Kepler's Laws Govern Awesome Comet Mission
Rosetta’s journey from launch in March 2004 to arrival at Comet 67P/Churyumov-Gerasimenko in August 2014, including 3 flybys of Earth and 1 of Mars. The journey couldn't have been made without an intimate knowledge of Kepler's laws.
Image: A series of photographs of comet Hartl
6 Intimate Comet Encounters
Feb. 14, 2011 will go down in history as the Valentine's Day when a comet was visited a second time. Comet Tempel 1 has now played host to two different NASA spacecraft; Deep Impact in 2005 and Stardust-NExT in 2011. This amazing scientific feat comes hot on the heels of another cometary encounter only a few months ago. The NASA mission called EPOXI flew past comet Hartley 2 on Nov. 4, 2010 coming within 700 kilometers (435 miles) of the icy body. Both Stardust-NExT and EPOXI (formerly known as Deep Impact) are recycled comet missions and both have seen Tempel 1 up-close. EPOXI and Stardust-NExT may be the first two missions to be recycled for two comet flybys, but they certainly are not the first mission to rendezvous with these mysterious "dirty snowballs." So far, with the help of our robotic space explorers, humanity has had a close-up look at six cometary nuclei in the aim of unraveling their secrets. Let's take a look at each encounter with imagery from other space probes.
Image: Giotto's view of Halley's nucleus (ESA
Unquestionably the most famous comet in history, Halley's Comet was a prime target for space agencies in 1986 during its 75- to 76-year orbit through the inner solar system. Comet science is still a developing field, but in 1986, very little was known about the composition of these interplanetary vagabonds. In October of that year, the 15-kilometer-long Halley's Comet was visited by the European Space Agency's Giotto mission. The half-ton probe came within 600 kilometers (373 miles) of the comet's nucleus, taking the first photographs of the outgassing vapor from discrete areas of the surface producing its tail and coma (the gas surrounding the nucleus). It was this mission that confirmed the "dirty snowball" theory of cometary composition: a mix of volatile ices and dust. However, Giotto was only able to get so close to the famous comet with the help of the "Halley Armada," a number of international spacecraft all tasked with observing this rare event. Giotto captured the closest imagery, but two Russia/France probes (Vega 1 and 2) and two Japanese craft (Suisei and Sakigake) observed from afar.
Image: Comet Borrelly just before Deep Space
At roughly half the size of Halley's comet, Comet Borrelly was found to have similar attributes to its famous cousin. The nucleus was also potato-shaped and blackened. Outgassing vapor was also observed coming from cracks in the nucleus crust where volatiles were exposed to sunlight, sublimating ices into space. NASA's Deep Space 1 probe flew past the comet with a close approach of 3,417 kilometers on Sept. 22, 2001.
Image: A Stardust image of Wild 2 during its
Comet Wild 2 -- pronounced "Vilt" after its Swiss discoverer Paul Wild who spotted it in 1978 -- underwent a dramatic alteration in 1974. It is calculated that due to a close pass of Jupiter in 1974, the 5 kilometer-wide comet now orbits the sun every 6 years as opposed to its leisurely 43 years before the gas giant bullied it. The orbital modification meant that Wild 2 was an ideal target for NASA's Stardust mission to lock onto. On Jan. 4, 2004, the Stardust probe gave chase, getting so close to the comet that it was able to collect particles from Wild 2's coma. This image was taken at a distance of less than 240 kilometers (149 miles). The Stardust sample return canister came back to Earth safely, landing in Utah on Jan. 15, 2006. The microscopic particles captured from the comet continue to provide a valuable insight into the organic compounds comets contain. Interestingly, the Stardust spacecraft has been granted a mission extension (dubbed New Exploration of Tempel 1 -- NExT). In 2011 it will rendezvous with comet Tempel 1 -- the scene of NASA's 2005 Deep Impact mission -- to analyze the crater that Deep Impact's impactor left behind on the cometary surface.
Image: The view from Deep Impact's impactor b
NASA's Deep Impact mission reached the eight-kilometer-wide (five-mile-wide) comet Tempel 1 in 2005. On July 4, the probe deliberately smashed its impactor into the comet's nucleus, producing a cloud of fine material. A crater -- 100 meters wide (328 feet) by 30 meters (98 feet) deep -- was left behind. A treasure trove of compounds were spotted by the Deep Impact spacecraft and the explosion could be observed from Earth. In 2011, the recycled Stardust-NExT mission visited comet Tempel 1 for the second time.
