Will an observer at the pole of Saturn be able to see its rings? The radius of Saturn is 60,000 km, the length of the rings is 5 times the radius of Saturn.
To determine if the rings are visible, you need to find the horizon distance r at the Saturn pole. We use the Pythagorean theorem r = √ (R + h) ^ 2 -R ^ 2, if you expand the brackets, we get r = √ R ^ 2 + 2Rh + h ^ 2 – R ^ 2. h is the height of the observer, let us assume that h = 2 m, R is the radius of Saturn. And then h ^ 2 can be ignored, because this is small compared to the radius of Saturn. As a result, we get r = √2Rh.
r = (2 * 60,000 * 0.002) ^ 0.5 = 15.5 (km). Saturn’s rings will not be visible from the pole, because will be over the horizon.
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