Bev Try Thinking does Geometry To A Light In The Sky | GeoGebra Walk-throughs

Bev: Let us know what the geometric properties of how you're doing what you're doing Because Nathan Oakley can't talk about it It appears that Witsit can't talk about it None of the globe guys can talk about it either! Is somebody saying that this idea of 1 degree change over 69 miles Is there anything wrong with what people can see there? Because this is how I understand a 1 degree change over 69 miles That's how I understand it Because on the land the 69 miles can be measured People could meas

ure that That's a distance, a measureable distance And the 1 degree is a change to a light in the sky also measurable This is verifiable this 1 degree over 69 miles Absolutely Let us know, how is the angle measured in reality any different than this? Let's see. Somebody, um, somebody do us a drawing. Let's have a look, see how it changes where the angles are measured. Because this is mine, this is my drawing You can look at it on the screen right now I drew this, this is my understanding of how

a 1 degree change over 69 miles occurs Petey: Well I think I can help you with this one Bev Of course your drawing doesn't describe reality at all and your understanding isn't right either I'll take you through some geometry in a second but can I ask you why you didn't draw your lines in from each observer to your light in the sky? Drawing them in would surely give you some indication as to where the star is wouldn't it? This first line is a list of observer angles to the star and the gap betwee

n each observer is 69 miles This will place the points on the xAxis in their relative positions Next is this rather complicated looking sequence which just creates each line of sight at the observed angle In this next line we ask GeoGebra to double check the previous line and measure the angles anyway And lastly, a table showing observer angles and distances So the first thing I want to do is remove the middle observer This leaves the observer looking at the star at 30° and the other one at 32°

and it would make sense for these lines to meet at the star wouldn't it because that's where these observers are looking at Let's follow those lines and we can see that they meet about here which is about 2000 miles from our observers and about 1000 miles up Let's put that back and reintroduce the one at 31° Let's follow these lines now Ok, so the first one meets about here That's the top 2 lines and then outer 2 lines meet about here and then the bottom 2 lines meet about here So there is 3 dif

ferent meeting places So the star is actually in 3 places there Let's put it back again and this time we'll introduce a couple more observers One observer will see the star at 20° Another one at 40 and another one at 75 This is our 20° observer Where's the star now well, who knows Is it here? Is it there? Our 40° observer, is the star here now? Or is it over there? This our 75° observer Is that the star? Is that the star? Who knows? It's really not working is it? It's not working at all. Bev: If

you were to lift up the 30 end of that the one that's on screen now if you were to lift that up would that angle still be the same? Or would you be measuring a larger angle? Or a smaller angle? Or would it be the same angle? Paper: Uh, the same angle would be only in a case that the star is really infinitely far, which is impossible. Petey: Well it's a bit pointless asking about this now, isn't it? Shall we look at some geometry that works? Right, so you don't need 3 guesses to know that this w

ill be a globe scenario We'll start off with the radius value of 3959 we have 3 sliders The first slider is going to control the observer's height That'll range from 0 miles to 200 miles which will put them in space We have a latitude slider That'll control where the observer is going to be between the equator and the north pole on the prime meridian And the last slider will control where the star is going to be on the yAxis This line creates a circle with radius r Think of this as the globe Ear

th cut in half where this is the prime meridian this'll be the north pole and this'll be the equator I've created point A and it is 1° south of the equator I'm going to use point A and I'm going to rotate it 91 times at 1° intervals right around the prime meridian That's this line Next is a ray from the centre of the Earth and it goes through our chosen latitude so there's 0° 90° and so on Next is our observer which is a little, tiny red dot here It's currently got no height, that means it's on

the surface I can lift this point up So that's directly up from the observer's point of view 200 miles into space Let's put that back on the surface This point here is our star and it's always tied to the yAxis It's currently 3000 miles from the centre of the Earth which actually places it inside the Earth but we can control its distance using this slider We'll come back to that This segment here joins the observer to the star This is a checkbox which allows me to just centre on the star as I mo

ve the slider This is our zenith distance or our co-altitude angle It doesn't make much sense at the moment because the star is so close And the distance between each of these points is 69.1 miles We don't need to see this A anymore What I'd like to do now is to move the star away So I'll click on this box so we centre on it and I'll move it away so it's currently at 3000 miles from the centre of the Earth 3*10^4 will be 30 thousand miles you can see there is a slight angle on this still and the

further we go, 300 thousand 3 million and so on, all the way up and if you look at this now it's almost hugging the yAxis If we go back down to the observer, this is the line here And it almost looks parallel with this yAxis It's not, we know it's not perfectly parallel but it is for intents and purposes So that's the star That's back at the observer Bev: Akumuvirus says there is 360 degrees in a circle and 69 miles between each degree Mm Don't think that's how it works is it? Petey: Well in th

is case it's closer to 69.1 miles per degree but yeah, that's exactly how it works. So in this case where our co-altiude is 60° that means we've got 60° left to go here so that's 60 * 69.1 miles that'll be our distance from our observer to the north pole This distance here will be 30 * 69.1 miles Bev: Now Tom Walbran says, The angle to the north star does not change if you are at 1ft, 100ft, 10,000ft or 20,000ft Petey: Here the observer is 200 miles straight up above their previous position and

the co-altitude angle hasn't changed in any meaningful way We're set at 5 decimal places here There's no trickery here the globe geometry just works whereas this does not Bev: Not only have we had Nathan Oakley to deal with but we've been dealing with the globe guys exactly the same thing, there's no difference They won't state their geometry either and as far as we're concerned I think neither of them have any geometric basis backing them at all! Petey: Anyway that's the end of this video If yo

u liked it, do give it a thumbs up for me and if you have any thoughts about how Bev might dismiss any of the globe geometry drop a comment down below and let me know That's it for now so I'll catch ya later!