Questions

My comments and analysis of graphics overview of the 12th's motions. It raises the following questions [as of January 2, 1999] in my mind.

Reference "side view" figure 2

With an entry angle of 32 degrees to the earth orbital plane, how can the 12th get any closer to earth than 22 Million miles? I calculated using a computer drawing package a distance of 44 million miles from 12 Th. to earth as it passes though the Earth's orbital plane with a 32 degree entry angle. The 22 Million miles is assuming it would pass directly over the top of earth. If it travels off to one side or another, then this distance is even greater. The 32 degrees is referenced in numerous places and also is the sum of 11 degree and 21 degree in Figure 1 that shows the 12th orbit. I suspect something is incorrect with the triangle, or the angle, or my understanding.

 

Reference Top View figure 2

Now if one factors out the above 32 degrees and looks at the angle the 12th makes with in the earth's orbital plane. This angle needs to be a minimum of 22 to 40 degrees to give a 14 million mile close approach. It also needs to be greater than zero degrees to get around the sun. This drawing says the 12th would need to be coming in from a direction that is off by 2-4 (9h-13h) or more hours from the direction it should be coming from (green arrow). Could it be there is something we don't understand about the orientation or size of the entry triangle?

 

Answer

 

Reference Front View figure 2

I could not find a reference to the angle between the orbital planes of the 12th and Earth's orbital plane. However if this entry triangle is correct and if 14 Million miles closest approach is correct. Then, this angle must be less than 30 degrees. Most probably it is closer to zero degrees than 30. My question at this time is - what is the angle between the two orbital planes (Earth's and 12th's) as viewed toward the incoming 12th, and viewed parallel to Earth's orbital plane?

 

Reference Top View figure 2

Looking at the link Path as Viewed from Earth link one sees that the earliest sighting point is about Sidereal 5h angle. Assuming for now this is close to dark star focal point. This drawing shows the rough position of the dark star off by about 25-30 degrees as compared to the position of the earth on say May 20th. Would be off a little more for May 15th. I can see some amount of slippage due to the lengthening day. Could it accumulate to 25 to 30 days of time? Questions - What is the Sidereal hour or angle for the 2ND focus or dark star, or if you prefer what day of the year would the sun and earth lie in the same angular orientation to the dark star 2nd focal point. What is the accumulated hours or days of slippage up to the point of stoppage or start of the shift which every you prefer?

Mike