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Homework 2 Solutions

# Homework 2 Solutions - S I O 1 T H E P L A N E T S H O M E...

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Unformatted text preview: S I O 1 : T H E P L A N E T S H O M E W O R K #2 S O L U T I O N S J A N 1 4 , 2 0 1 1 1 : Parallax (From section 2 . 1 , and the Sun lecture) Explain how to calculate the distance to a star. ( 2 points) Distances to stars are calculated using parallax shift. An observer located on Earth can measure the shift in the position of a nearby star relative to a distant star. This shift, measured in arcseconds (or 1 / 3600 degrees), will change as the Earth orbits the Sun, but will be nearly equal at opposing orbital positions (e.g. the Autumnal and Spring equinox). Figure 1 demonstrates the geometry of the calculation: Using r = 1 AU, the distance from the Earth to Sun, one can calculate either the star-to-Sun distance (in the figure, D S ), or the star-to-Earth distance ( D E ) using simple geometry. Recall a few trigonometric relations for a right triangle: tan θ = r / D S , or sin θ = r / D E . EARTH: A ~ SUN m B A A A A A A A A A A A A A A A ~ A A A K θ θ d D S D E r Ψ Ω B m Ω m m Ω A ~ Figure 1 : Cartoon of parallax for the Earth-Sun system (modified from figure 2 . 1 in the text): The distance to star Ω is calculated by measuring its angular shift θ in the sky (from a stationary point on Earth), relative to a distant star ( Ψ ) at opposing points in orbit ( A , B , e.g. at Autumn and Spring). The distance is then calculated using simple geometry (congruent angles) and the distance from the Earth to the Sun ( r = 1 AU). Although d D S , the shift is very small, which makes D S very great....
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Homework 2 Solutions - S I O 1 T H E P L A N E T S H O M E...

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