Measuring distances to stars (Stellar Parallax - Detailed Explanation)

Measuring distances to stars (Corrected and Re-uploaded)
𝗜𝗻𝗱𝗲𝘅:
⏲ 0:00 Intro
⏲ 0:13 Measuring angles by using theodolite
⏲ 0:48 Parallax
⏲ 1:16 Measuring distances to stars
⏲ 3:12 Radian and arcsecond as parallax angle
⏲ 4:09 Parsec
⏲ 5:04 Limitations of Stellar Parallax
⏲ 5:22 Outro

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📄𝗧𝗿𝗮𝗻𝘀𝗰𝗿𝗶𝗽𝘁𝗶𝗼𝗻:
In order to understand how the distances to nearby stars are measured, we need to understand how angles are measured after a position change and what the parallax effect is.

Here’s a simple version of a theodolite – an instrument used for measuring angles, both horizontally and vertically. For example, if we set it up with respect to this car, after the car moves and then stops, we can determine this angle.

Suppose we’re traveling on a train and look out of the window. We can see nearby objects like trees, buildings, electricity poles, and traffic signs go by fast whereas things that are further away, such as mountains, clouds, the Sun or the Moon appear to drift by slowly. This is due to the parallax effect and it applies to stars as well.

Because of the parallax effect, if we observe a nearby star throughout the year, we’ll notice that the star’s position changes with respect to the far-away, background stars due to Earth’s motion around its orbit. Although the background stars also shift slightly in position for the same reason, they’re too far away for us to detect their motions easily and they appear to be fixed. In order to measure a star’s distance, we use simple geometry . We know the length of the baseline and we just need to find the so-called parallax angle.

If we observe a star twice in a year at six-month intervals, we can measure the star’s change in position and determine the parallax angle by using an instrument like a theodolite. After finding the parallax angle, we just need to write down the tangent formula for this angle. So, the distance of a nearby star can be found using the formula: d = 1AU/tangent of the parallax angle.

Applying the parallax method to nearby stars, the parallax angle will always be very small. For example, the nearest star to the sun, Proxima Centauri, has a parallax angle of just .00021 of a degree. Since it’s the nearest star to Sun, it has the largest parallax angle. Stars that are farther away have even smaller parallax angles.

If we consider the parallax angle in radians, we don’t need to calculate the tangent of parallax angle, since the tangent of a very small angle in radians is almost equal to the angle. So the formula becomes simpler: d = 1AU/parallax angle (in radians). But astronomers generally use arcseconds instead of degrees or radians. 1 arcsecond is 1/3600th of a degree and 1/206,265 of a radian. If we rearrange the formula using 1 arcsecond as the parallax angle, the formula becomes d = 206,265AU/1arcsecond.

Astronomers define a new distance unit, the parsec, which is equal to 206,265 AU and is the distance to a star which has a parallax angle of 1 arcsecond. Now the formula becomes: distance in parsecs = 1/parallax angle (in arcseconds). For example, the parallax angle of Proxima Centauri is .768 arcsecond. So the distance of Proxima is 1/0.768 which is equal to 1.302 parsecs. Since 1 parsec equals 3.26 light-years, the distance of Proxima Centauri can also be given as 4.25 light-years.

Distances to stars that are more than about 100 parsecs away can’t be obtained using the parallax effect. This is because the shift in position of the star – in other words the parallax angle – is too small to measure.

#parallax #distance #stars

[murthyvvbs]

Very wonderful background music, heart soothing. I felt very relaxed & tranquilised😂😊

[ZFoxandMcFalcon]

This is the video I was looking for. Everyone's videos for parallax kept omitting the measure of the angle, which is crucial for the measure

[livaastros]

This is the only video that seems to understand the problem of the lack of angular measurement.

[Adn]

Tysm, tysm, tysm i was confused that how astronomers measure angle ty 😃😃😃😃😃

[RuhaanT]

Great video! i subscribed ! im gonna watch more of your videos now! you deserve way more than 2130 subscibers!

[JohnKater]

over 10 video explanations in and the penny drops here. Thank you for explaining the practical harnessing of the angle by the observer. It seems obvious now, but I needed someone to free me of trying to second guess.

[boriskaragiannis]

when was the last time Stellar parallax was used in order to verify ANY stellar distance...?....they only use the red-shift theory now witch is totally false