Astronomy - Measuring Distance, Size, and Luminosity (9 of 30) Distance using parallax angle
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- čas přidán 6. 04. 2014
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In this video I will find distances of far away stars using angle of parallex.
nice video, i struggled a bit with the reason for including 57.3 in the formula instead of using the traditional tan(Angle). Leaving this comment to clarify for others. The formula he uses is built under the assumption that 'Tan(Angle) = Angle', this is apparently called the 'Small Angle Approximation'. It seems to be the idea that when you apply the 'Tan' function to any sufficiently small angle, the difference will be insignificant enough to ignore completely. This allows him to change the formula from 'd/D = Tan(Angle)' to 'd/D = Angle/57.3', he is simply converting the angle in degrees to radians by dividing the angle in degrees by the value of 1 radian in degrees (180/pi = 1 rad in degrees = ~57.3). The reason this is confusing is because if you are not aware of the 'small angle approximation' assumption he uses, it looks as thought 57.3 is some sort of constant (to me anyways). I only watched this one video so i may have missed this explanation in a previous episode, just thought I would leave a neat explanation in layman's terms for any novices such as myself (or possible lazy fucks who missed the last video like myself).
57.3 is the number of degrees in a radian. The measurement of the angles is in Radians not degrees
Trigonometry was not invented when these methods were developed so angles and length had to be calculated by geometry only. The stated formula is what can be called geometric solution to find length.
Thanks!
Michael, you are gonna be the reason I survive my courses again this semester! Thank you ^_^
This parallax angle formula only seems to work for stars that are 90* to the sun and at the celestial sun equator. We can only see stars on the dark side of earth away from sun, which is not 90*. How does one get the angle of a star for oneself, which tool, what time of night is best to collect data? The timing to collect the data of star angle at point A in summer, and B in Winter, would it have to be taken at a certain degree the earth is rotated. I don't think it is possible to measure star distance. Way to many error-able factors that cancel the equation. example. atmospheric distortion... may cause closer objects to appear to be moving. Especially during climate change, winter to summer.... that's vastly different moisture in the sky, which causes light deflection. It could cause the whole lower sky to shift a few degrees, no?
Love from INDIA 🇨🇮 JAI HIND
Thank you. Welcome to the channel!
Hi Michel, thanks for the video. I got the equations, but how do you measure the actual value of the parallax angle, after you take the two measurements of the star's location from different locations of the earth's orbit?
It is the angle with reference to the background stars that do not move because they are so far away.
Michel van Biezen, I was referring to the issue of finding the actual value of the angle, e.g., do you use a sextant to find the actual parallax angle, or some other method?
@@manjus3 I can't find a answer to that one either. starting to think its impossible and that its actually possible that the stars are actually very close, less than few thousand kms. And that we were lied to.
What is the reason on identifying angles 1 and 2 if they are not used in the calculation? Or are they?
In this case we replaced theta with 1 arc second = 1 degree / 3600
The same stellar distance D for one arcsec (p) can be found by using:
tangent(p) = opposite/adjacent;
tan (1/3600) = 1au(93,000,000 miles)/D (stellar distance);
.00004848 = 1 au /D;
D = 206,264 au = 1 parsec = 3.26 light years.
I was struck by the simplicity and power of basic trigonometry when I first learned about it in high school more than 50 years ago, and remain so.
You are correct. That is a good method to use.
Excellent! Thank you!
Glad you enjoyed it! 🙂
Sorry if this is a silly question but I didn't get where the 57.3º came from. What part of the parallax does this radiant belong to? Thanks
+Kelly Tabares 57.3 degrees is the number of degrees in one radian
You draw a circle. Now make an arc on the circumference. The length of the arc should be equal to the radius. The angle which this arc makes at the center is called one radiant which is approximately 57.3 in degree. You know 360 degrees = 400 gradients = 2 pi radiant. This are just different units of measuring angles.
how d/D equals theta/57.3? How is that arrived at?
By measuring the shifting of the 'near' star, is effect of bend space (which bends light obviously) taken into account? Since a tiny change in the shift measurement results in an enormous change in the outcome of the calculation? Is that correct?
If the stars were perfectly lined up, that could have an effect in the measurement. Typically the stars are not lined up (that is only done to show how the technique works).
