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3.3e describe the method of heliocentric parallax to determine distances to nearby stars 3.3f recall the definition of one parsec (pc) Heliocentric parallax (measurements made with the Sun at the centre) are carried out as seen in the diagram. The view of a nearby star is taken on one day of the year from the Earth. When 6 months has passed and the Earth is on the other side of its orbit around the Sun, the view of the star has changed. The angular shift can be measured by the telescope used (how much the angle of view has changed for the star during half a year). January 1st Distant star field Earth orbit Nearby star Sun July 1st Appearance of star on July 1st Appearance of star on January 1st The parallax angle ( π ) is measured in seconds of arc (arcsec). 1˚ = 60 minutes of arc 1 minute of arc = 60 seconds of arc 1˚ = 3,600 arcsec Stars closer to Earth give rise to larger parallax angles. Above 100 l.y. results give too small an angle to be measured and other methods to measure the distances of stars have to be used. Trigonometry allows details from a right-angled triangle to be worked out:- 300,000,000 km January 1st Nearby star SUN Angular shift of star July 1st 150,000,000 km Using the upper right-angled triangle, half the angular shift gives the parallax angle π π Trigonometry gives us Tangent π = OPPOSITE = ADJACENT 150,000,000 DISTANCE TO STAR This converts to DISTANCE TO STAR = 150,000,000 km Tangent (The distance in km can then be converted to parsecs) π Distances in km to nearby stars would give rise to very large numbers and the use of a parsec becomes helpful as a unit. One parsec (1pc) is the distance at which a star has a parallax angle Π of 1 arcsec 150,000,000 km Shown on a similar diagram, 1 parsec can be seen:- 1 arcsec π 1 parsec An excellent simulation by Professor Terry Herter at Cornell University shows clearly the way heliocentric parallax works:1). 2). 3). 4). 5). Click on the link below (Java needs to be on your computer to operate the model. This can be downloaded free of charge from the internet) When the screen shows the parallax model, left click on the area once Move the orange star to the left using the mouse Left click on ‘Show Bounds’ Left click on ‘Animate’ - if the Earth does not rotate around the Sun, just place the cursor over Earth, hold the mouse down and move Earth around the orbit of the Sun. Note how the star moves compared with the background stars between the red and blue boundary markers. The orange star can be repositioned to show how stars further away from Earth hardly move across the background stars. Heliocentric Parallax http://www.astro.cornell.edu/academics/courses/astro1101/java/parallax/parallax.htm#instructions Simulation credit : Professor Terry Herter, Cornell University Picture credits : (Sun) SOHO/ESA&NASA (Earth) NASA/JSC-Apollo 17