Explore the universe

Ever look up at the sky and wonder how we know so much about our universe, even though most of it is too far away to visit? Mathematics is an amazingly powerful tool that lets us understand things even if we can’t observe them directly. More and more people are becoming interested about our galaxy, space travel, and whether we’re alone in the universe. Thanks to new technologies (powered by mathematics, of course!), we're able to explore increasingly more remote regions of space. So, if you're dreaming of exploring space, make sure to pay attention in mathematics class—it's your secret tool for space adventures!

This question tests the ability of students to employ mathematical concepts, facts and procedures and reasoning to solve mathematically-formulated problems to obtain mathematical conclusions.

This is a level 2 problem. At Level 2, students can interpret and recognise situations in contexts that require no more than direct inference. They can extract relevant information from a single source and make use of a single representational mode. Students at this level can employ basic algorithms, formulae, procedures or conventions to solve problems involving whole numbers. They are capable of making literal interpretations of results.

70% of PISA participants got this one right.

Why are "average distances" provided in this problem? Why not just "distance"? You may be fascinated by the reason:

In our solar system, planets' orbits are ellipses, not perfect circles, and the Sun is located at one of the foci of these ellipses, not at the dead center. The point in their orbit that is farthest away from the Sun is called the aphelion, and the point in their orbit that is closest to the Sun is called the perihelion.

Planets orbiting the Sun can be likened to a choreographed dance in space. Imagine a group of dancers moving in a pattern where they sometimes come closer together and sometimes drift further apart. Similarly, as planets travel in their elliptical orbits, they experience changes in their distance from the Sun. Due to gravitational forces, they move a bit more quickly as they draw nearer to the Sun, and they slow down a bit as they drift further away. The "average distance" from the Sun is a key factor in maintaining the stability of each planet's orbit in this cosmic dance, balancing the varying distances as the planet moves closer to and farther from the Sun.