User talk:Saros136/sandbox

Orbit of Mars Orbit of Venus

Comet of 1664
The Great Comet of 1664, or 1664 W1, was discovered in Spain in November 1664 and last viewed, with a telescope, in March  1665. Its brightness reached magnitude -1 when it passed closest to the Earth in late December at a distance of 0.17 au. The comet was very widely observed and was a subject of treatises by important astronomers, and even more writers treated it in a religious or astrological manner.

Most astronomers at the time held to an old and unquestioned assumption that permanent bodies traveled in circular orbits, and transitory objects showed rectilinear motion.

Those who believed comets had permanent and circular (or closed) orbits included Jean-Dominique Cassini, Adrien Auzout, Pierre Petit,  Giovanni Borelli, among others. Cassini was an expert observer who believed the comet of 1664 had a circular orbit centered at Sirius. Auzout created an ephemeris ,based on four or five observations in December, that had rough positions from November 1664 to February 1665. He did not support Cassini's idea that the comet orbited a star, but still believed that comets might return. Petit thought the comet, and comets in general, had elliptical orbits; he also wrongly it was also seen in 1618 and reappeared about every 46 years. Borelli, assuming, for the sake of calculation, a heliocentric earth orbit, concluded the path was probably elliptical or at least closed. Saros136 (talk) 05:10, 24 October 2012 (UTC)

Orbit of Uranus
Uranus has an orbit with a semimajor axis of 19.22 astronomical units ( 2.87 Tm)—large enough to make the Terameter, a billion km, a convenient metric unit. Its eccentricity is 0.046. The planet's perihelion and aphelion distances are 18.28 and 20.10 astronomical units. The planet orbits the Sun in 84 years, traveling 121 AU, making the average orbital speed 6.8 km/s.

Changes in the orbit
Both the semimajor axis and eccentricity of Uranus are slowly and steadily decreasing.

resonances
Uranus is in a near 2:1 resonance with Neptune.

Closest approaches to Earth and other planets
Uranus is nearest to Earth at 17.29 au (2.830 Tm). This minimum distance will decrease to 17.25 au in several centuries.

The only planets that are ever nearer to Uranus than 10 au are Saturn and Neptune. These are not frequent: the closest in time happens in 1988 for Saturn and in 2509 for Neptune.

oppositions
Opposition is when the geocentric longitudes of the Sun and Uranus differ by 180 °, which happens at intervals of 369.7 days.

table
From VSOP87. 1 Terameter= 1000 Million km

2003 approach
In 2003 the minimum distance between Earth and Mars was only 55.76 Gm, less than it had been in nearly 60,000 years.

justification for new table of perihelion and aphelion distances.
There are a few differences here. I've included astronomical units, for one. The units aren't named in each cell, only one in the header. The biggest one is in the number of significant figures given, never more than five.

The last table presented the calculations as being valid to the km. And Standish's 250-year best linear fit to ephemerides DE405 (The calculated positions) is used. This is often taken to be the authoritative mean elements, but it is no mean and there is nothing special about the time frame. A different range would have given him different numbers. (In fact he also made a fit to a 6,000 year range which would give much different numbers in the table). He made it for use in low-accuracy calculations.

There is no one perihelion or aphelion distance for a body. Using the simple approach of calculating it from elements shows the mean elements of VSOP87 (or VSOP2013) agree more closely with those of Newcomb more than a century ago than with Standish's best fit. The differences are due to the method, not accuracy.

I say the best way to determine the perihelion and aphelion distances is to to use the actual calculated distances. Although we use an average or median, it makes a difference what the range is...so there is still a problem in using too many places.

Here is an example of what I found with Uranus using Solex. They all round off to 2735 Gm That is the same as in the last table, but this way we can see that 4 places is the most precise possible value for perihelion that is accurate.

Uranus is actually in the midst of a longer and nearly linear decrease in perihelion distances, from 1000-3000 the average is 2736. This is a case where VSOP87 is worse, with 2742 Gm. If the table used the longer term 6000 year JPL best fit the value would be 2736. 

Mercury, Venus, Earth, and Mars have far more frequent ones, and strong linear changes over longer periods than other planets. Taking averages over maybe two or three centuries is good. Here are using some mean elements. VSOP87 (from the space age) and the old ones coming from Simon Newcomb(1st three), F.E. Ross(Mars) and Gaillot (last four) They are in Astronomical Formulæ for Calculators, by Jean Meeus

WGS84
WGS84 It came with some very technical papers.

Pluto
I'm excited that there are now analytic theories of planetary motion that include Pluto, and there are online elements for the solutions of TOP2013, the Theory of the Outer Planets by the Institut de mécanique céleste et de calcul des éphémérides (IMCCE) along with VSOP2013. the abstract is here.

The elements are in radians for angles and the numbers in general are in a less familiar format. So I made a spreadsheetwith elements and other figures derived from them, and in degrees and julian days and years, online. Saros136 (talk) 22:08, 25 November 2015 (UTC)

The mean elements here are from the Theory of the Outer Planets (TOP2013) solution by the Institut de mécanique céleste et de calcul des éphémérides (IMCCE). They refer to the standard equinox J2000 and the barycenter of the Solar System and the epoch is J2000.

TOP2013
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 * orbit ref=