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27 January, 08:08

Suppose we imagine the Sun to be about the size of a grapefruit. How big an area would the orbits of the nine planets of the Solar System cover?

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  1. 27 January, 08:14
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    size at this scale of the solar system is 10⁸ m²

    Explanation:

    For this exercise we can use a direct proportions rule or rule of three.

    If the radius of the Sun is 7 10⁸ m is equal to the radius of a grapefruit is on average about 5 cm, the radius of the orbit of the plant is x

    Mercury

    r1 = 5.8 10¹⁰m

    x = r1 / r_Sum 5

    x = 5.8 10¹⁰/7 10⁸

    x = 82 m

    We repeat the same formula with all the radii of the orbit, the results in the table

    Numb name r_orbit (m) x (m) A (m2)

    0 Sun 7 10⁸ 1 3.14

    1 mercury 5.8 10¹⁰ 8.2 10¹ 2.0 10⁴

    2 venus 1 10¹¹ 1.4 10² 6.2 10⁴

    3 Earth 1.5 10¹¹ 2.1 10² 1.4 10⁵

    4 Mars 2.3 10¹¹ 3.2 10² 3.2 10⁵

    5 Jupiter 7.8 10¹¹ 1.1 10³ 3.8 10⁶

    6 Saturn 1.4 10¹² 2 10³ 1.3 10⁷

    7 Uranus 2.9 10¹² 4.1 10³ 5.3 10⁷

    8 Neptune 4.5 10¹² 6.4 10³ 1.3 10⁸

    9 Pluto 5.9 10¹² 8.4 10³ 2.2 10⁸

    The area of a circle is

    A = π R²

    Mercury

    A = π 80²

    A = 2.0 14 m²

    The other values are in the table

    The size at this scale of the solar system is 10⁸ m²
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