Question

A student prepared an Earth/Moon model in which the two spheres were 100 m apart. What were the diameters of the spheres?

Answer 1

D₁ = 3.31 m

D₂ = 0.9 m

Step-by-step explanation:

First, we will find the scaling factor of the model:

`Scaling\ Factor = S.F = (Distance\ between\ Earth\ and\ moon\ in\ Model)/(Distance\ between\ Earth\ and\ moon\ in\ Actual)\\S.F = (100\ m)/(384400000\ m)\\`

S.F = 2.6 x 10⁻⁷

Now, the diameter of 1st sphere, that is Earth will be:

`D_(1) = (S.F)(Actual\ Diameter\ of\ Earth)\\D_(1) = (2.6\ x 10^(-7)\ m)(12742000\ m)\\`

D₁ = 3.31 m

Now, the diameter of 2nd sphere, that is Moon will be:

`D_(2) = (S.F)(Actual\ Diameter\ of\ Moon)\\D_(2) = (2.6\ x 10^(-7)\ m)(3474200\ m)\\`

D₂ = 0.9 m