NEPTUNE TO FINISH ITS FIRST REVOLUTION IN 2011 SINCE DISCOVERY IN 1846  
  by  Dr. R C Kapoor*
  rck@iiap.res.in, rckapoor48@gmail.com

Neptune the blue coloured eighth planet of the Solar System shall be completing its first revolution of the Sun this year since its discovery in 1846. Its mean distance from the Sun is 30.066 AU and orbital period 60,216 days or 164.793 years. Unexplained deviations in the orbit of the planet Uranus, ever since its accidental discovery on March 13, 1781 by William Herschel, led astronomers to believe that there was some unknown body farther out that was the cause. John Adams and Urbain Le Verrier carried out independent analysis of discrepancies in the observed and calculated positions of Uranus and predicted in 1845 the mass and orbit of the perturbing body. The planet was discovered on September 23, 1846 by Johann Galle and Heinrich d’Arrest from Berlin Observatory very near the predicted position. Neptune is thus the first planet found by mathematical prediction rather than by observation. In less than three weeks of the discovery, its biggest satellite Triton was discovered on Oct 10, 1846 by William Lassell. The second satellite, Nereid, was discovered by G P Kuiper in 1949.

Neptune is only slightly smaller but more massive than Uranus, has 13 satellites, and a thin ring system that was discovered in 1984. Its orbit is nearly circular. Its atmosphere is dominantly hydrogen (80%), with helium 19% and methane 1%, and a very small admixture of other compounds. Its interior may be water rich. However little in abundance, the atmospheric methane absorbs red light and gives a blue hue to the planet; its average temperature is – 235°C. 'It is 3.887 times bigger and 17.132 times more massive than the Earth.

Neptune completes one orbit since discovery in 2011, on July 12.9000 when it reaches approximately the same heliocentric longitude 329°.1020 as at discovery. That makes it Neptune’s one year! For us, that will be on July 13, 03:06 IST'. Neptune is currently in between the Capricornus and Aquarius constellations, between the stars Delta Capricorni and Lambda Aquari to be precise. One needs a moderate sized telescope to view it as it is faint for the powers of binoculars or small telescopes.

The heliocentric longitude is measured at the centre of the Sun, also called the ecliptic longitude, measured clockwise from the vernal equinox. The apparent position of a planet is given in terms of its geocentric longitude. To that we make a correction specific to the location on the Earth by allowing for shape and size of the Earth. That gives us topocentric positions. Specific to Berlin, Neptune passes close to its discovery point three times in the year 2011, on Feb 12, Oct 28 and Nov 22, 2011 according to the British astronomer Derek Jones. In fact, on Nov 22, 2011 it will pass by its apparent discovery position from 33 arcsec, the closest of the three conjunctions. The reason for the three opportunities is Neptune’s parallax. For its distance of about 30 AU, it is 1/30 radians, or about 2 degrees. Because of this parallax, the planet shall be moving back and forth about its heliocentric longitude (of discovery) against the background stars, as the Earth proceeds in its orbit. This is similar to the retrograde motion of the other outer planets. By Feb 12, 2011 it had not completed its orbit and on Oct 28 and Nov 22 it will have overshot, i.e., completed more than one revolution.

Neptune will be in opposition in Aquarius on Aug 22, 2011, around 00 UT. That means the planet, 28.995 AU from us, rises around when the Sun sets in the west and shall be up all night.

*The author is an astrophysicist, formerly with the Indian Institute of Astrophysics.

Teaching algae to make fuel

13,000 cancers each year down to drinking

About one in ten cancers in men and one in 33 cancers in women in Western Europe is caused by alcohol, a European study has calculated.

That amounts to at least 13,000 cases of cancer a year in the UK, according to the report published in the British Medical Journal – around 9,000 in men and 4,000 in women.

The researchers, including scientists at the Cancer Epidemiology Unit at Oxford University, argue that a substantial proportion (40 to 98%) of the cancers attributable to alcohol occurred in individuals who drank more than the recommended guidelines, which suggest upper limits of two drinks a day in men and one drink a day in women. 

‘This research supports existing evidence that alcohol causes cancer and that the risk increases even with drinking moderate amounts,’ said Dr Naomi Allen of the Cancer Epidemiology Unit at Oxford University, one of the authors of the study.

The group looked at how different levels of drinking affect the risk of cancer using data from the European Prospective Investigation of Cancer (EPIC). They combined this with figures on how much people drink, to give the number of cancers that can be attributed to alcohol. 

The study focussed on the following countries: France, Italy, Spain, United Kingdom, The Netherlands, Greece, Germany and Denmark.

The EPIC study is funded by Cancer Research UK, the Medical Research Council and other European agencies. It is one of the largest studies into the links between diet and cancer involving more than half a million people in Europe.

Shattering art to reconstruct the past

Destroying ancient Greek art has become something of a specialty for Hijung (Valentina) Shin.