@@MichelvanBiezen what about our sun, doesn't it have any effect on the bending of light that we see?
We can only see those effects (on light passing the Sun very closely) during a total solar eclipse. I any other circumstance it is not detectable.
How did they know that they were forming a perfect right triangle, and not that the star had moved. What about the distance from the earth to the center of the sun, how did we figure out the distance to the sun and it's size?
The motion of stars is so slow that we cannot detect it visually over a period of many years. We can only detect the motion through the shift of the light's frequency and wavelength.
How do you measure the parralax angle ?
You measure the position of the star relative to other stars much farther away
Question, can we find the distance between the two stars after finding their distance from the sun ?
Yes, by measuring the angle between them from the Earth.
Is it true that the near star is not moving relative to the Milky way centre, and that the Milky way as a body is not revolving? I once saw a simulation where time was speeded up everything in the universe was in motion.
Everything moves relative to everything else. However, some motions are much slower (and take much more time) than other motions.
@@MichelvanBiezen ok slow but moving, so relative to the half year period between pictures taken, the actual movement of the star is negligible? And the inflating universe? The inflation only would have no effect on the shifting if we were in the actual centre of the universe or is my brain playing tricks?
When we say: "slow", we mean slow. Those other motions are imperceptible over time frames of a few years.
From the previous video we haven't conclude the distances between earth and sun. There is an unknown A.U value.
So how did we figure out the distance to the sun for this equation?
The first good estimate for the distance to the Sun was determined by watching the transit of Venus across the disc of the Sun from two different vantage points on the Earth (around 1643). It was a brillant feat.
hi can you please explain to me how did we get 57.3 again?
When you divide 360 degrees by 2 pi ( = 2 x 3.14159 radians in a circle) then you get 57.3 degrees / radian
okay so this method works for Proxima Centauri star right ?
Can humans really measure an arc second (1/3600) in the real world, or is that strictly to teach the concept?
They can measure angles that are just a small fraction of an arc second.
@@MichelvanBiezen HOW?
Please be honest, can this method accurately measure star distances?
It is one of the most accurate methods, but we can only measure the distance to the closest 8000 stars or so with this method.
@@MichelvanBiezen i'm convinced that stars are far away, whatever they are, but i'm not exactly convinced that it is possible to understand the universe from our position.
Our ability of extracting information and understanding from our observations in the various spectra of the electomagnetic radiation us outstanding. We have learned a lot over the years. (See the remainder of the astronomy playlists)
Yes, yes all is clear except how do you measure the parallax angle!!!
Telescopes are made to measure the angle very accurately when pointing at objects.
What I mean is this: The parallax angle is the angular separation of distant stars observed from the object Star whose distance from Earth we want to measure. Fine, why this angular separation is the same as the angular separation between those distant stars observed from Earth (or from the Earth orbit). Although the distant stars are very far away such that they appear fixed during Earth rotation around the sun, we can suppose that these angles are approximately equal, but this reason is still not satisfactorily...Thank you very much.
Nevermind, I figure this out. Distant stars are so far away and such the light from them comes parallel regardless the position of Earth around the sun. The key was to draw a better picture and realize the parallelism. So, the angular separation measured from Earth is about half the angular separation (between distant stars) as they would been measured from the object Star. Bottom line, from Earth we can measured the parallax angle directly. Thank you sir for your informative video. Regards!
I'm still not feeling this as in the real world you will see two stars (dots) eg o .
but you have no idea which is closer or bigger
then 6 months later you will look again and see either
-they are closer eg o .
-or they are further apart o .
-or no change ie they are very far away.
does this really tell you how far away they are or does it just tell you how much they are in the same plane? eg all those things 100m miles from earth, would all be in the same plane, relative to us (eg for this example we are the centre, planes are derived using Earth as center/focal point.
eg this experiment should make clear what I mean.
Someone places two balls at a distance from me. I don't know their size or distance and have no other cues to get this info.
Left hand side ball A ball B right hand side
I judge them to be 1 unit apart.
I move to the left. only 3 things can happen.
