Parallax Project

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Stellar Parallax By Gavi Strauss

Models of the Solar System •

Early models of the solar system placed the earth at the center and assumed that the earth didn’t move

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The heliocentric model required the earth to orbit the sun •

This model was historically rejected because many people thought the earth didn’t move through space

The Historical Parallax Measurement •

The parallax measurement was the first proof that the earth moves through space and is therefore not at the center of the solar system

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The first parallax measurement was made by Prussian scientist Friedrich Bessel

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Though many before him attempted this, the measurement was not successfully made until 1838 •

This detected parallax was less than two hundred thousandths of a degree and could not be measured without a very precise telescope

Apparent Movement •

In a moving reference frame, objects that are closer appear to move faster than objects that are farther away •

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Ex. If you look out the window of a moving car, the highway barriers appears to move faster than the distant trees

Since the earth moves, this phenomenon also occurs with stars •

Relative to distant stars, closer ones appear to move faster

Stellar Parallax •

A close star’s position relative to more distant stars changes slightly throughout the year

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By comparing the picture of a constellation taken 6 months apart, a shift in the close star’s position can be observed

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The name for this shift is parallax

Measuring Parallax •

The close star whose parallax was measured was 61 Cygni, a in the constellation Cygnus

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The next slide is data from Redshift on the position of 61 Cygni on January 1st 2014 at 7:00 am and June 1st 2014 at 7:00 am that has been overlaid

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Change the opacity of the first image to observe the shift in 61 Cygni’s relative position

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Notice that the other stars also have parallaxes •

Their parallaxes are smaller because they are farther away

Confirmation Using Right Ascension and Declination •

To calculate the parallax, data was collected from RedShift on 61 Cygni’s Right Ascension and Declination were compared to those of V Cyngi and Gienah Cygni, two neighboring stars •

Right Ascension and Declination are based on the mostly uniform movement of the star map so instead of tracking the position in the sky of 61 Cygni, they track its relative position to other stars

Calculating Parallax •

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61 Cygni •

Right Ascension change: 0.0526° or 12.6 arcseconds

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Declination change: -0.00917° or 33 arcseconds

The total shift of 61 Cygni •

sqrt((12.6)^2+(33)^2)=35.3 arcseconds

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Unfortunately, the measurement of this angle is much larger than Bessel’s was

Bessel’s calculation •

61 Cygni’s parallax was 0.00001742°

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0.00001742° x (2.778 x10^-4 arcseconds/ 1°)= 0.06271 arcseconds

Calculating Distance •

The half distance between these measurements taken in January and June is 1 AU

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Using similar triangles, this known distance and 61 Cygni’s parallax can be used to calculate the actual distance to the star

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1/(0.06271/2)= 31.89 parsecs

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31.89 parsecs x (3.262 lightyears/1 parsec)= 104.0 light years