citizenzen
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I never claimed that our current understanding about the positions of planets was "perfect". What human knowledge could be described that way?
It is however a close enough "approximation" for us to spend billions of dollars on a space program that has sent probes that have either landed or flown by seven planets. I think it's safe to say that it's been capably demonstrated that we know where these planets are.
In case you haven't been paying attention to this fascinating aspect of modern-day science, here's a brief run-down...
Mercury
As of January 2008, the Mariner 10 and MESSENGER missions have been the only missions that have made close observations of Mercury. MESSENGER made a fly-by of Mercury on 14 January 2008, to further investigate the observations made by Mariner 10 in 1975 (Munsell, 2006b). A third mission to Mercury, scheduled to arrive in 2020, BepiColombo is to include two probes. BepiColombo is a joint mission between Japan and the European Space Agency. MESSENGER and BepiColombo are intended to gather complementary data to help scientists understand many of the mysteries discovered by Mariner 10's flybys.
Venus
Venus was the first target of interplanetary flyby and lander missions and, despite one of the most hostile surface environments in the solar system, has had more landers sent to it (nearly all from the Soviet Union) than any other planet in the solar system. The first successful Venus flyby was the American Mariner 2 spacecraft, which flew past Venus in 1962. Mariner 2 has been followed by several other flybys by multiple space agencies often as part of missions using a Venus flyby to provide a gravitational assist en route to other celestial bodies. In 1967 Venera 4 became the first probe to enter and directly examine the atmosphere of Venus. In 1970 Venera 7 became the first successful lander to reach the surface of Venus and by 1985 it had been followed by eight additional successful Soviet Venus landers which provided images and other direct surface data. Starting in 1975 with the Soviet orbiter Venera 9 some ten successful orbiter missions have been sent to Venus, including later missions which were able to map the surface of Venus using radar to pierce the obscuring atmosphere.
Mars
The exploration of Mars has been an important part of the space exploration programs of the Soviet Union (later Russia), the United States, Europe, and Japan. Dozens of robotic spacecraft, including orbiters, landers, and rovers, have been launched toward Mars since the 1960s. These missions were aimed at gathering data about current conditions and answering questions about the history of Mars. The questions raised by the scientific community are expected to not only give a better appreciation of the red planet but also yield further insight into the past, and possible future, of Earth.
Asteroids and comets
Until the advent of space travel, objects in the asteroid belt were merely pinpricks of light in even the largest telescopes, their shapes and terrain remaining a mystery. Several asteroids have now been visited by probes, the first of which was Galileo, which flew past two: 951 Gaspra in 1991, followed by 243 Ida in 1993. Both of these lay near enough to Galileo's planned trajectory to Jupiter that they could be visited at acceptable cost. The first landing on an asteroid was performed by the NEAR Shoemaker probe in 2000, following an orbital survey of the object. The dwarf planet Ceres and the asteroid 4 Vesta, two of the three largest asteroids, are targets of NASA's Dawn mission, launched in 2007.
While many comets have been closely studied from Earth sometimes with centuries-worth of observations, only a few comets have been closely visited. A few long-period comets are currently the furthest known objects in the solar system. In 1985, the International Cometary Explorer conducted the first comet fly-by (21P/Giacobini-Zinner) before joining the Halley Armada studying the famous comet. The Deep Impact probe smashed into 9P/Tempel to learn more about its structure and composition while the Stardust mission returned samples of another comet's tail. The Philae lander will attempt to land on a comet in 2014.
Hayabusa was an unmanned spacecraft developed by the Japan Aerospace Exploration Agency to return a sample of material from a small near-Earth asteroid named 25143 Itokawa to Earth for further analysis. Hayabusa was launched on 9 May 2003 and rendezvoused with Itokawa in mid-September 2005. After arriving at Itokawa, Hayabusa studied the asteroid's shape, spin, topography, colour, composition, density, and history. In November 2005, it landed on the asteroid to collect samples. The spacecraft returned to Earth on 13 June 2010.
Jupiter
The exploration of Jupiter has consisted solely of a number of automated NASA spacecraft visiting the planet since 1973. A large majority of the missions have been "flybys", in which detailed observations are taken without the probe landing or entering orbit; the Galileo spacecraft is the only one to have orbited the planet. As Jupiter is believed to have only a relatively small rocky core and no real solid surface, a landing mission is nearly impossible.
Saturn
Saturn has been explored only through unmanned spacecraft launched by NASA, including one mission (Cassini–Huygens) planned and executed in cooperation with other space agencies. These missions consist of flybys in 1979 by Pioneer 11, in 1980 by Voyager 1, in 1982 by Voyager 2 and an orbital mission by the Cassini spacecraft which entered orbit in 2004 and is expected to continue its mission well into 2010.
Uranus
The exploration of Uranus has been entirely through the Voyager 2 spacecraft, with no other visits currently planned. Given its axial tilt of 97.77°, with its polar regions exposed to sunlight or darkness for long periods, scientists were not sure what to expect at Uranus. The closest approach to Uranus occurred on January 24, 1986. Voyager 2 studied the planet's unique atmosphere and magnetosphere. Voyager 2 also examined its ring system and the moons of Uranus including all five of the previously known moons, while discovering an additional ten previously unknown moons.
Neptune
The exploration of Neptune began with the August 25, 1989 Voyager 2 flyby, the sole visit to the system as of 2009. The possibility of a Neptune Orbiter has been discussed, but no other missions have been given serious thought.
