If we represent the sun as volleyball (diameter =65cm)how far away would be find earth in this model? Note the suns actual diameter is 1.4x10^9 meters.
To find the scale distance between the volleyball-sized sun and the Earth in this model, we need to determine the ratio between the actual diameter of the sun and the volleyball's diameter.
Let's set up the proportion:
Actual diameter of the sun / Scale diameter of the sun = Actual distance to the Earth / Scale distance to the Earth
Actual diameter of the sun = 1.4 x 10^9 meters
Scale diameter of the sun = 65 cm = 0.65 meters (as given)
Substituting these values in, we have:
1.4 x 10^9 meters / 0.65 meters = Actual distance to the Earth / Scale distance to the Earth
Now, we can solve for the scale distance to the Earth.
Scale distance to the Earth = (1.4 x 10^9 meters / 0.65 meters) × Actual distance to the Earth
To calculate the scale distance, we need to know the actual distance from the sun to the Earth. As the average distance is about 1.496 x 10^11 meters, we can substitute this value into the equation.
Scale distance to the Earth = (1.4 x 10^9 meters / 0.65 meters) × 1.496 x 10^11 meters
By calculating this expression, we can find the scale distance between the volleyball-sized sun and the Earth in this model.
Note: Make sure to convert the result from meters to a more relatable unit, like centimeters, to be consistent with the scale of the model.