Another object, , was seen nearby 5 hours later, but this time just "inside" the F Ring. Because of the different location of the second object, it was given a fresh designation, although their interpretation as a single object on a F-ring crossing orbit is also possible. Such an object might also be orbiting at a bit different inclination to the F ring, thereby not actually passing through the ring material even though it was being seen both radially inward and outward of it.
If a solid object after all, would be 3−5 km in diameter based on brightness, and might be a shepherd satellite for the farther edge of Saturn's F ring.
S/2004 S 4
Even though astronomers tried to find it again, it has not been reliably seen since. Notably, an imaging sequence covering an entire orbital period at 4 km resolution taken on 15 November, 2004 failed to find the object. This suggests that it was a clump of material that had disappeared by that time.
An interpretation where S3 and S4 are or were a single object on a F-ring crossing orbit is also possible. Such an object might also be orbiting at a bit different inclination to the F ring, thereby not actually passing through the ring material even though it was being seen both radially inward and outward of it.
If a solid object after all, would be 3−5 km in diameter based on brightness.
S/2004 S 6
It was first seen by scientists in pictures taken by the Cassini-Huygens probe on October 28, 2004, and announced on 8 November that year. It appears to be the best tracked object in this area with at least five possible sightings in the period till late 2005. In comparison, two objects in the F ring's area ( and ) that were first seen months earlier have not been found again with any confidence. Nevertheless, it continues to be unclear whether there is a solid core to or whether it is just a dust clump that will disappear in years or months. Notably, an imaging sequence covering an entire orbital period at 4 km resolution taken on 15 November, 2004 (soon after 's discovery) failed to find the object, while it has been seen again later. The lighting conditions in 's part of the orbit were different during these two sightings, however, with the discovery being made when the area was strongly backlit by the sun. A suggested resolution of the absence in November is that 's visibility is primarily due to a diffuse cloud of fine dust that is much brighter in forward scattered light (the conditions of the discovery image), and that the solid core (if any) is small.
The dusty halo seen in pictures is big, being around 2000 km in lengthwise extent. The solid object, if any, would be no bigger than 3−5 km in diameter based on brightness.
Joel Hastings Metcalf
Joel Hastings Metcalf (January 4, 1866–February 23, 1925) was an American astronomer.
Metcalf graduated from Harvard Divinity School in 1892. He served as a Unitarian minister in Burlington, Vermont and then later in Taunton, Massachusetts, Winchester, Massachusetts and Portland, Maine.
He found or co-found many comets, such as 23P/Brorsen-Metcalf and 97P/Metcalf-Brewington; he also found many asteroids.
Gräfendorf
Gräfendorf is a municipality in the district of Main-Spessart in Bavaria in Germany, near Würzburg, Aschaffenburg and Frankfurt. As of 2006, 1,411 people live in Gräfendorf.
Imaginary number
Imaginary numbers are numbers that are made from combining a real number with the imaginary unit, called "i", where "i" is defined as formula_1. They are defined separately from the negative real numbers in that they are a square root of a negative real number (instead of a positive real number). This is not possible with real numbers, as there is no real number that will multiply by itself to get a negative number (e.g., formula_2 and formula_3). The set of imaginary numbers are sometimes denoted by the letter formula_4.
One way of thinking about imaginary numbers is to say that they are to negative numbers what negative numbers are to positive numbers. If we say "go east by -1 mile", it is the same as if we had said "go west by 1 mile". If we say "go east by i miles", it means the same thing as if we had said "go north by 1 mile". Similarly, if we say "go east by -i mile", it means the same as if we had said "go south by 1 mile".
Adding is easy too. If we say "go east by 1 + i miles" it means the same as if we had said "go east by one mile and north by one mile".
Multiplying two imaginary numbers is a lot like multiplying a positive number with a negative number. If we say "go east by 2 × -3 miles", it means "rotate all of the way around (so that you are now facing west) and go 2×3 = 6 miles". Imaginary numbers work the same, except that you can rotate part way. If we say go "east by 2×3i miles", it means the same as if we had said "rotate until you are facing north, and then go 2×3 = 6 miles"
Subtractions such as 5 - 9 used to be impossible until negative numbers were invented, just as taking the square root of a negative number used to be impossible until imaginary numbers were invented. The square root of 9 is 3, but the square root of −9 is not −3. This is because −3 x −3 = +9, not −9. For a long time, it seemed as though there was no answer to the square root of −9.
This is why mathematicians invented the imaginary number, "i", and said that it is the main square root of −1. The square root of −1 is not a real number, so this definition creates a new type of number, just like fractions create numbers like 2/3 that are not counting numbers like 4 or 10, and negative numbers create numbers that are less than 0. Sometimes, mathematicians seem rather comfortable using a number that is so unusual, but the name "imaginary" should not fool you because "i" is as valid a number as 3 or 145,379.
Many branches of science and engineering have found uses for this number. For example. electrical engineers need "i" to understand how an electric circuit will work when they are designing it (electrical engineers use "j" instead of "i" to avoid confusion with the symbol for the current). As another example. certain branches of physics such as quantum physics and high energy physics use "i" as often as they use any other regular number. Many of the equations in the world simply cannot be solved without "i".
Imaginary numbers can be mixed with numbers we are more familiar with. For example, a real number such as "2" can be added to an imaginary number such as "3i" to create "2+3i". These kinds of mixed numbers are known as complex numbers.
Eric Maskin
Eric Stark Maskin (born December 12, 1950) is an American economist. In 2007, he won the Nobel Prize in Economics with Leonid Hurwicz and Roger Myerson. He is the Albert O. Hirschman Professor of Social Science at the Institute for Advanced Study, and a visiting Professor at Princeton University.
Maskin was born in New York City, New York on December 12, 1950, to a non-religious Jewish family, and grew up in Alpine, New Jersey. He graduated from Tenafly High School in Tenafly, New Jersey in 1968, and then studied at Harvard University where he received his A.B. and Ph.D. After he got his Ph.D., Maskin went to the University of Cambridge in 1976 where he was a research fellow at Cambridge College. He taught at Massachusetts Institute of Technology from 1977-1984 and from 1985-2000 at Harvard, where he was the Louis Berkman Professor of Economics. In 2000, he moved to the Institute for Advanced Study in Princeton, New Jersey.