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?

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

wavelength divides in half and speed stays the same.