Mars has an orbit with a semimajor axis of 1.524 astronomical units (228 million kilometers), and an eccentricity of 0.0934. The planet orbits the Sun in 687 days and travels 9.55 AU in doing so, making the average orbital speed 24 km/s. Mars has an orbit with a semimajor axis of 1.524 astronomical units (228 million kilometers), and an eccentricity of 0.0934. The planet orbits the Sun in 687 days and travels 9.55 AU in doing so, making the average orbital speed 24 km/s. The eccentricity is greater than that of every other planet except Mercury, and this causes a large difference between the aphelion and perihelion distances—they are 1.6660 and 1.3814 AU. Mars is in the midst of a long-term increase in eccentricity. It reached a minimum of 0.079 about 19 millennia ago, and will peak at about 0.105 after about 24 millennia from now (and with perihelion distances a mere 1.3621 astronomical units). The orbit is at times near circular: it was 0.002 1.35 million years ago, and will be about 0.01 a million years into the future. The maximum eccentricity between those two minima is 0.12. Mars reaches opposition when there is a 180° difference between the geocentric longitudes of it and the Sun. At a time near opposition (within 8½ days) the Earth–Mars distance is as small as it will get during that 780-day synodic period. Every opposition has some significance because Mars is visible from Earth all night, high and fully lit, but the ones of special interest happen when Mars is near perihelion, because this is when Mars is also nearest to Earth. One perihelic opposition is followed by another either 15 or 17 years later. In fact every opposition is followed by a similar one 7 or 8 synodic periods later, and by a very similar one 37 synodic periods (79 years) later. In the so-called perihelic opposition Mars is closest to the Sun and is particularly close to Earth: Oppositions range from about 0.68 AU when Mars is near aphelion to only about 0.37 AU when Mars is near perihelion. Mars comes closer to Earth than any other planet save Venus at its nearest—56 versus 40 million km. The distances have been declining over the years, and in 2003 the minimum distance was 55.76 Gm, nearer than any such encounter in almost 60,000 years (57617 BC). This modern record will be beaten in 2287, and the record before 3000 will be set in 2729 at 55.65. By 4000, the record will stand at 55.44. The distances will continue to decrease for about 24,000 years. Until the work of Johannes Kepler (1571–1630), a German astronomer, it was believed, or assumed, that planets traveled in circular orbits around the Sun. When Kepler studied Danish astronomer Tycho Brahe's careful observations of Mars's position in the sky on many nights, Kepler realized that Mars's orbit could not be a circle. After considerable analysis, Kepler discovered that Mars's orbit was an ellipse, with the Sun occupying one of the elliptical orbit's two focal points. This, in turn, led to Kepler's discovery that all planets orbit the Sun in elliptical orbits, with the Sun at one of the two focal points. This became the first of Kepler's three laws of planetary motion. From the perspective of all but the most demanding, the path of Mars is simple. An equation in Astronomical Algorithms that assumes an unperturbed elliptical orbit predicts the perihelion and aphelion times with an error of 'a few hours'. Using orbital elements to calculate those distances agrees to actual averages to at least five significant figures. Formulas for computing position straight from orbital elements typically do not provide or need corrections for the effects of other planets. For a higher level of accuracy the perturbations of planets are required. These are well known, and are believed to be modeled well enough to achieve high accuracy. These are all of the bodies that need to be considered for even many demanding problems. When Aldo Vitagliano calculated the date of close Martian approaches in the distant past or future, he tested the potential effect caused by the uncertainties of the asteroid belt models by running the simulations both with and without the biggest three asteroids, and found the effects were negligible. Observations are much better now, and space age technology has replaced the older techniques. E. Myles Standish wrote: 'Classical ephemerides over the past centuries have been based entirely upon optical observations:almost exclusively, meridian circle transit timings. With the advent of planetary radar, spacecraft missions, VLBI, etc., the situation for the four inner planets has changed dramatically.' (8.5.1 page 10) For DE405, created in 1995, optical observations were dropped and as he wrote 'initial conditions for the inner four planets were adjusted to ranging data primarily…' The error in DE 405 is known to be about 2 km and is now sub-kilometer.