In 1471, Regiomontanus (Johannes Muller of Konigsberg) posed the following question: "At what point of the Earth's surface does the visual angle of a perpendicularly suspended rod appear largest?"
From his answer it is clear that he thought that the Earth was flat. The problem can be solved using differential calculus, but that was only developed two centuries later. Can you think of a simpler way of solving it? Take the lower end of the rod as a distance a above the plane and the upper end as a distance b above the plane.
Question 2.
Now assume that the Saturn is spherical (radius r), and the "rod" is actually Saturn's Ring System which is above its Equator. At what latitude does the visual angle appear greatest now? A simple equation will do. This one is due to Hermann Martus, apparently in 1907.
Question 3.
As it happens Saturn is not spherical. Suppose that you are aboard an air balloon just above the cloud layer of Saturn's atmosphere. Assuming that Saturn is an ellipse of rotation, otherwise known as an oblate spheroid, with polar radius r and equatorial radius s>r, can you now find the best vantage point to view Saturn's rings? Again, a simple equation will do. This one is due to yours truly (1995.)
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Question 1.
In 1471, Regiomontanus (Johannes Muller of Konigsberg) posed the following question: "At what point of the Earth's surface does the visual angle of a perpendicularly suspended rod appear largest?"
From his answer it is clear that he thought that the Earth was flat. The problem can be solved using differential calculus, but that was only developed two centuries later. Can you think of a simpler way of solving it? Take the lower end of the rod as a distance a above the plane and the upper end as a distance b above the plane.
Question 2.
Now assume that the Saturn is spherical (radius r), and the "rod" is actually Saturn's Ring System which is above its Equator. At what latitude does the visual angle appear greatest now? A simple equation will do. This one is due to Hermann Martus, apparently in 1907.
Question 3.
As it happens Saturn is not spherical. Suppose that you are aboard an air balloon just above the cloud layer of Saturn's atmosphere. Assuming that Saturn is an ellipse of rotation, otherwise known as an oblate spheroid, with polar radius r and equatorial radius s>r, can you now find the best vantage point to view Saturn's rings? Again, a simple equation will do. This one is due to yours truly (1995.)
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