As of January 2008, the Mariner 10 and MESSENGER missions have been the only missions that have made close observations of Mercury. MESSENGER made a fly-by of Mercury on 14 January 2008, to further investigate the observations made by Mariner 10 in 1975 (Munsell, 2006b). A third mission to Mercury, scheduled to arrive in 2020, BepiColombo is to include two probes. BepiColombo is a joint mission between Japan and the European Space Agency. MESSENGER and BepiColombo are intended to gather complementary data to help scientists understand many of the mysteries discovered by Mariner 10's flybys.
Venus
Venus was the first target of interplanetary flyby and lander missions and, despite one of the most hostile surface environments in the solar system, has had more landers sent to it (nearly all from the Soviet Union) than any other planet in the solar system. The first successful Venus flyby was the American Mariner 2 spacecraft, which flew past Venus in 1962. Mariner 2 has been followed by several other flybys by multiple space agencies often as part of missions using a Venus flyby to provide a gravitational assist en route to other celestial bodies. In 1967 Venera 4 became the first probe to enter and directly examine the atmosphere of Venus. In 1970 Venera 7 became the first successful lander to reach the surface of Venus and by 1985 it had been followed by eight additional successful Soviet Venus landers which provided images and other direct surface data. Starting in 1975 with the Soviet orbiter Venera 9 some ten successful orbiter missions have been sent to Venus, including later missions which were able to map the surface of Venus using radar to pierce the obscuring atmosphere.
Mars
The exploration of Mars has been an important part of the space exploration programs of the Soviet Union (later Russia), the United States, Europe, and Japan. Dozens of robotic spacecraft, including orbiters, landers, and rovers, have been launched toward Mars since the 1960s. These missions were aimed at gathering data about current conditions and answering questions about the history of Mars. The questions raised by the scientific community are expected to not only give a better appreciation of the red planet but also yield further insight into the past, and possible future, of Earth.
Asteroids and comets
Until the advent of space travel, objects in the asteroid belt were merely pinpricks of light in even the largest telescopes, their shapes and terrain remaining a mystery. Several asteroids have now been visited by probes, the first of which was Galileo, which flew past two: 951 Gaspra in 1991, followed by 243 Ida in 1993. Both of these lay near enough to Galileo's planned trajectory to Jupiter that they could be visited at acceptable cost. The first landing on an asteroid was performed by the NEAR Shoemaker probe in 2000, following an orbital survey of the object. The dwarf planet Ceres and the asteroid 4 Vesta, two of the three largest asteroids, are targets of NASA's Dawn mission, launched in 2007.
While many comets have been closely studied from Earth sometimes with centuries-worth of observations, only a few comets have been closely visited. A few long-period comets are currently the furthest known objects in the solar system. In 1985, the International Cometary Explorer conducted the first comet fly-by (21P/Giacobini-Zinner) before joining the Halley Armada studying the famous comet. The Deep Impact probe smashed into 9P/Tempel to learn more about its structure and composition while the Stardust mission returned samples of another comet's tail. The Philae lander will attempt to land on a comet in 2014.
Hayabusa was an unmanned spacecraft developed by the Japan Aerospace Exploration Agency to return a sample of material from a small near-Earth asteroid named 25143 Itokawa to Earth for further analysis. Hayabusa was launched on 9 May 2003 and rendezvoused with Itokawa in mid-September 2005. After arriving at Itokawa, Hayabusa studied the asteroid's shape, spin, topography, colour, composition, density, and history. In November 2005, it landed on the asteroid to collect samples. The spacecraft returned to Earth on 13 June 2010.
Jupiter
The exploration of Jupiter has consisted solely of a number of automated NASA spacecraft visiting the planet since 1973. A large majority of the missions have been "flybys", in which detailed observations are taken without the probe landing or entering orbit; the Galileo spacecraft is the only one to have orbited the planet. As Jupiter is believed to have only a relatively small rocky core and no real solid surface, a landing mission is nearly impossible.
Saturn
Saturn has been explored only through unmanned spacecraft launched by NASA, including one mission (Cassini–Huygens) planned and executed in cooperation with other space agencies. These missions consist of flybys in 1979 by Pioneer 11, in 1980 by Voyager 1, in 1982 by Voyager 2 and an orbital mission by the Cassini spacecraft which entered orbit in 2004 and is expected to continue its mission well into 2010.
Uranus
The exploration of Uranus has been entirely through the Voyager 2 spacecraft, with no other visits currently planned. Given its axial tilt of 97.77°, with its polar regions exposed to sunlight or darkness for long periods, scientists were not sure what to expect at Uranus. The closest approach to Uranus occurred on January 24, 1986. Voyager 2 studied the planet's unique atmosphere and magnetosphere. Voyager 2 also examined its ring system and the moons of Uranus including all five of the previously known moons, while discovering an additional ten previously unknown moons.
Neptune
The exploration of Neptune began with the August 25, 1989 Voyager 2 flyby, the sole visit to the system as of 2009. The possibility of a Neptune Orbiter has been discussed, but no other missions have been given serious thought.
And it turns out NASA also provides a web-tool for finding planetary positions by date. It can be found at NASA - JPL Solar System Simulator. I would tend to trust its results based on the resume above. And it corroborates the findings I have previously posted.
Planetary alignment? Pish Posh. 