Image: A close-up of comet Hartley 2 (NASA)
The fifth space probe encounter with a comet happened on Nov. 4, 2010. NASA's recycled Deep Impact probe -- now the EPOXI mission -- visited comet Hartley 2, examining its strange-shaped nucleus. Described as a "peanut" or "chicken drumstick," this comet is an oddity. During its close approach of under 700 kilometers (435 miles), EPOXI photographed the comet's irregular topography: two rough lobes connected by a smooth center. Jets of gas could be seen being ejected from discrete locations. During the Hartley 2 flyby press conference at NASA's Jet Propulsion Laboratory (JPL), mission scientists expressed their surprise that these jets of vapor are being emitted from sun-facing
shaded regions on the comet surface. Needless to say, analysis of the Hartley 2 flyby data will keep scientists busy for some time to come. "This is an exploration moment," remarked Ed Weiler, NASA's Associate Administrator for the Science Mission Directorate, during the conference.
Image: Tempel 1 as seen by Stardust-NExT at c
Most recently, on Feb. 14, 2011, the veteran Stardust-NExT (New Exploration of Tempel) mission made history by visiting a comet for the second time. Comet Tempel 1 was first encountered by NASA's Deep Impact mission in 2005 after smashing the cometary nucleus with an impactor. This second encounter provides scientists with an unprecedented opportunity to study the same comet after six years of orbiting the sun. Preliminary findings suggest Tempel 1 has undergone some erosion during those six years in deep space. Also, the impact crater left behind by Deep Impact was imaged during the Stardust-NExT flyby and it appears to match the size and shape predicted after the 2005 impact. However, the crater appears to be smoother than expected, so further work will need to be done to analyze the 72 photographs taken by this most recent flyby to understand the processes shaping the comet's nucleus.
I am sure that you, like me, followed the 'Wake Up Rosetta' campaign with great interest, as the tiny European explorer was awoken from its 31 month slumber. It is great to see that after all that time the systems have come back online and the craft is fully functional, ready for its rendezvous with Comet 67P/Churyumov-Gerasimenko this November. I only wish my car was so reliable.
As I followed the updates, my mind drifted off to how wonderful it is that we can actually send man made objects many millions of kilometers to tiny pieces of rock and actually arrive in the right place at the right time -- particularly as the targets are often moving at many thousands of kilometers per hour themselves. Navigating around the solar system is a tricky business but it was made a whole lot easier with the 'discovery' of three laws that govern planetary motion.
It was back in the 1600's that Johannes Kepler published his three laws of planetary motion and they are still as relevant today as they were over 400 years ago. Not only do they govern the motion of the planets around the sun but they also govern the motion of moons around planets and even exoplanets around distant stars. The laws have been invaluable in understanding not only the movements of the planets in our own solar system but also help us learn about families of new planets in the depths of our galaxy.
The first of the laws states that all planets in our solar system move in elliptical orbits with the sun at one of the points of focus of the ellipse. That is not surprising, perhaps as many of us have grown up knowing that the Earth's orbit and indeed the orbits of all the planets are elliptical.
An ellipse is essentially a squashed circle and you can imagine how it might have two points of focus if you first visualize a circle with a point at its center. If you were to squash the circle from top and bottom, the central dot would split in two and both would move outward. In the case of the planets in the solar system; the sun is found at one of these points and it is that point that they all appear to orbit.
Kepler's second law states that a line joining the sun to a planet, known as the radius vector, sweeps out equal areas of space over equal time intervals. Put another way, planets move faster when they are closer to the sun and slower when further away. But it is Kepler's third and final law that was only published ten years after the first two which describes the mathematical relationship between the time it takes for a planet to complete an orbit and its distance from the sun. In the words of Kepler, "...the square of the orbital period of a planet is directly proportional to the cube of its mean distance from the sun." This means that we can measure how long an object takes to orbit the sun from simple observation and by knowing that, we can calculate its average distance with some accuracy.
Understanding these three laws gives us a great understanding as to the movement of the planets around the solar system and using them in conjunction with other laws -- such as Newton's laws of motion and small corrections for Einstein's general relativity -- means that we can navigate our way around the solar system and do it with such accuracy that we know exactly where Comet Churyumov-Gerasimenko will be 10 years after Rosetta was launched!