The Tusk: Comments Better than Blog

I agree, George. Give most all of the kudos to Jonny. And he did do a great job of educating us (me, at least). TLE had some goodies, too. A discussion like this of any event/body would be awesome. Let it be noted that when Jonny overstepped the facts, into his opinion, he admitted it afterward and retracted it. I WOULD be interested in knowing where Jonny plugs in his values, if it is something available on the Internet. I'd also ask for the equations, but I am not ambitious enough anymore to try to understand them. There was a time when I would have tried. :-)

Hi Steve, I have no idea whether there is an applet on the web to plug different values. There may well be, but the equations I used to calculate the separation distances are actually pretty straight forward. I basically used 3D Cartesian geometry to calculate the separation distances. This may sound horrible, what it amounts to is just using Pythagoras to find teh length of a line in 3 dimensions. For those who studied high school mathematics, they will recall that Pythagoras tells us that for a right angled triangle the sum of teh square of the two shortest sides will equal the square of the longest side (i.e. the hypotenuse). Mathematically this is given by a^2 + b^2 = c^2. This can be rearranged to solve for c by c = sqrt(a^2 + b^2) where "sqrt" means take the square root of what is inside the brackets. If we use Cartesian co-ordinates, (x, y) then if we have two points (x1, y1) and (x2, y2), then we can calculate the distance D between them using Pythagoras namely D = sqrt[(x1-x2)^2 + (y1-y2)^2] If you extend this to three dimensions with a co-ordinate (x, y, z) then the above equation simply becomes D = sqrt((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2] For orbits all you need do to calculate the separation between two objects is to know their Cartesian co-ordinates using the sun (or more accurately the solar system barycentre) as the origin. Orbits can be expressed in two forms, the common one is using the orbital elements, which uses the eccentricity, inclination, semi-major axis etc, and all you need to do to work out where an object is is to know its perihelion date, and the time from perihelion. The other method is to use Cartesian co-ordinates, which expresses the position of the object as well as the component of the instantaneous velocity and acceleration component in each of the Cartesian axes. This all sounds complex, but is straight forward since you can use the JPL Horizons program to generate the data for you for any given time period (once you work out how to set up the parameters in the program). So if you get it to calculate the position of two objects in Cartesian co-ordinates with respect to the sun at any given time, then you can simply use Pythagoras to find the distance between them. I used a short cut and imported the data into excel, and then entered in the Pythagorean formula to calculate the desired separation distance. I then imported the data into a better graphing package (Origin Pro 8) so that it would look prettier than the cheap and nasty looking Excel graphs (also Origin has a better graphics exporter than Excel). I hope this helps show that it is not an overly complicated thing to do, since JPL Horizons does the hard work for you, leaving you to enjoy the results.

The dates for the A/Saxon chronicle are not generally regarded as secure in all instances, in the period between 749 and 892, when mss A (Winchester) kicked in. Hence, historians currently rely on the memory of the compiler of Winchester A mss and even then the year is liable to be corrected in modern editions for various reasons. For instance the 'red cross' in 773 is adjusted to 776. The entry for 793 follows the entry for 792 which has been corrected to 794. Swanton's translation suggests the 773 (776) entry referred to aurora borealis, visible in northern Britain. This is unusual in one way but not if a big coronal discharge had occurred. The A/Saxon chronicle is full of portents and the 793 one sounds a bit like a heavy shower of meteors. Steve Mitchell has an article in one of the SIS journals setting out all comet and aurora references, 'Comets as chronological markers'

To clarify when I brought in the discussion of the year 793/794 it was to show that the anglo-saxon chronicle and Roger of Wendover describe the same events, but that Roger typically ascribes them as occurring later than the anglo-saxon chronicle. I was not inferring that the 793 accounts are in anyway related to the 775 event, though the former is interesting in itself. Also, it does not prove that either one of them is the correct dating or even has anything to do with the 775 event, but merely shows that they could indeed be describing the same event in the same year. Taken at face value, we have historical documents that report of events occurring in the sky at attributed to the same time that we have physical evidence of some celestial event occurring.