-if they are in the same plane the apparent distance closes (like rugby goal posts as you move from the centre towards the touchline)
-if they are in a different plane and A is further back then B then the apparent distance expands (eg think rugby goal posts again, where they are directly in front of you, almost perpendicular to you, but not quite. B is closer to you. Initially the apparent distance between the posts is small but as you move left it will seemingly expand.
-If they are in a different plane and B is further back then A then the distance closes then they merge, then the distance expands (but I strongly suspect that the tiny (in comparison to cosmic distances) won't allow this outcome for the stars). Again a rugby goal post example could be used here but I won't belabour the point.
Thus I still have no idea how far away they are, at least not wrt the info presented in this video. I think!
PS I also tried this with by sticking two pens in blu tack at different distances and walking to the left away from them in a parallel plane, this is useful way to visualise these examples, and shows the observations above to be correct.
Ps I'm no scientist or mathematician so if anyone answers this please don't blind me with jargon, if you know something you should be able to explain it without jargon!
In order to get to the final value of 1 parsec equal to 3.26 ly, the earth-sun distance (astronomical unit) needs to be expressed in KMS, i.e., 150 million Kms.
From all these loose calculations, I wonder how did they send Voyager to Pluto. Voyager has no navigation system. It is a moving object in 3D space.
The Voyager spacecraft were launched in the late 1970s It is amazing that they are still working.
Walked past a lamp while throwing trash, figuring if one can calculate the distance to the Woods seen in the distance. Ended up here.
Why do I get the impression that most people who explain this, jump over several steps as to suddenly to end up saying ”so we get the what is known as” which is taken as a given, but jumps the steps as to how the first came to the conclussion? Propably just me. Ny mind ends up going blank when they start using words which sound foreign to me, like someone had pulled the carpet from under my feet.
If you can not explain something to a novice, are your really grasping it or just convincing yourself that you do? Maybe those who like math and are aquainted with calculations do, but god this is boring.
You're like the guy who walks into a cinema in the middle of a movie and starts asking a bunch of questions. Don't be that guy! This video is #9 in a series of 30. Watch from the start to get the info you want.
SpottedSharks
Granted. I just end up nodding off when it comes to math. So me wanting everything to be self explanatory from the get go is to be expected.
Kya bol rahe ho sir hindi to bollo
Sorry, we don't speak Hindi
This all wrong. How can you use a simply way to measure. The formula doesn't take into account how light travel through space it only takes into account how light travels through air. Also, it doesn't take into account how gravity bends light. It doesn't take into account the space time that is bending around the sun and earth. It doesn't take into account the temperature of space and how light travels through it. It doesn't take into account that after a certain point parallel lines are no longer parallel. It doesn't take into account the movement of any heavenly body or the rotation of the earth. This formula uses currency math (math used inside earths closed system, used for counting money, used to find area for square, doesn't take into account any force being imposed, all parallel lines are always parallel), it doesn't use language math (math which includes all forces being imposed, parallel are only parallel for a certain distance as long as no force is being imposed). In other words, you can't measure something like that using this equation because it doesn't take into effect any forces being imposed on the light that is traveling. I just completely just proved your theory and equation.
I just completely just proved your theory and equation. WRONG!
The video is correct (but you are welcome to disagree). When you state: "The formula doesn't take into account how light travel through space it only takes into account how light travels through air", the difference is not significant and therefore does not affect the math. When you state: Also, it doesn't take into account how gravity bends light", thet effect which is real again does not affect the calculations in any significant way.
@@MichelvanBiezen lol. OF COURSE EVERY BIT OF IMFORTATION MATTERS NO MATTER HOW SMALL. Small when you talking 93 billion millions is huge compared to 23 miles. SO YES IT DOES MATTER. What about the time and rotation of the earth. It takes 8 minutes for light from the sun to reach the earth by then the earth would have rotated yet there is no variable for any motion. You are compeletly wrong in every way.
@@MichelvanBiezen You can't use currency math to calculate that which has forces being applied to it. To properly calculate this, you would need to add all variables to it not just some simply triangular math used in structural engineering.
I didn't say they didn't matter. I just said they were not significant in relation to the topic at hand. What you are doing is saying the equivalent of claiming that the answer is wrong when one states it is 10 and you say that is all wrong it is 10.0000001