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?

Question

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.

HIX Tutor · Accepted Answer

undefined To find the distance to place Pluto in a scale model of the Solar System using an orange to represent the Sun, we need more information. Please provide the scale you would like to use for the model.

Alexander Acosta · Answer

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

The plotting distance for Pluto is s X 39.5 X 23400 cm, and the scale factor for the Earth's radius is s = 5/109 cm. If I had used five or more correct significant digits (sd) in each set of data, I would have almost precisely calculated 42472 cm = 425 meters.

Ariana Acosta · Answer

Just over 424 metres away.

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.

HIX Tutor · Answer

undefined To determine the distance we need to place Pluto in the scale model, we'll compare the diameter of the orange representing the Sun (10 cm) to the actual diameter of the Sun (1,391,000 km).

Step 1: Calculate the scale factor:
    Actual diameter of the Sun (1,391,000 km) divided by the diameter of the orange (10 cm).

Step 2: Determine the distance to Pluto:
    Multiply the scale factor from Step 1 by the average distance from the Sun to Pluto (5,913,520,000 km).

Step 3: Convert the result to a more manageable unit if needed:
    If the result is too large, like in kilometers, we can convert it to a unit like meters or miles.

You'll then have the distance to put Pluto in your scale model of the Solar System! Feel free to follow up with any additional questions.

Christopher Ales · Answer

undefined About 39 meters away.