Question

Problem 3 Scale of the Solar System The real diameters of the Sun and Earth are approximately 1.4 million kilometers and 12,800 kilometers, respectively. The Earth-Sun distance is approximately 150 million kilometers. Calculate the sizes of Earth and the Sun, and the distances between them in a scale model that is one 10-billionth the size of the actual solar system. Show your work clearly.

Answer 1

Step-by-step explanation:

Let the diameter of the Sun in the model be = x

Scale used in the model =
`(1)/(10^(10))=10^(-10)`

`(x)/(D)=10^(-10)`

The real diameters of the Sun ,D= 1.4 million kilometers =
`1.4* 10^6 km`

`x=1.4* 10^6 km* 10^(-10)=1.4* 10^(-4) km=14 cm`

`1 km = 100,000 cm`

The diameter of the sun in the model is 14 cm.

The real diameters of the Earth,d = 12,800 km

Let the diameter of the Earth in the model be = y

Scale used in the model =
`(1)/(10^(10))=10^(-10)`

`(y)/(d)=10^(-10)`

`y=12,800 km* 10^(-10)=1.28* 10^(-6) km=0.128 cm`

The diameter of the Earth in the model is 0.128 cm.

The Earth-Sun distance ,l =
`150* 10^6 km=1.5* 10^8 km`

Let the Earth-Sun distance in the model be = z

`(z)/(l)=10^(-10)`

`z=1.5* 10^8 km* 10^(-10)=1.5* 10^(-2) km=1500 cm`

The distances between Earth-Sun in the model is 1500 cm.