104, meaning that it is 0.34 times Titan's orbit distance at its closest to Titan.

Hyperion also has the unusual quality of chaotic rotation, tumbling chaotically with a timescale approximately that of its orbit; most other Saturnian satellites, at least out to Iapetus, have one side permanently facing Saturn.

Looking further outward, one can see Iapetus and Phoebe, with distances 3 and 11 times that of Titan, and periods 5 and 35 times that of Titan. One would watch Iapetus go retrograde as Titan passes it, and one would watch Phoebe change from retrograde to direct as it got near Saturn's direction (its orbit is retrograde -- the other direction from the other satelltes). This is from the parallax effect created by Titan's orbit, and that can be used to work out the satellites' distances.

And once one does so, one finds that the beyond-Titan satellites also follow Kepler's Third Law -- even Phoebe. And like the inside-Titan satellites, it would be hard to see any details of these ones without a telescope. But even overall brightness can tell us something; Iapetus is ten times brighter on its trailing hemisphere than on its leading one; that means that it will be ten times brighter when 90 degrees ahead of the Sun than 90 degrees behind.

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Looking beyond Phoebe, one discovers the Sun, which looks like a brilliant spark about 3' across. It moves much more slowly with respect to the stars than the other celestial bodies we've mentioned; it has a period of 674 Titan days. And it's far enough away so that its Titan-orbit parallax (3') is difficult to measure directly. One could get more precision by watching Rhea eclipse the Sun or Titan eclipse Rhea, but one only gets a parallax across Rhea's orbit, or 1.3'.

But once one gets a fix on the Sun's distance, one finds it to be even bigger than Saturn - 11 times bigger. And its seeming orbit around Saturn violates Kepler's Third Law rather drastically.

But in the neighborhood of the Sun, one can see the planet Jupiter, which gets as far away as 33 degrees from the Sun, and the inner planets, which get as far as 9 degrees from the Sun (Mars). They also can be found to follow Kepler's Third Law, but with a different proportionality constant. And when one plugs in the Sun's apparent motion around Saturn, one finds a good fit, indicating that Saturn also moves around the Sun. Meaning that the center of the Universe may be the Sun and not Saturn.

With a telescope, one can easily see not only Jupiter's Galilean satellites, but also the Earth's Moon. And once one does so, one can easily verify that the Galileans also follow Kepler's Third Law, with yet another proportionality constant. And one can also see not only the Galileans, but also the Earth's Moon, getting eclipsed, though the latter is a relatively rare event. And while one can make out some surface details of Jupiter, it would be very hard to do that with the inner planets; the biggest of them (Earth) has an angular size of 1.8 seconds of arc.

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One may then go on to discover Newton's Laws of Motion and Law of Gravity, and even show how they account for all these motions, including the resonance effects. By measuring Titan's surface gravity and size, one can show that Saturn is 4300 times more massive -- and check that by showing that Titan forces Hyperion's orbit eccentricity. And also measure the masses of Mimas, Enceladus, Tethys, and Dione in the same way with the help of their orbit resonances, and get some clues as to Saturn's internal mass distribution with the help of the gravitational effects of its equatorial bulge.

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Looking outside the Solar System would be roughly the same as for the Earth, except that one has a 10 times larger parallax across Saturn's orbit. This means that one can find parallax distances 10 times farther, and therefore for 1000 times as many stars.

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One can do much of this discovery in the infrared as well as in visible light, especially at the 1-micron windows; the 20-micron window has the problem of being close to the thermal peak of 30 microns due to Titan's typical temperature of 90 K. Its optical depth is about 1, meaning that its luminosity per unit solid angle is close to that of Saturn and its satellites, meaning that they will be hard to see unless one can resolve them. The Sun has much larger luminosity, meaning that one will not need to resolve it to see it. One will need 30' resolution as opposed to its angular size of 3'.

With passive radio, one can observe not only the Sun and Jupiter, but likely also the Earth. Saturn's presence could be inferred by the eclipses it causes, though that will be much harder for its satellites.

But with active radio, that is, radar, one can see much more. One may need some motivation for doing radar observations; there may not be much if one has no knowledge of anything above Titan's clouds and haze.

But once one does, one will be able to see Saturn's rings and other satellites, though Saturn itself is much less radar-reflective. But one can infer Saturn's presence from the rings' Doppler shifts and satellites' motions, and get precise distance data to complement visible-light and infrared angular-position data. Radar would be much more difficult for the rest of the Solar System, however; radar-reflection intensity goes as (distance)^(-4), and some objects' larger sizes would only partially compensate.

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I have found some nice rendered views of that satellite; here are some pictures from it:



110 km altitude The upper haze's scattering produces the blue light.



90 km altitude The haze starts turning brownish as it becomes thicker.



70 km altitude In the middle of the thickest haze; the view stars getting clearer.



25 km altitude The haze starts becoming thin.

According to the article, only 1/10 of sunlight makes it through Titan's atmosphere to its surface, meaning that only 1/100 gets out. But I've been unable to find details on how much of the atmosphere's extinction of traveling light, as it is called, is absorption, and how much is scattering.

If it's mostly scattering, as with Earth clouds, then most of the light will have made several scatters, and there will be little incident light remaining. When I first wrote this, it is a cloudy day with plenty of light, but I can't see the Sun. But if it's mostly absorption, then most of the light will be surviving incident light, and one can see beyond the clouds.

I'd like to get an extra-solar probe out to look at the Solar System from the outside looking in at 2-3 ly out.

First, it would take an awfully long time to send a probe out there. And to make a long story short, it would require a lot more spacefaring capability than we have at the moment -- heavier spacecraft to transmit over that distance, propulsion systems with greater exhaust velocity, advanced autonomy and possibly self-repair, etc.

And second, it would be very hard to make out any details. From 1 parsec, the Sun would be magnitude -0.15, and would be one of the brightest stars in the sky, but the planets would be much dimmer and very close. The Earth is mag +22 at 1" max separation, and Jupiter is mag +20 at 5" max separation. So the spacecraft would have to send out an eclipser to make the planets visible.