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SOLUTION TO EXERCISE 6

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motion: TOC for Knowledge Concepts, Exercises, and Solutions



(a) The distance from Mars to the Sun is 1.52 astronomical units (AU), and 1 AU = 
150,000,000 km.  The diameter of the Sun is 1,390,000 km.  The number of radians 
an object subtends is the ratio of its diameter
to its distance, so from Mars, the Sun subtends

    1,390,000 km / (1.52 * 150,000,000)km  =  0.0061 radian.
    This is equivalent to  0.0061 * 57.3  =  0.35 degrees
    which is equivalent to 0.35   * 3600  =  1260 arcseconds

(b) My outstretched arm, from my eye to my fingertip, is about 80 cm.
The diameter of a dime is about 1.5 cm.  Your measurements may vary.
In my case, the dime subtends an angle of

    1.5 cm / 80 cm = 0.019 radian.  

Compared to the Sun seen from Mars, this subtends 

    0.019 / 0.0061 = over 3 times more arc.