For her senior thesis at Princeton, Shin, a computer science major from Yongin, South Korea, is working to perfect her method for shattering stone frescoes painted thousands of years ago -- a technique designed to return the art to its former glory.

"I'm actually breaking things inside a computer," she said. "If we can simulate how the art was destroyed, it will help us piece the shards back together again."

The artworks in question were frescoes found on Thera, an Aegean island also known as Santorini that was devastated by a volcano around 1650 B.C. The eruption destroyed the island's Hellenic civilization, including the frescoes painted on town walls, burying the remnants for millennia.

 In recent decades, archaeologists have begun excavating the ancient ruins, but face the daunting task of sorting through the debris and reconstructing the frescoes one shard at a time. Shin's project developed as part of an effort by Princeton computer scientists to aid these archaeologists in their work.

Princeton traveled to Akrotiri -- a site on Thera that had flourished in the Late Bronze Age, around 1630 B.C. -- to begin studying the methods used by archaeologists to piece together the fresco fragments unearthed at the site. The group led by Szymon Rusinkiewicz, an associate professor of computer science, invented a laser-based scanning system to record measurements of the shape, size and color patterns of the shards.

The math of the Rubik’s cube
New research establishes the relationship between the number of squares in a Rubik’s-cube-type puzzle and the maximum number of moves required to solve it.

Unfortunately, for cubes bigger than the standard Rubik’s cube — with, say, four or five squares to a row, rather than three — adequately canvassing starting positions may well be beyond the computational capacity of all the computers in the world. But in a paper to be presented at the 19th Annual European Symposium on Algorithms in September, researchers from MIT, the University of Waterloo and Tufts University establish the mathematical relationship between the number of squares in a cube and the maximum number of moves necessary to solve it. Their method of proof also provides an efficient algorithm for solving a cube that’s in its worst-case state.

Computer science is concerned chiefly with the question of how long algorithms take to execute, but computer scientists measure the answer to this question in terms of the number of elements the algorithm acts upon. The execution time of an algorithm that finds the largest number in a list, for instance, is proportional to the length of the list. A “dumb” algorithm for sorting the numbers in the list from smallest to largest, however, will have an execution time proportional to the square of the length of the list.

Solution with a twist

Erik Demaine, an associate professor of computer science and engineering at MIT; his father, Martin Demaine, a visiting scientist at MIT’s Computer Science and Artificial Intelligence Laboratory; graduate student Sarah Eisenstat; Anna Lubiw, who was Demaine’s PhD thesis adviser at the University of Waterloo; and Tufts graduate student Andrew Winslow showed that the maximum number of moves required to solve a Rubik’s cube with N squares per row is proportional to N2/log N. “That that’s the answer, and not N2, is a surprising thing,” Demaine says.

The standard way to solve a Rubik’s cube, Demaine explains, is to find a square that’s out of position and move it into the right place while leaving the rest of the cube as little changed as possible. That approach will indeed yield a worst-case solution that’s proportional to N2. Demaine and his colleagues recognized that under some circumstances, a single sequence of twists could move multiple squares into their proper places, cutting down the total number of moves.

But finding a way to mathematically describe those circumstances, and determining how often they’d arise when a cube was in its worst-case state, was no easy task. “In the first hour, we saw that it had to be at least N2/log N,” Demaine says. “But then it was many months before we could prove that N2/log N was enough moves.”

Because their method of analysis characterizes the cases in which multiple squares can be moved into place simultaneously, it provides a way to recognize those cases, and thus an algorithm for solving a disordered cube. The algorithm isn’t quite optimal: It always requires a few extra moves. But as the number of squares per face increases, those moves dwindle in significance.

Go configure

The Rubik’s cube is an instance of what’s called a configuration problem, the best-known example of which involves finding the most efficient way to reorganize boxes stacked in a warehouse. It’s possible, Demaine says, that the tools he and his colleagues have developed for studying the Rubik’s cube could be adapted to such problems.

But Demaine is also a vocal defender of research that doesn’t have any obvious applications. “My life has been driven by solving problems that I consider fun,” he says. “It’s always hard to tell at the moment what is going to be important. Studying prime numbers was just a recreational activity. There was no practical importance to that for hundreds of years until cryptography came along.”

But, he adds, “the aesthetic is not just to look at things that are fun but also look at problems that are simple. I think the simpler the mathematical problem, the more likely that it’s going to arise in some important practical application in the future. And the Rubik’s cube is kind of the epitome of simplicity.”

“Erik is always very interested in extending the reach of popular mathematics,” says Marc van Kreveld, an associate professor in the Department of Information and Computing Sciences at Utrecht University in the Netherlands, who designs puzzles in his spare time. “That’s really one of the things that he tries to do, to bring across that mathematics is not just some boring area of study, but it’s actually fun, and you can do a lot with it, and it’s beautiful.”

“Erik’s a very brilliant person,” van Kreveld adds. “He is already very successful in his hard-core research. But the popularizing is also very necessary, I think. You should not underestimate the importance of motivating students to learn.”