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20 August, 03:35

The smallest detail visible with ground-based solar telescopes is about 1 arc second. How large a region (in km) does this represent on the Sun? Hint: Use the small-angle formula: angular diameter (in arc seconds) 2.06 ✕ 105 = linear diameter distance. (Note: The average distance to the Sun can be found in Celestial profile: The Sun.)

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  1. 20 August, 04:01
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    x = 727.5 km

    Explanation:

    With the conditions given using trigonometry, we can find the tangent

    tan θ = CO / CA

    With CO the opposite leg and CE is the adjacent leg which is the distance from the Tierral to Sun

    D = 150 10⁶ km (1000m / 1 km)

    D = 150 10⁹ m.

    We must take the given angle to radians.

    1º = 3600 arc s

    π rad = 180º

    θ = 1 arc s (1º / 3600 s arc) (pi rad / 180º) =

    θ = 4.85 10⁻⁶ rad

    That angle is extremely small, so we can approximate the tangent to the angle

    θ = x / D

    x = θ D

    x = 4.85 10-6 150 109

    x = 727.5 103 m

    x = 727.5 km
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