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14 May, 08:51

On a scale where the Sun is about the size of a grapefruit and the Earth is about 15 meters away, how far away are the nearest stars besides the Sun?

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  1. 14 May, 09:17
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    The nearest star would be approximately 4064km away from the sun.

    Explanation:

    The distance between the sun and the earth (in real life) is 147.36 * 10^6 km i. e. 1.4736 * 10^11m. In the analogy, we're told the distance from the earth to the grapefruit sized sun is only 15m. Hence, if we're to find a ratio of the real distance to the analogical distance, it would be given as

    Real distance : Analogical distance

    = 1.4736*10^11 : 15

    = 9.824*10^9 : 1

    This means that 1m in the analogical scale is equivalent to 9.824*10^9m in reality.

    The nearest stars to the sun are about 4.22 light-years from the earth. In meters, that is

    4.22 light-years * 9.461 * 10^15

    = 3.9924 * 10^16m

    Note: 1 light-year = 9.461 * 10^15m

    Using the analogical scale, the nearest star would then be

    (3.9924 * 10^16) / (9.824 * 10^9) = 4063925.08m = 4063.925km

    Therefore, if the sun was the size of a grapefruit, the nearest star would be approximately 4064km away from the sun.
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