Question

Suppose that now you want to make a scale model of the solar system using the same ball bearing to represent the sun. How far from it would you place a sphere representing the earth? (Center to center distance please.) The distance from the center of the sun to the center of the earth is 1.496×10111.496×1011 m and the radius of the sun is 6.96×1086.96×108 m.

Answer 1

Answer:

d = 0.645 m (assuming a radius of the ball bearing of 3 mm)

Explanation:

The given information is:

• The distance from the center of the sun to the center of the earth is 1.496x10¹¹m = $d_{e}$
• The radius of the sun is 6.96x10⁸m = $r_{s}$

We need to assume a radius for the ball bearing, so suppose that the radius is 3 mm = $r_{b}$.  

First, we need to find how many times the radius of the sun is bigger respect to the radius of the ball bearing, which is given by the following equation:

$\frac{r_{s}}{r_{b}} = \frac{6.96\cdot 10^{8}m}{3\cdot 10^{-3}m} = 2.32\cdot 10^{11}$

Now, we can calculate the distance from the center of the sun to the center of the sphere representing the earth, $d_{s}$:  

[tex] d_{s} = \frac{d_{e}}{r_{s}/r_{b}} = \frac{1.496 \cdot 10^{11} m}{2.32\cdot 10^{11}} = 0.645 m

I hope it helps you!