Testing TYCHOS: PVP Parallax Experiments

Simon Shack's (Tycho Brahe-inspired) geoaxial binary system. Discuss the book and website for the most accurate configuration of our solar system ever devised - which soundly puts to rest the geometrically impossible Copernican-Keplerian model.

Testing TYCHOS: PVP Parallax Experiments

Postby hoi.polloi on April 14th, 2018, 2:06 am

I have an idea now, after thinking a bit more about how the TYCHOS's parallax can be best measured. And it, of course, has to do with the notion of how to best test stellar parallax in general.

To preface, we want to start with an understanding of the TYCHOS principle of parallax. As I illustrated in the previous post:

We can adjust for our rotating time reference ("the position of midnight" in the summer solstice faces the opposite direction from "the position of midnight" in the winter solstice) with the following idea:

360 degrees / 365.22 days is approx. 0.9857 degrees.
86400 seconds per day / 365.22 days is about 236.57 seconds.
24,900 miles / 365.22 days is about 68.178 miles.

Every 24 hours, our "midnight" moves by about 0.9857 degrees or 3.94 minutes of our day or 68 miles away on the equator. Well, let's just use 4 minutes and 110 km (roughly 68 miles).

Image


To expand on this thinking, let us expand the scope of our experiment and achieve the most "night" we can reasonably expect to get ideal viewing conditions. Consider about 4 months, or about 1/3 of a year, and we should expect to see a much greater difference in stellar parallax compared with minute measurements of a single week. Still focusing on the solstice, but this time let us move to the "outer" parallax visible during the Northern hemisphere's "Winter" which from Ecuador's midnight will be roughly in the direction of star Procyon.

So in order to face a reasonably precise parallel direction each night (we must take into account the PVP) we might say that we can take great parallax measurements at times that move our measurement time by about 3.94 minutes away from midnight in each direction. On the equator with the winter solstice being our "focal midnight", without having to move our work station, these times calculate to be good enough for comparison. Please note that I have selected a few clusters of consecutive days so that we can maximize observations under different conditions. (Ecuador during rainy season would be problematic but the same experimental parameters apply to anywhere in the world that gets a good dark and clear Winter period).

parallax_checker_3.gif


Critical extreme A — risks light pollution at such a time close to dawn but let's assume this could still provide some great star visibility.
October 21, 2018 : 04:00 (am)
October 22, 2018 : 03:56 (am)
October 23, 2018 : 03:52 (am)

Novemb. 5, 2018 : 03:01 (am)
Novemb. 6, 2018 : 02:57 (am)
Novemb. 7, 2018 : 02:53 (am)

Novemb. 20, 2018 : 02:02 (am)
Novemb. 21, 2018 : 01:58 (am)
Novemb. 22, 2018 : 01:54 (am)

Decembr. 5, 2018 : 01:03 (am)
Decembr. 6, 2018 : 00:59 (am)
Decembr. 7, 2018 : 00:55 (am)

Decembr. 20, 2018 : 00:04 (am)
Decembr. 21, 2018 : 00:00 (am) — Solstice period
Decembr. 21, 2018 : 23:56 (pm) — note each period is about 23 hrs and 56.06 minutes apart and here is the best demonstration
Decembr. 22, 2018 : 23:52 (pm)

January 4, 2019 : 23:01 (pm)
January 5, 2019 : 22:57 (pm)
January 6, 2019 : 22:53 (pm)

January 19, 2019 : 22:02 (pm)
January 20, 2019 : 21:58 (pm)
January 21, 2019 : 21:54 (pm)

February 3, 2019 : 21:03 (pm)
February 4, 2019 : 20:59 (pm)
February 5, 2019 : 20:55 (pm)

February 18, 2019 : 20:04 (pm)
February 19, 2019 : 20:00 (pm)
February 20, 2019 : 19:56 (pm)

March 4, 2019 : 19:08 (pm)
March 5, 2019 : 19:04 (pm)
March 6, 2019 : 19:00 (pm)
Critical extreme B — let's stop at 7pm here as another "light pollution" buffer

So how many days' difference can we see between these dates? Let's call it 135 days and give ourselves the nice round calculation for the PVP distance of: 135 days x 24 hours x 1.60169 km = 5189.4756 km

A whopping 5,000 km (and a little extra) on Earth's journey to test stellar parallax!

