# If we stood on the surface of a Jovian moon, Saturn would appear as a dot. Why doesn't Saturn appear like this in a telescope?

Images from the conjunction like these show Saturn just a bit smaller than Jupiter. However, if you were in the vicinity of Jupiter, Saturn would still appear as a dot to the naked eye, wouldn't it? If so, why is Saturn recognizable as a planet through a telescope in which Jupiter is also seen as a planet? As if they were actually very close to each other, at about the same distance from the Sun. I mean, if you recognize Jupiter in a telescope, shouldn't Saturn behind it look like a dot, unless you have a much, much larger zoom in which Jupiter would appear too close to match into the whole image while being too unsharp anyway?

Telescopes magnify, they don't bring you closer.

So if from Earth Jupiter has an apparent radius of 0.01 degrees (measured as an angle because it is the apparent size)

And if Saturn has an apparent angle of 0.005 degrees, then if you magnify 100x then Jupiter will have an apparent size of 1 degree, and Saturn would have a size of 0.5 degrees. Magnification just increases the angular size in proportion

But if You go to Jupiter you have travelled less than half the distance to Saturn.
So saturn is still small. Travelling closer does not make everything increase in size in proportion.

You can see this simply: Stand where you can see something 20 metres of so away, and where you can see into the hills (etc) in the background. Walk towards the thing. Note that the thing appears to get bigger as you approach, but the distant hills don't change size. Travelling closer does not magnify everything in proportion.

Telescopes don't "bring things closer" they "magnify".

• Wouldn't the hills look about the same both in binoculars and with the naked eye closer? Whatever, why does Saturn have half the apparent radius than Jupiter in the first place even though it's so much farther? If Uranus and Neptune were close to them, would they appear of similar size too, would we see four planets then? Sorry if my questions sound very greenhornish. Dec 26 '20 at 14:36
• As @James K pointed out, Saturn is more than twice the distance of Jupiter. Place one of your fingers twice as far from your eye as another finger, and it will look half the size of the closest fingers. So, Saturn looks about half the angular size of Jupiter. QED. Uranus and Neptune are slightly less than the physical diameter of Jupiter and Saturn, but they’re respectively about 4 and about 8 times further from Jupiter, so they look quite small—about 3.5 and about 2.25 arcseconds, respectively, against Jupiter’s 40 arcsecs and Saturn’s 17 arcsecs (all on average). Dec 26 '20 at 16:19
• No. If you have a ball 20 meters away and you have binoculars that magnify x2. You look at the hills in the binoculars and they are x2. You look at the ball and it is x2. Now you walk 10 meters towards the ball. The ball is now x2 without binoculars. But the hills are not. This is such a common notion that you can easily confirm. Telescopes don't bring you closer. The magnify it is different. Dec 26 '20 at 16:23
• Thank you, now I see. Dec 26 '20 at 16:56

Saturn has a diameter of about 116,000 km and is about 1.4 billion km from Earth. For Jupiter, the corresponding numbers are 140,000 and about 800 million km (the distances vary somewhat as the planets move around the Sun. The size of the images of the planets is determined by the ratios of these, so Saturn is about $$\frac{116000}{1400000000} = 0.00008$$ radians and Jupiter about $$\frac{140000}{800000000} = 0.000175$$ radians as seen from Earth. Both are too small to show a disk to the naked eye, but a suitable telescope will show you two disks, one about twice the size of the other.

Seen from, say, Callisto (one of the moons Jupiter), Jupiter is about 1.8 million km away, and Saturn, at its closest, about 600 million kilometers. So, we can do the same calculations. Saturn subtends an angle of $$\frac{116000}{600000000} = 0.000193$$ a little bigger than Jupiter seen from Earth, but still star-like. Jupiter occupies about $$\frac{140000}{1800000} = 0.077$$ radians -- about 10 times as big as a full moon.

• But the distance from Jupiter to Saturn is the same, so why do you see Saturn in a telescope planet-like at the same zoom as when you would see Jupiter from Callisto? And at these vast distances it's better to use AU I suggest. Dec 26 '20 at 13:31
• Moving closer is not the same as zooming. AU is ood for the distances, but not the diameters. Dec 26 '20 at 14:02