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The Sun is at a distance of 1.5 x 10¹¹ m from the Earth and its angular diameter as seen from Earth is 2000 seconds of arc. Find the Sun's diameter.
- 2.45 x 10¹⁰ m
- 1.45 x 10¹⁰ m
- 1.45 x 10⁹ m
- 0.14 x 10⁹ m
Correct answer: 1.45 x 10⁹ m
Solution
Convert the angular diameter to radians: 2000 arcsec = 2000 * (1/3600) degrees = 0.5556 degrees = 0.5556 * (pi/180) rad = 9.696 x 10⁻³ rad. Then D = distance * angle = 1.5 x 10¹¹ * 9.696 x 10⁻³ = 1.454 x 10⁹ m, approximately 1.45 x 10⁹ m.
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