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How large in the night sky would Saturn look from Titan's surface? I believe they are tidally locked.

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up vote 14 down vote accepted

The angular size of the object can be calculated by basic trigonometry: $\theta=2\cdot \arctan(r/d)$, where $r$ is the radius of the object you're viewing, and $d$ is the distance between you and the object ($\theta$ is the angle).

The average (volumetric) radius of Saturn is 58,232 km. The distance between Titan and Saturn is 1,221,830 km. Plugging the numbers in gives an angular size of 5.46°. Doing the same for our moon gives you 0.52°. Dividing one by the other gives you a factor of $\sim 10.5$ difference.

 

Note 1: When you do this math with a calculator, verify you get the correct results for the moon from Earth before you go on to something else. You may encounter issues where the results of your arctan() function will be given in radians, not degrees. If the math gives you a weird result, multiply by $180/\pi \approx 57.3$.

Note 2: Saturn would not actually be visible from the surface of Titan due to the thick atmosphere of the moon. Also, tidal locking has nothing to do with this problem other than if Saturn may be visible from an arbitrary location on Titan (if you could see through its atmosphere).

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Thanks for your detailed answer. Its a shame that saturn couldn't be seen as it would be HUGE! –  Mike S Jan 5 '12 at 0:16
    
And the ring tip to tip would appear as big as 14 degrees –  user12996 Oct 12 '12 at 15:39
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@MikeS: just as an FYI: we've actually sent a lander to Titan. And it recorded video: esa.int/SPECIALS/Cassini-Huygens/SEMKVQOFGLE_0.html –  Jerry Schirmer Oct 12 '12 at 16:32
    
We need to get our asses in gear and tera form that moon ASAP. Clean up the atmosphere and its good to go! :) –  Mike S Oct 18 '12 at 5:45

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