Question

Suppose we want to construct an accurate scale model of the Solar System and we use an orange (diameter 10 cm) to represent the Sun. How far away would we have to put Pluto?

You will need to use the fact that 1 Astronomical Unit is 23,400 times the radius of the Earth, the Sun has a radius 109 times that of the Earth and the semi-major axis of Pluto's orbit is 39.5 AU.

Answer 1

Relating to the specified data for use, the answer is 42399 cm = 424 meters, nearly, from the center of the orange

Explanation:

The scale factor is s = 5/109 cm, for radius of the Earth, and the plotting distance for Pluto is s X 39.5 X 23400 cm. Had I used 5 or more correct significant digits (sd) in every data used, I would get 42472 cm = 425 meters, nearly.

Answer 2

Just over 424 metres away.

Explanation:

The sun's diameter is 1,391,000 km, so the scale you would be using is 1,391,000 km = 10 cm, or 1 cm = 139,100 km.

The distance between the sun and Pluto is 5,906,380,000 km, so on the scale you have proposed, you would need to position Pluto (5,906,380,000 / 139,100) = 42,461 cm away from the orange.

So the answer is 424.61 metres.