A scale diagram of the solar system shows distances from the Sun using a fixed scale, such as 1 cm to a stated number of kilometres. To interpret it, multiply a measured length by the scale to get the real distance, and reverse the process to draw one.
This lesson follows orbital motion and force direction and belongs to space physics.
How do you use the scale?
The scale tells you what 1 cm on paper stands for. Suppose 1 cm represents 5.0 × 107 km.
- To find a real distance: measure the length in cm, then multiply by 5.0 × 107 km per cm.
- To find a drawing distance: divide the real distance by 5.0 × 107 km per cm.
- Keep the unit of the scale: the answer is in km here, so convert only at the end if the question asks for metres.
Check the Cambridge syllabus for the planet facts in your exam year.
The order of the planets from the Sun is Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune. The four nearer planets are rocky. The four further out are much larger and are mainly gas or ice.
Worked example
On an invented diagram, 1 cm represents 5.0 × 107 km. Use these approximate distances from the Sun: Earth 1.5 × 108 km, Jupiter 7.8 × 108 km, Neptune 4.5 × 109 km. How far from the Sun is each planet drawn?
Earth: 1.5 × 108 ÷ 5.0 × 107 = 3.0 cm.
Jupiter: 7.8 × 108 ÷ 5.0 × 107 = 15.6 cm.
Neptune: 4.5 × 109 ÷ 5.0 × 107 = 90 cm.
Now add the sizes.
Earth’s diameter is about 1.3 × 104 km. On this scale it would be 1.3 × 104 ÷ 5.0 × 107 = 2.6 × 10-4 cm, which is 0.0026 mm. That is far too small to draw.
So a diagram that shows the planets as visible circles is not showing their sizes to the same scale as their distances.
Light travel time as a cross-check. Earth is 1.5 × 1011 m from the Sun. Light at 3.0 × 108 m/s takes 1.5 × 1011 ÷ 3.0 × 108 = 500 s, about 8.3 minutes.
The mistake to watch for
A common slip is to read a neat diagram as if the planets were evenly spaced or drawn to one scale.
Mistaken answer: “Neptune is 4 times as far from the Sun as Saturn because it is the fourth picture beyond it.”
The picture position is not the distance. Only the measured length and the stated scale give the real distance.
The correction: measure, then multiply by the scale. A second common slip is forgetting the units of the scale, for example giving 15.6 cm as the real distance.
Check yourself
Use 1 cm = 5.0 × 107 km where needed.
1. Saturn is about 1.4 × 109 km from the Sun. How far from the Sun would it be on the diagram?
Show answer
1.4 × 109 ÷ 5.0 × 107 = 28 cm.
2. An invented planet is drawn 60 cm from the Sun. What is its real distance?
Show answer
60 × 5.0 × 107 = 3.0 × 109 km, so 3.0 × 109 km.
3. Light from the Sun takes about 500 s to reach Earth. Why does it take longer to reach Jupiter, and approximately how long if Jupiter is 7.8 × 1011 m away?
Show answer
Jupiter is further away, and light travels at a constant speed in space. Time = 7.8 × 1011 ÷ 3.0 × 108 = 2600 s, which is about 43 minutes.
Where this leads next
Next, see where the Sun’s energy comes from in a star’s energy source at syllabus level. For diagram questions where you must choose a method before calculating, the reasoning board for diagrams offers a structured way to plan, and the bounds and rounding explainer helps you judge how many figures to give.
If scale and unit conversions are where your marks leak, online one-to-one Physics tuition lets a teacher check your working line by line.