Now this may seem like a drop in the bucket compared with the expected billions and millions of kilometers' distance of the stars. Yet it should be a very good test that will take less than half a year, and if we're correct we'll have further proved the greatest known model of our solar system. In fact, we only really need the two critical extremes of A & B to make a good comparison, but with high enough resolution I think we'll find it very useful to create a short "animation" from all these dates for the following reasons:

1. To allow us to account for known wiggles of the stars as these micro motions pertain to binary movement of the stars (to remove this factor from parallax and so as not to confuse the star points' "internal" motions with parallax)

2. To correct for other potential atmospheric distortions and give more chances of useful parallax data as time progresses (and conversely, more time to correct for any early mistakes in the data recording)

3. More references and confirmations so that the fractions of seconds differences in Earth's rotation can be accounted for and there are more references to overlap the images in animation software

and

4. Of course, to more easily allow human eyes to track and view the motion (like fast forwarding a weather radar formation) once the animation is completed

What do you think? Can we write a grant for this project so that we can just get a decent telescope and start this great experiment come October?

parallax exp.jpg
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Re: Testing TYCHOS: PVP Parallax Experiment I

Postby hoi.polloi on April 14th, 2018, 6:01 pm

If the experiment were conducted in the same way for several years in a row, of course, you would gain that much more parallax to compare.

The point of designing this experiment to not have to move our "eye"/camera is to make precision "easy" (as opposed to rotating our view with the Earth's rotation).

We might call the former experiment, designed above, as the "pseudo-parallel frame of reference technique". (Pseudo-parallel because the Earth is actually making a slow curve through space, not a straight ray).

We might design another one which I will describe below, as the "rotating frame of reference technique". This will produce a more instant and greater parallax but must be recorded through more atmosphere and therefore risks greater distortion.
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Re: Testing TYCHOS: PVP Parallax Experiments

Postby hoi.polloi on April 14th, 2018, 10:16 pm

So let's try another experiment as well. This can serve as a "back up" experiment that is done on the critical date of the Winter Solstice, when Earth's PVP curve brings us closest (by mere kilometers but nevertheless closest) to the distant stars. Let's start by turning a second camera/telescope/rig in the following orientations:

East at 7pm on December 21
West at 4am on December 22

As you can see, since we are on the equator, we should only have to rotate directly along Earth's ecliptic.

pax4_measure.GIF


Now with this measurement alone, we can see that we have rotated 9/24 around Earth's center (and the additional PVP scooting of about 14.4 km). Earth's rotation in 9 hours brings us through space about:

triangel.jpg


About 11,788.7 km (+14.4 km) = 11,803.1 km of opportunity for parallax! (In a single 9-hour span giving us over twice what is achieved across 4 months). (This is using an estimated radius of 6380 km for Earth).

We could even set up a camera to track that area of space and record the entire time.

But, unfortunately, while this technique does produce much more parallax it also means peering through much more atmosphere and therefore more distortion of star positions. It also means we need to calculate as precisely as possible the two times that we will be equidistant from the stars (as Earth rotates our telescope is carried closer to the "outside" of Earth's circumference closest to the stars, then back again in the circular motion of Earth's rotation on itself.) There may be some distortion with all the parabolic movement towards and then away from our target stars if video were taken instead of just snapshots to exactly equivalent East and West views.

All in all, the potential for too much distortion (combined with limited time and means) makes this experiment less ideal than the longer experiment I designed in the first post. In that method (the first post) we minimize star distortion and bring ourselves closest to the stars (sparing us a balloon ride that may net even more accurate data) while maintaining very consistent distance and maximizing the lateral "passing by the stars" movement that we are trying to isolate. The distortion in the first experiment would be neutralized to atmospheric conditions and the curve on the PVP which brings us "closest" to our target stars during the solstice. However these may be negligible in the long run since even in a full year, Earth will only curve on its orbit by 0.01420454545 (periodic) degrees. (1/25344)
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