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