User:DianaCLnomad/sandbox

Here I am

Neptune has an orbit with a semi-major axis of {30.110 AU (4498 million km), and an eccentricity of 0.009456. It is distinguished from the other by planets by being the farthest, slowest moving, and near-circular orbit. It travels 189.183 AU b=30.1087 length= 189.183

Uranus
I changed the date of the next perihelion to August 17 2050. I have three sources: VSOP87 Bretagnon's complete VSOP87 model. It gives the 17th.

http://vo.imcce.fr/webservices/miriade/?forms IMCCE Observatoire de Paris / CNRS I calculated for a series of dates, five or ten days apart, in August 2050, using an interpolation formula from Astronomical Algorithms. Perihelion came very early on the 17th. INPOP planetary theory

And using the JPL Horizons web service in the same way: Aug 17.46 https://ssd.jpl.nasa.gov/horizons.cgi#results Just before noon.

Further Uranus
I checked the range rates on Horizons here. Vectors at noon each day. The sign changed twice. From negative-positive-negative-positive. Same goes for the rdot numbers on the Horizons batch file posted as a reference. And for distances, The 19th and the 15th have the lowest. (At 00:00) At noon, the 14th, 18th, and 19th have the lowest. The kind of oddities that at other times also arise in cases with slow-moving bodies near perihelion. This is why with Uranus I much prefer using the best fit curve with a formula for an extreme value, and with positions at least 10 days apart. Pluto is an odder case.

The differences in distance predictions between it and IMCEE http://vo.imcce.fr/webservices/miriade/?forms are minute: 30 km on August 17 0:00 here. 18.283075301 AU (using epoch 2470030.5, 20, 1 - day, TT) vs 1.828307553450090E+01 from Horizons. (Horizons, of course, gives far more digits than are meaningful.) The distances from the IMCEE decline daily, reach a minimum on the 17th, and increase daily. DianaCLnomad (talk) 15:03, 8 September 2021 (UTC)

Geodesy reference
Geodesy: Introduction to Geodetic Datum and Geodetic Systems by Lu, Qu, Qiao states "The total area of GRS80 Ellipsoid is approximately 510,065,597 km^2." This comes right after giving the formula for the surface area of an ellipsoid. (I got a result 26 km^2 greater on my spreadsheet using full precision figures). But this article has a value about 1800 square km greater. The numbers here lead to a value the same as that from WGS84 and GRS80 to the tenth of a square kilometer. 510065623.4 DianaCLnomad (talk) 21:08, 15 September 2021 (UTC)

Mars dimensions
The surface area and volume figures needed correction. The equatorial figure and flattening lead to an accurate polar radius and mean radius that agree with the infobox and other sources. The volume and surface area numbers were wrong. The volume mistake may have just been an entry mistake, 1.618 should be 1.6118. The surface area was more in error. It should be 144.37. DianaCLnomad (talk) 22:44, 18 September 2021 (UTC)

Next point
Indeed. The moons complicate it. The barycentric frame is better. If we applied your test to the next perihelion of Neptune, the date would be moved back to October 20. (2042-Oct-20 16:00:00.0000) Using the test for the last perihelion of Pluto would require an even bigger change: to. some date in 1990. (Jan 19 has a minimum distance. 0.5094212655h at	29.65639232 au. ) DianaCLnomad (talk) 19:13, 22 September 2021 (UTC)

Close up Uranus
I simplified it. Took the Horizons output, body centric, The output was every six hr. Sampled points 18 hr apart, with the midpoint being the one with the slowest range-rate. There was no surprise: the 19th was closer than the 14th. By about 5 km! For people with extreme confidence in Horizons, that small difference, at about 20 au, would be significant enough to make the call. 14.67835477 day 18.28307550 au, 19.04125029 date 18.28307547 au I say the are so close it would be better to average the times. It goes on the 16th. Same as calculated before using Horizons output. DianaCLnomad (talk) 20:01, 27 September 2021 (UTC)